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30,351 | networkx.classes.function | add_star | Add a star to Graph G_to_add_to.
The first node in `nodes_for_star` is the middle of the star.
It is connected to all other nodes.
Parameters
----------
G_to_add_to : graph
A NetworkX graph
nodes_for_star : iterable container
A container of nodes.
attr : keyword arguments, optional (default= no attributes)
Attributes to add to every edge in star.
See Also
--------
add_path, add_cycle
Examples
--------
>>> G = nx.Graph()
>>> nx.add_star(G, [0, 1, 2, 3])
>>> nx.add_star(G, [10, 11, 12], weight=2)
| def add_star(G_to_add_to, nodes_for_star, **attr):
"""Add a star to Graph G_to_add_to.
The first node in `nodes_for_star` is the middle of the star.
It is connected to all other nodes.
Parameters
----------
G_to_add_to : graph
A NetworkX graph
nodes_for_star : iterable container
A container of nodes.
attr : keyword arguments, optional (default= no attributes)
Attributes to add to every edge in star.
See Also
--------
add_path, add_cycle
Examples
--------
>>> G = nx.Graph()
>>> nx.add_star(G, [0, 1, 2, 3])
>>> nx.add_star(G, [10, 11, 12], weight=2)
"""
nlist = iter(nodes_for_star)
try:
v = next(nlist)
except StopIteration:
return
G_to_add_to.add_node(v)
edges = ((v, n) for n in nlist)
G_to_add_to.add_edges_from(edges, **attr)
| (G_to_add_to, nodes_for_star, **attr) | [
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|
30,353 | networkx.readwrite.json_graph.adjacency | adjacency_data | Returns data in adjacency format that is suitable for JSON serialization
and use in JavaScript documents.
Parameters
----------
G : NetworkX graph
attrs : dict
A dictionary that contains two keys 'id' and 'key'. The corresponding
values provide the attribute names for storing NetworkX-internal graph
data. The values should be unique. Default value:
:samp:`dict(id='id', key='key')`.
If some user-defined graph data use these attribute names as data keys,
they may be silently dropped.
Returns
-------
data : dict
A dictionary with adjacency formatted data.
Raises
------
NetworkXError
If values in attrs are not unique.
Examples
--------
>>> from networkx.readwrite import json_graph
>>> G = nx.Graph([(1, 2)])
>>> data = json_graph.adjacency_data(G)
To serialize with json
>>> import json
>>> s = json.dumps(data)
Notes
-----
Graph, node, and link attributes will be written when using this format
but attribute keys must be strings if you want to serialize the resulting
data with JSON.
The default value of attrs will be changed in a future release of NetworkX.
See Also
--------
adjacency_graph, node_link_data, tree_data
| def adjacency_data(G, attrs=_attrs):
"""Returns data in adjacency format that is suitable for JSON serialization
and use in JavaScript documents.
Parameters
----------
G : NetworkX graph
attrs : dict
A dictionary that contains two keys 'id' and 'key'. The corresponding
values provide the attribute names for storing NetworkX-internal graph
data. The values should be unique. Default value:
:samp:`dict(id='id', key='key')`.
If some user-defined graph data use these attribute names as data keys,
they may be silently dropped.
Returns
-------
data : dict
A dictionary with adjacency formatted data.
Raises
------
NetworkXError
If values in attrs are not unique.
Examples
--------
>>> from networkx.readwrite import json_graph
>>> G = nx.Graph([(1, 2)])
>>> data = json_graph.adjacency_data(G)
To serialize with json
>>> import json
>>> s = json.dumps(data)
Notes
-----
Graph, node, and link attributes will be written when using this format
but attribute keys must be strings if you want to serialize the resulting
data with JSON.
The default value of attrs will be changed in a future release of NetworkX.
See Also
--------
adjacency_graph, node_link_data, tree_data
"""
multigraph = G.is_multigraph()
id_ = attrs["id"]
# Allow 'key' to be omitted from attrs if the graph is not a multigraph.
key = None if not multigraph else attrs["key"]
if id_ == key:
raise nx.NetworkXError("Attribute names are not unique.")
data = {}
data["directed"] = G.is_directed()
data["multigraph"] = multigraph
data["graph"] = list(G.graph.items())
data["nodes"] = []
data["adjacency"] = []
for n, nbrdict in G.adjacency():
data["nodes"].append({**G.nodes[n], id_: n})
adj = []
if multigraph:
for nbr, keys in nbrdict.items():
for k, d in keys.items():
adj.append({**d, id_: nbr, key: k})
else:
for nbr, d in nbrdict.items():
adj.append({**d, id_: nbr})
data["adjacency"].append(adj)
return data
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|
30,362 | networkx.classes.function | all_neighbors | Returns all of the neighbors of a node in the graph.
If the graph is directed returns predecessors as well as successors.
Parameters
----------
graph : NetworkX graph
Graph to find neighbors.
node : node
The node whose neighbors will be returned.
Returns
-------
neighbors : iterator
Iterator of neighbors
| def all_neighbors(graph, node):
"""Returns all of the neighbors of a node in the graph.
If the graph is directed returns predecessors as well as successors.
Parameters
----------
graph : NetworkX graph
Graph to find neighbors.
node : node
The node whose neighbors will be returned.
Returns
-------
neighbors : iterator
Iterator of neighbors
"""
if graph.is_directed():
values = chain(graph.predecessors(node), graph.successors(node))
else:
values = graph.neighbors(node)
return values
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|
30,365 | networkx.algorithms.shortest_paths.weighted | all_pairs_bellman_ford_path | Compute shortest paths between all nodes in a weighted graph.
Parameters
----------
G : NetworkX graph
weight : string or function (default="weight")
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number.
Returns
-------
paths : iterator
(source, dictionary) iterator with dictionary keyed by target and
shortest path as the key value.
Examples
--------
>>> G = nx.path_graph(5)
>>> path = dict(nx.all_pairs_bellman_ford_path(G))
>>> path[0][4]
[0, 1, 2, 3, 4]
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
See Also
--------
floyd_warshall, all_pairs_dijkstra_path
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
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|
30,366 | networkx.algorithms.shortest_paths.weighted | all_pairs_bellman_ford_path_length | Compute shortest path lengths between all nodes in a weighted graph.
Parameters
----------
G : NetworkX graph
weight : string or function (default="weight")
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number.
Returns
-------
distance : iterator
(source, dictionary) iterator with dictionary keyed by target and
shortest path length as the key value.
Examples
--------
>>> G = nx.path_graph(5)
>>> length = dict(nx.all_pairs_bellman_ford_path_length(G))
>>> for node in [0, 1, 2, 3, 4]:
... print(f"1 - {node}: {length[1][node]}")
1 - 0: 1
1 - 1: 0
1 - 2: 1
1 - 3: 2
1 - 4: 3
>>> length[3][2]
1
>>> length[2][2]
0
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
The dictionary returned only has keys for reachable node pairs.
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
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|
30,367 | networkx.algorithms.shortest_paths.weighted | all_pairs_dijkstra | Find shortest weighted paths and lengths between all nodes.
Parameters
----------
G : NetworkX graph
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
weight : string or function
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edge[u][v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number or None to indicate a hidden edge.
Yields
------
(node, (distance, path)) : (node obj, (dict, dict))
Each source node has two associated dicts. The first holds distance
keyed by target and the second holds paths keyed by target.
(See single_source_dijkstra for the source/target node terminology.)
If desired you can apply `dict()` to this function to create a dict
keyed by source node to the two dicts.
Examples
--------
>>> G = nx.path_graph(5)
>>> len_path = dict(nx.all_pairs_dijkstra(G))
>>> len_path[3][0][1]
2
>>> for node in [0, 1, 2, 3, 4]:
... print(f"3 - {node}: {len_path[3][0][node]}")
3 - 0: 3
3 - 1: 2
3 - 2: 1
3 - 3: 0
3 - 4: 1
>>> len_path[3][1][1]
[3, 2, 1]
>>> for n, (dist, path) in nx.all_pairs_dijkstra(G):
... print(path[1])
[0, 1]
[1]
[2, 1]
[3, 2, 1]
[4, 3, 2, 1]
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
The yielded dicts only have keys for reachable nodes.
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
| (G, cutoff=None, weight='weight', *, backend=None, **backend_kwargs) | [
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|
30,368 | networkx.algorithms.shortest_paths.weighted | all_pairs_dijkstra_path | Compute shortest paths between all nodes in a weighted graph.
Parameters
----------
G : NetworkX graph
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
weight : string or function
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number or None to indicate a hidden edge.
Returns
-------
paths : iterator
(source, dictionary) iterator with dictionary keyed by target and
shortest path as the key value.
Examples
--------
>>> G = nx.path_graph(5)
>>> path = dict(nx.all_pairs_dijkstra_path(G))
>>> path[0][4]
[0, 1, 2, 3, 4]
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
See Also
--------
floyd_warshall, all_pairs_bellman_ford_path
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
| (G, cutoff=None, weight='weight', *, backend=None, **backend_kwargs) | [
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|
30,369 | networkx.algorithms.shortest_paths.weighted | all_pairs_dijkstra_path_length | Compute shortest path lengths between all nodes in a weighted graph.
Parameters
----------
G : NetworkX graph
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
weight : string or function
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number or None to indicate a hidden edge.
Returns
-------
distance : iterator
(source, dictionary) iterator with dictionary keyed by target and
shortest path length as the key value.
Examples
--------
>>> G = nx.path_graph(5)
>>> length = dict(nx.all_pairs_dijkstra_path_length(G))
>>> for node in [0, 1, 2, 3, 4]:
... print(f"1 - {node}: {length[1][node]}")
1 - 0: 1
1 - 1: 0
1 - 2: 1
1 - 3: 2
1 - 4: 3
>>> length[3][2]
1
>>> length[2][2]
0
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
The dictionary returned only has keys for reachable node pairs.
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
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|
30,371 | networkx.algorithms.connectivity.connectivity | all_pairs_node_connectivity | Compute node connectivity between all pairs of nodes of G.
Parameters
----------
G : NetworkX graph
Undirected graph
nbunch: container
Container of nodes. If provided node connectivity will be computed
only over pairs of nodes in nbunch.
flow_func : function
A function for computing the maximum flow among a pair of nodes.
The function has to accept at least three parameters: a Digraph,
a source node, and a target node. And return a residual network
that follows NetworkX conventions (see :meth:`maximum_flow` for
details). If flow_func is None, the default maximum flow function
(:meth:`edmonds_karp`) is used. See below for details. The
choice of the default function may change from version
to version and should not be relied on. Default value: None.
Returns
-------
all_pairs : dict
A dictionary with node connectivity between all pairs of nodes
in G, or in nbunch if provided.
See also
--------
:meth:`local_node_connectivity`
:meth:`edge_connectivity`
:meth:`local_edge_connectivity`
:meth:`maximum_flow`
:meth:`edmonds_karp`
:meth:`preflow_push`
:meth:`shortest_augmenting_path`
| @nx._dispatchable
def edge_connectivity(G, s=None, t=None, flow_func=None, cutoff=None):
r"""Returns the edge connectivity of the graph or digraph G.
The edge connectivity is equal to the minimum number of edges that
must be removed to disconnect G or render it trivial. If source
and target nodes are provided, this function returns the local edge
connectivity: the minimum number of edges that must be removed to
break all paths from source to target in G.
Parameters
----------
G : NetworkX graph
Undirected or directed graph
s : node
Source node. Optional. Default value: None.
t : node
Target node. Optional. Default value: None.
flow_func : function
A function for computing the maximum flow among a pair of nodes.
The function has to accept at least three parameters: a Digraph,
a source node, and a target node. And return a residual network
that follows NetworkX conventions (see :meth:`maximum_flow` for
details). If flow_func is None, the default maximum flow function
(:meth:`edmonds_karp`) is used. See below for details. The
choice of the default function may change from version
to version and should not be relied on. Default value: None.
cutoff : integer, float, or None (default: None)
If specified, the maximum flow algorithm will terminate when the
flow value reaches or exceeds the cutoff. This only works for flows
that support the cutoff parameter (most do) and is ignored otherwise.
Returns
-------
K : integer
Edge connectivity for G, or local edge connectivity if source
and target were provided
Examples
--------
>>> # Platonic icosahedral graph is 5-edge-connected
>>> G = nx.icosahedral_graph()
>>> nx.edge_connectivity(G)
5
You can use alternative flow algorithms for the underlying
maximum flow computation. In dense networks the algorithm
:meth:`shortest_augmenting_path` will usually perform better
than the default :meth:`edmonds_karp`, which is faster for
sparse networks with highly skewed degree distributions.
Alternative flow functions have to be explicitly imported
from the flow package.
>>> from networkx.algorithms.flow import shortest_augmenting_path
>>> nx.edge_connectivity(G, flow_func=shortest_augmenting_path)
5
If you specify a pair of nodes (source and target) as parameters,
this function returns the value of local edge connectivity.
>>> nx.edge_connectivity(G, 3, 7)
5
If you need to perform several local computations among different
pairs of nodes on the same graph, it is recommended that you reuse
the data structures used in the maximum flow computations. See
:meth:`local_edge_connectivity` for details.
Notes
-----
This is a flow based implementation of global edge connectivity.
For undirected graphs the algorithm works by finding a 'small'
dominating set of nodes of G (see algorithm 7 in [1]_ ) and
computing local maximum flow (see :meth:`local_edge_connectivity`)
between an arbitrary node in the dominating set and the rest of
nodes in it. This is an implementation of algorithm 6 in [1]_ .
For directed graphs, the algorithm does n calls to the maximum
flow function. This is an implementation of algorithm 8 in [1]_ .
See also
--------
:meth:`local_edge_connectivity`
:meth:`local_node_connectivity`
:meth:`node_connectivity`
:meth:`maximum_flow`
:meth:`edmonds_karp`
:meth:`preflow_push`
:meth:`shortest_augmenting_path`
:meth:`k_edge_components`
:meth:`k_edge_subgraphs`
References
----------
.. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
"""
if (s is not None and t is None) or (s is None and t is not None):
raise nx.NetworkXError("Both source and target must be specified.")
# Local edge connectivity
if s is not None and t is not None:
if s not in G:
raise nx.NetworkXError(f"node {s} not in graph")
if t not in G:
raise nx.NetworkXError(f"node {t} not in graph")
return local_edge_connectivity(G, s, t, flow_func=flow_func, cutoff=cutoff)
# Global edge connectivity
# reuse auxiliary digraph and residual network
H = build_auxiliary_edge_connectivity(G)
R = build_residual_network(H, "capacity")
kwargs = {"flow_func": flow_func, "auxiliary": H, "residual": R}
if G.is_directed():
# Algorithm 8 in [1]
if not nx.is_weakly_connected(G):
return 0
# initial value for \lambda is minimum degree
L = min(d for n, d in G.degree())
nodes = list(G)
n = len(nodes)
if cutoff is not None:
L = min(cutoff, L)
for i in range(n):
kwargs["cutoff"] = L
try:
L = min(L, local_edge_connectivity(G, nodes[i], nodes[i + 1], **kwargs))
except IndexError: # last node!
L = min(L, local_edge_connectivity(G, nodes[i], nodes[0], **kwargs))
return L
else: # undirected
# Algorithm 6 in [1]
if not nx.is_connected(G):
return 0
# initial value for \lambda is minimum degree
L = min(d for n, d in G.degree())
if cutoff is not None:
L = min(cutoff, L)
# A dominating set is \lambda-covering
# We need a dominating set with at least two nodes
for node in G:
D = nx.dominating_set(G, start_with=node)
v = D.pop()
if D:
break
else:
# in complete graphs the dominating sets will always be of one node
# thus we return min degree
return L
for w in D:
kwargs["cutoff"] = L
L = min(L, local_edge_connectivity(G, v, w, **kwargs))
return L
| (G, nbunch=None, flow_func=None, *, backend=None, **backend_kwargs) | [
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|
30,375 | networkx.algorithms.simple_paths | all_simple_edge_paths | Generate lists of edges for all simple paths in G from source to target.
A simple path is a path with no repeated nodes.
Parameters
----------
G : NetworkX graph
source : node
Starting node for path
target : nodes
Single node or iterable of nodes at which to end path
cutoff : integer, optional
Depth to stop the search. Only paths of length <= cutoff are returned.
Returns
-------
path_generator: generator
A generator that produces lists of simple paths. If there are no paths
between the source and target within the given cutoff the generator
produces no output.
For multigraphs, the list of edges have elements of the form `(u,v,k)`.
Where `k` corresponds to the edge key.
Examples
--------
Print the simple path edges of a Graph::
>>> g = nx.Graph([(1, 2), (2, 4), (1, 3), (3, 4)])
>>> for path in sorted(nx.all_simple_edge_paths(g, 1, 4)):
... print(path)
[(1, 2), (2, 4)]
[(1, 3), (3, 4)]
Print the simple path edges of a MultiGraph. Returned edges come with
their associated keys::
>>> mg = nx.MultiGraph()
>>> mg.add_edge(1, 2, key="k0")
'k0'
>>> mg.add_edge(1, 2, key="k1")
'k1'
>>> mg.add_edge(2, 3, key="k0")
'k0'
>>> for path in sorted(nx.all_simple_edge_paths(mg, 1, 3)):
... print(path)
[(1, 2, 'k0'), (2, 3, 'k0')]
[(1, 2, 'k1'), (2, 3, 'k0')]
When ``source`` is one of the targets, the empty path starting and ending at
``source`` without traversing any edge is considered a valid simple edge path
and is included in the results:
>>> G = nx.Graph()
>>> G.add_node(0)
>>> paths = list(nx.all_simple_edge_paths(G, 0, 0))
>>> for path in paths:
... print(path)
[]
>>> len(paths)
1
Notes
-----
This algorithm uses a modified depth-first search to generate the
paths [1]_. A single path can be found in $O(V+E)$ time but the
number of simple paths in a graph can be very large, e.g. $O(n!)$ in
the complete graph of order $n$.
References
----------
.. [1] R. Sedgewick, "Algorithms in C, Part 5: Graph Algorithms",
Addison Wesley Professional, 3rd ed., 2001.
See Also
--------
all_shortest_paths, shortest_path, all_simple_paths
| def _bidirectional_dijkstra(
G, source, target, weight="weight", ignore_nodes=None, ignore_edges=None
):
"""Dijkstra's algorithm for shortest paths using bidirectional search.
This function returns the shortest path between source and target
ignoring nodes and edges in the containers ignore_nodes and
ignore_edges.
This is a custom modification of the standard Dijkstra bidirectional
shortest path implementation at networkx.algorithms.weighted
Parameters
----------
G : NetworkX graph
source : node
Starting node.
target : node
Ending node.
weight: string, function, optional (default='weight')
Edge data key or weight function corresponding to the edge weight
ignore_nodes : container of nodes
nodes to ignore, optional
ignore_edges : container of edges
edges to ignore, optional
Returns
-------
length : number
Shortest path length.
Returns a tuple of two dictionaries keyed by node.
The first dictionary stores distance from the source.
The second stores the path from the source to that node.
Raises
------
NetworkXNoPath
If no path exists between source and target.
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
In practice bidirectional Dijkstra is much more than twice as fast as
ordinary Dijkstra.
Ordinary Dijkstra expands nodes in a sphere-like manner from the
source. The radius of this sphere will eventually be the length
of the shortest path. Bidirectional Dijkstra will expand nodes
from both the source and the target, making two spheres of half
this radius. Volume of the first sphere is pi*r*r while the
others are 2*pi*r/2*r/2, making up half the volume.
This algorithm is not guaranteed to work if edge weights
are negative or are floating point numbers
(overflows and roundoff errors can cause problems).
See Also
--------
shortest_path
shortest_path_length
"""
if ignore_nodes and (source in ignore_nodes or target in ignore_nodes):
raise nx.NetworkXNoPath(f"No path between {source} and {target}.")
if source == target:
if source not in G:
raise nx.NodeNotFound(f"Node {source} not in graph")
return (0, [source])
# handle either directed or undirected
if G.is_directed():
Gpred = G.predecessors
Gsucc = G.successors
else:
Gpred = G.neighbors
Gsucc = G.neighbors
# support optional nodes filter
if ignore_nodes:
def filter_iter(nodes):
def iterate(v):
for w in nodes(v):
if w not in ignore_nodes:
yield w
return iterate
Gpred = filter_iter(Gpred)
Gsucc = filter_iter(Gsucc)
# support optional edges filter
if ignore_edges:
if G.is_directed():
def filter_pred_iter(pred_iter):
def iterate(v):
for w in pred_iter(v):
if (w, v) not in ignore_edges:
yield w
return iterate
def filter_succ_iter(succ_iter):
def iterate(v):
for w in succ_iter(v):
if (v, w) not in ignore_edges:
yield w
return iterate
Gpred = filter_pred_iter(Gpred)
Gsucc = filter_succ_iter(Gsucc)
else:
def filter_iter(nodes):
def iterate(v):
for w in nodes(v):
if (v, w) not in ignore_edges and (w, v) not in ignore_edges:
yield w
return iterate
Gpred = filter_iter(Gpred)
Gsucc = filter_iter(Gsucc)
push = heappush
pop = heappop
# Init: Forward Backward
dists = [{}, {}] # dictionary of final distances
paths = [{source: [source]}, {target: [target]}] # dictionary of paths
fringe = [[], []] # heap of (distance, node) tuples for
# extracting next node to expand
seen = [{source: 0}, {target: 0}] # dictionary of distances to
# nodes seen
c = count()
# initialize fringe heap
push(fringe[0], (0, next(c), source))
push(fringe[1], (0, next(c), target))
# neighs for extracting correct neighbor information
neighs = [Gsucc, Gpred]
# variables to hold shortest discovered path
# finaldist = 1e30000
finalpath = []
dir = 1
while fringe[0] and fringe[1]:
# choose direction
# dir == 0 is forward direction and dir == 1 is back
dir = 1 - dir
# extract closest to expand
(dist, _, v) = pop(fringe[dir])
if v in dists[dir]:
# Shortest path to v has already been found
continue
# update distance
dists[dir][v] = dist # equal to seen[dir][v]
if v in dists[1 - dir]:
# if we have scanned v in both directions we are done
# we have now discovered the shortest path
return (finaldist, finalpath)
wt = _weight_function(G, weight)
for w in neighs[dir](v):
if dir == 0: # forward
minweight = wt(v, w, G.get_edge_data(v, w))
vwLength = dists[dir][v] + minweight
else: # back, must remember to change v,w->w,v
minweight = wt(w, v, G.get_edge_data(w, v))
vwLength = dists[dir][v] + minweight
if w in dists[dir]:
if vwLength < dists[dir][w]:
raise ValueError("Contradictory paths found: negative weights?")
elif w not in seen[dir] or vwLength < seen[dir][w]:
# relaxing
seen[dir][w] = vwLength
push(fringe[dir], (vwLength, next(c), w))
paths[dir][w] = paths[dir][v] + [w]
if w in seen[0] and w in seen[1]:
# see if this path is better than the already
# discovered shortest path
totaldist = seen[0][w] + seen[1][w]
if finalpath == [] or finaldist > totaldist:
finaldist = totaldist
revpath = paths[1][w][:]
revpath.reverse()
finalpath = paths[0][w] + revpath[1:]
raise nx.NetworkXNoPath(f"No path between {source} and {target}.")
| (G, source, target, cutoff=None, *, backend=None, **backend_kwargs) | [
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|
30,376 | networkx.algorithms.simple_paths | all_simple_paths | Generate all simple paths in the graph G from source to target.
A simple path is a path with no repeated nodes.
Parameters
----------
G : NetworkX graph
source : node
Starting node for path
target : nodes
Single node or iterable of nodes at which to end path
cutoff : integer, optional
Depth to stop the search. Only paths of length <= cutoff are returned.
Returns
-------
path_generator: generator
A generator that produces lists of simple paths. If there are no paths
between the source and target within the given cutoff the generator
produces no output. If it is possible to traverse the same sequence of
nodes in multiple ways, namely through parallel edges, then it will be
returned multiple times (once for each viable edge combination).
Examples
--------
This iterator generates lists of nodes::
>>> G = nx.complete_graph(4)
>>> for path in nx.all_simple_paths(G, source=0, target=3):
... print(path)
...
[0, 1, 2, 3]
[0, 1, 3]
[0, 2, 1, 3]
[0, 2, 3]
[0, 3]
You can generate only those paths that are shorter than a certain
length by using the `cutoff` keyword argument::
>>> paths = nx.all_simple_paths(G, source=0, target=3, cutoff=2)
>>> print(list(paths))
[[0, 1, 3], [0, 2, 3], [0, 3]]
To get each path as the corresponding list of edges, you can use the
:func:`networkx.utils.pairwise` helper function::
>>> paths = nx.all_simple_paths(G, source=0, target=3)
>>> for path in map(nx.utils.pairwise, paths):
... print(list(path))
[(0, 1), (1, 2), (2, 3)]
[(0, 1), (1, 3)]
[(0, 2), (2, 1), (1, 3)]
[(0, 2), (2, 3)]
[(0, 3)]
Pass an iterable of nodes as target to generate all paths ending in any of several nodes::
>>> G = nx.complete_graph(4)
>>> for path in nx.all_simple_paths(G, source=0, target=[3, 2]):
... print(path)
...
[0, 1, 2]
[0, 1, 2, 3]
[0, 1, 3]
[0, 1, 3, 2]
[0, 2]
[0, 2, 1, 3]
[0, 2, 3]
[0, 3]
[0, 3, 1, 2]
[0, 3, 2]
The singleton path from ``source`` to itself is considered a simple path and is
included in the results:
>>> G = nx.empty_graph(5)
>>> list(nx.all_simple_paths(G, source=0, target=0))
[[0]]
>>> G = nx.path_graph(3)
>>> list(nx.all_simple_paths(G, source=0, target={0, 1, 2}))
[[0], [0, 1], [0, 1, 2]]
Iterate over each path from the root nodes to the leaf nodes in a
directed acyclic graph using a functional programming approach::
>>> from itertools import chain
>>> from itertools import product
>>> from itertools import starmap
>>> from functools import partial
>>>
>>> chaini = chain.from_iterable
>>>
>>> G = nx.DiGraph([(0, 1), (1, 2), (0, 3), (3, 2)])
>>> roots = (v for v, d in G.in_degree() if d == 0)
>>> leaves = (v for v, d in G.out_degree() if d == 0)
>>> all_paths = partial(nx.all_simple_paths, G)
>>> list(chaini(starmap(all_paths, product(roots, leaves))))
[[0, 1, 2], [0, 3, 2]]
The same list computed using an iterative approach::
>>> G = nx.DiGraph([(0, 1), (1, 2), (0, 3), (3, 2)])
>>> roots = (v for v, d in G.in_degree() if d == 0)
>>> leaves = (v for v, d in G.out_degree() if d == 0)
>>> all_paths = []
>>> for root in roots:
... for leaf in leaves:
... paths = nx.all_simple_paths(G, root, leaf)
... all_paths.extend(paths)
>>> all_paths
[[0, 1, 2], [0, 3, 2]]
Iterate over each path from the root nodes to the leaf nodes in a
directed acyclic graph passing all leaves together to avoid unnecessary
compute::
>>> G = nx.DiGraph([(0, 1), (2, 1), (1, 3), (1, 4)])
>>> roots = (v for v, d in G.in_degree() if d == 0)
>>> leaves = [v for v, d in G.out_degree() if d == 0]
>>> all_paths = []
>>> for root in roots:
... paths = nx.all_simple_paths(G, root, leaves)
... all_paths.extend(paths)
>>> all_paths
[[0, 1, 3], [0, 1, 4], [2, 1, 3], [2, 1, 4]]
If parallel edges offer multiple ways to traverse a given sequence of
nodes, this sequence of nodes will be returned multiple times:
>>> G = nx.MultiDiGraph([(0, 1), (0, 1), (1, 2)])
>>> list(nx.all_simple_paths(G, 0, 2))
[[0, 1, 2], [0, 1, 2]]
Notes
-----
This algorithm uses a modified depth-first search to generate the
paths [1]_. A single path can be found in $O(V+E)$ time but the
number of simple paths in a graph can be very large, e.g. $O(n!)$ in
the complete graph of order $n$.
This function does not check that a path exists between `source` and
`target`. For large graphs, this may result in very long runtimes.
Consider using `has_path` to check that a path exists between `source` and
`target` before calling this function on large graphs.
References
----------
.. [1] R. Sedgewick, "Algorithms in C, Part 5: Graph Algorithms",
Addison Wesley Professional, 3rd ed., 2001.
See Also
--------
all_shortest_paths, shortest_path, has_path
| def _bidirectional_dijkstra(
G, source, target, weight="weight", ignore_nodes=None, ignore_edges=None
):
"""Dijkstra's algorithm for shortest paths using bidirectional search.
This function returns the shortest path between source and target
ignoring nodes and edges in the containers ignore_nodes and
ignore_edges.
This is a custom modification of the standard Dijkstra bidirectional
shortest path implementation at networkx.algorithms.weighted
Parameters
----------
G : NetworkX graph
source : node
Starting node.
target : node
Ending node.
weight: string, function, optional (default='weight')
Edge data key or weight function corresponding to the edge weight
ignore_nodes : container of nodes
nodes to ignore, optional
ignore_edges : container of edges
edges to ignore, optional
Returns
-------
length : number
Shortest path length.
Returns a tuple of two dictionaries keyed by node.
The first dictionary stores distance from the source.
The second stores the path from the source to that node.
Raises
------
NetworkXNoPath
If no path exists between source and target.
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
In practice bidirectional Dijkstra is much more than twice as fast as
ordinary Dijkstra.
Ordinary Dijkstra expands nodes in a sphere-like manner from the
source. The radius of this sphere will eventually be the length
of the shortest path. Bidirectional Dijkstra will expand nodes
from both the source and the target, making two spheres of half
this radius. Volume of the first sphere is pi*r*r while the
others are 2*pi*r/2*r/2, making up half the volume.
This algorithm is not guaranteed to work if edge weights
are negative or are floating point numbers
(overflows and roundoff errors can cause problems).
See Also
--------
shortest_path
shortest_path_length
"""
if ignore_nodes and (source in ignore_nodes or target in ignore_nodes):
raise nx.NetworkXNoPath(f"No path between {source} and {target}.")
if source == target:
if source not in G:
raise nx.NodeNotFound(f"Node {source} not in graph")
return (0, [source])
# handle either directed or undirected
if G.is_directed():
Gpred = G.predecessors
Gsucc = G.successors
else:
Gpred = G.neighbors
Gsucc = G.neighbors
# support optional nodes filter
if ignore_nodes:
def filter_iter(nodes):
def iterate(v):
for w in nodes(v):
if w not in ignore_nodes:
yield w
return iterate
Gpred = filter_iter(Gpred)
Gsucc = filter_iter(Gsucc)
# support optional edges filter
if ignore_edges:
if G.is_directed():
def filter_pred_iter(pred_iter):
def iterate(v):
for w in pred_iter(v):
if (w, v) not in ignore_edges:
yield w
return iterate
def filter_succ_iter(succ_iter):
def iterate(v):
for w in succ_iter(v):
if (v, w) not in ignore_edges:
yield w
return iterate
Gpred = filter_pred_iter(Gpred)
Gsucc = filter_succ_iter(Gsucc)
else:
def filter_iter(nodes):
def iterate(v):
for w in nodes(v):
if (v, w) not in ignore_edges and (w, v) not in ignore_edges:
yield w
return iterate
Gpred = filter_iter(Gpred)
Gsucc = filter_iter(Gsucc)
push = heappush
pop = heappop
# Init: Forward Backward
dists = [{}, {}] # dictionary of final distances
paths = [{source: [source]}, {target: [target]}] # dictionary of paths
fringe = [[], []] # heap of (distance, node) tuples for
# extracting next node to expand
seen = [{source: 0}, {target: 0}] # dictionary of distances to
# nodes seen
c = count()
# initialize fringe heap
push(fringe[0], (0, next(c), source))
push(fringe[1], (0, next(c), target))
# neighs for extracting correct neighbor information
neighs = [Gsucc, Gpred]
# variables to hold shortest discovered path
# finaldist = 1e30000
finalpath = []
dir = 1
while fringe[0] and fringe[1]:
# choose direction
# dir == 0 is forward direction and dir == 1 is back
dir = 1 - dir
# extract closest to expand
(dist, _, v) = pop(fringe[dir])
if v in dists[dir]:
# Shortest path to v has already been found
continue
# update distance
dists[dir][v] = dist # equal to seen[dir][v]
if v in dists[1 - dir]:
# if we have scanned v in both directions we are done
# we have now discovered the shortest path
return (finaldist, finalpath)
wt = _weight_function(G, weight)
for w in neighs[dir](v):
if dir == 0: # forward
minweight = wt(v, w, G.get_edge_data(v, w))
vwLength = dists[dir][v] + minweight
else: # back, must remember to change v,w->w,v
minweight = wt(w, v, G.get_edge_data(w, v))
vwLength = dists[dir][v] + minweight
if w in dists[dir]:
if vwLength < dists[dir][w]:
raise ValueError("Contradictory paths found: negative weights?")
elif w not in seen[dir] or vwLength < seen[dir][w]:
# relaxing
seen[dir][w] = vwLength
push(fringe[dir], (vwLength, next(c), w))
paths[dir][w] = paths[dir][v] + [w]
if w in seen[0] and w in seen[1]:
# see if this path is better than the already
# discovered shortest path
totaldist = seen[0][w] + seen[1][w]
if finalpath == [] or finaldist > totaldist:
finaldist = totaldist
revpath = paths[1][w][:]
revpath.reverse()
finalpath = paths[0][w] + revpath[1:]
raise nx.NetworkXNoPath(f"No path between {source} and {target}.")
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|
30,377 | networkx.algorithms.dag | all_topological_sorts | Returns a generator of _all_ topological sorts of the directed graph G.
A topological sort is a nonunique permutation of the nodes such that an
edge from u to v implies that u appears before v in the topological sort
order.
Parameters
----------
G : NetworkX DiGraph
A directed graph
Yields
------
topological_sort_order : list
a list of nodes in `G`, representing one of the topological sort orders
Raises
------
NetworkXNotImplemented
If `G` is not directed
NetworkXUnfeasible
If `G` is not acyclic
Examples
--------
To enumerate all topological sorts of directed graph:
>>> DG = nx.DiGraph([(1, 2), (2, 3), (2, 4)])
>>> list(nx.all_topological_sorts(DG))
[[1, 2, 4, 3], [1, 2, 3, 4]]
Notes
-----
Implements an iterative version of the algorithm given in [1].
References
----------
.. [1] Knuth, Donald E., Szwarcfiter, Jayme L. (1974).
"A Structured Program to Generate All Topological Sorting Arrangements"
Information Processing Letters, Volume 2, Issue 6, 1974, Pages 153-157,
ISSN 0020-0190,
https://doi.org/10.1016/0020-0190(74)90001-5.
Elsevier (North-Holland), Amsterdam
| def transitive_closure_dag(G, topo_order=None):
"""Returns the transitive closure of a directed acyclic graph.
This function is faster than the function `transitive_closure`, but fails
if the graph has a cycle.
The transitive closure of G = (V,E) is a graph G+ = (V,E+) such that
for all v, w in V there is an edge (v, w) in E+ if and only if there
is a non-null path from v to w in G.
Parameters
----------
G : NetworkX DiGraph
A directed acyclic graph (DAG)
topo_order: list or tuple, optional
A topological order for G (if None, the function will compute one)
Returns
-------
NetworkX DiGraph
The transitive closure of `G`
Raises
------
NetworkXNotImplemented
If `G` is not directed
NetworkXUnfeasible
If `G` has a cycle
Examples
--------
>>> DG = nx.DiGraph([(1, 2), (2, 3)])
>>> TC = nx.transitive_closure_dag(DG)
>>> TC.edges()
OutEdgeView([(1, 2), (1, 3), (2, 3)])
Notes
-----
This algorithm is probably simple enough to be well-known but I didn't find
a mention in the literature.
"""
if topo_order is None:
topo_order = list(topological_sort(G))
TC = G.copy()
# idea: traverse vertices following a reverse topological order, connecting
# each vertex to its descendants at distance 2 as we go
for v in reversed(topo_order):
TC.add_edges_from((v, u) for u in nx.descendants_at_distance(TC, v, 2))
return TC
| (G, *, backend=None, **backend_kwargs) | [
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|
30,380 | networkx.algorithms.dag | ancestors | Returns all nodes having a path to `source` in `G`.
Parameters
----------
G : NetworkX Graph
source : node in `G`
Returns
-------
set()
The ancestors of `source` in `G`
Raises
------
NetworkXError
If node `source` is not in `G`.
Examples
--------
>>> DG = nx.path_graph(5, create_using=nx.DiGraph)
>>> sorted(nx.ancestors(DG, 2))
[0, 1]
The `source` node is not an ancestor of itself, but can be included manually:
>>> sorted(nx.ancestors(DG, 2) | {2})
[0, 1, 2]
See also
--------
descendants
| def transitive_closure_dag(G, topo_order=None):
"""Returns the transitive closure of a directed acyclic graph.
This function is faster than the function `transitive_closure`, but fails
if the graph has a cycle.
The transitive closure of G = (V,E) is a graph G+ = (V,E+) such that
for all v, w in V there is an edge (v, w) in E+ if and only if there
is a non-null path from v to w in G.
Parameters
----------
G : NetworkX DiGraph
A directed acyclic graph (DAG)
topo_order: list or tuple, optional
A topological order for G (if None, the function will compute one)
Returns
-------
NetworkX DiGraph
The transitive closure of `G`
Raises
------
NetworkXNotImplemented
If `G` is not directed
NetworkXUnfeasible
If `G` has a cycle
Examples
--------
>>> DG = nx.DiGraph([(1, 2), (2, 3)])
>>> TC = nx.transitive_closure_dag(DG)
>>> TC.edges()
OutEdgeView([(1, 2), (1, 3), (2, 3)])
Notes
-----
This algorithm is probably simple enough to be well-known but I didn't find
a mention in the literature.
"""
if topo_order is None:
topo_order = list(topological_sort(G))
TC = G.copy()
# idea: traverse vertices following a reverse topological order, connecting
# each vertex to its descendants at distance 2 as we go
for v in reversed(topo_order):
TC.add_edges_from((v, u) for u in nx.descendants_at_distance(TC, v, 2))
return TC
| (G, source, *, backend=None, **backend_kwargs) | [
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|
30,381 | networkx.algorithms.dag | antichains | Generates antichains from a directed acyclic graph (DAG).
An antichain is a subset of a partially ordered set such that any
two elements in the subset are incomparable.
Parameters
----------
G : NetworkX DiGraph
A directed acyclic graph (DAG)
topo_order: list or tuple, optional
A topological order for G (if None, the function will compute one)
Yields
------
antichain : list
a list of nodes in `G` representing an antichain
Raises
------
NetworkXNotImplemented
If `G` is not directed
NetworkXUnfeasible
If `G` contains a cycle
Examples
--------
>>> DG = nx.DiGraph([(1, 2), (1, 3)])
>>> list(nx.antichains(DG))
[[], [3], [2], [2, 3], [1]]
Notes
-----
This function was originally developed by Peter Jipsen and Franco Saliola
for the SAGE project. It's included in NetworkX with permission from the
authors. Original SAGE code at:
https://github.com/sagemath/sage/blob/master/src/sage/combinat/posets/hasse_diagram.py
References
----------
.. [1] Free Lattices, by R. Freese, J. Jezek and J. B. Nation,
AMS, Vol 42, 1995, p. 226.
| def transitive_closure_dag(G, topo_order=None):
"""Returns the transitive closure of a directed acyclic graph.
This function is faster than the function `transitive_closure`, but fails
if the graph has a cycle.
The transitive closure of G = (V,E) is a graph G+ = (V,E+) such that
for all v, w in V there is an edge (v, w) in E+ if and only if there
is a non-null path from v to w in G.
Parameters
----------
G : NetworkX DiGraph
A directed acyclic graph (DAG)
topo_order: list or tuple, optional
A topological order for G (if None, the function will compute one)
Returns
-------
NetworkX DiGraph
The transitive closure of `G`
Raises
------
NetworkXNotImplemented
If `G` is not directed
NetworkXUnfeasible
If `G` has a cycle
Examples
--------
>>> DG = nx.DiGraph([(1, 2), (2, 3)])
>>> TC = nx.transitive_closure_dag(DG)
>>> TC.edges()
OutEdgeView([(1, 2), (1, 3), (2, 3)])
Notes
-----
This algorithm is probably simple enough to be well-known but I didn't find
a mention in the literature.
"""
if topo_order is None:
topo_order = list(topological_sort(G))
TC = G.copy()
# idea: traverse vertices following a reverse topological order, connecting
# each vertex to its descendants at distance 2 as we go
for v in reversed(topo_order):
TC.add_edges_from((v, u) for u in nx.descendants_at_distance(TC, v, 2))
return TC
| (G, topo_order=None, *, backend=None, **backend_kwargs) | [
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|
30,384 | networkx.drawing.layout | arf_layout | Arf layout for networkx
The attractive and repulsive forces (arf) layout [1]
improves the spring layout in three ways. First, it
prevents congestion of highly connected nodes due to
strong forcing between nodes. Second, it utilizes the
layout space more effectively by preventing large gaps
that spring layout tends to create. Lastly, the arf
layout represents symmetries in the layout better than
the default spring layout.
Parameters
----------
G : nx.Graph or nx.DiGraph
Networkx graph.
pos : dict
Initial position of the nodes. If set to None a
random layout will be used.
scaling : float
Scales the radius of the circular layout space.
a : float
Strength of springs between connected nodes. Should be larger than 1. The greater a, the clearer the separation ofunconnected sub clusters.
etol : float
Gradient sum of spring forces must be larger than `etol` before successful termination.
dt : float
Time step for force differential equation simulations.
max_iter : int
Max iterations before termination of the algorithm.
References
.. [1] "Self-Organization Applied to Dynamic Network Layout", M. Geipel,
International Journal of Modern Physics C, 2007, Vol 18, No 10, pp. 1537-1549.
https://doi.org/10.1142/S0129183107011558 https://arxiv.org/abs/0704.1748
Returns
-------
pos : dict
A dictionary of positions keyed by node.
Examples
--------
>>> G = nx.grid_graph((5, 5))
>>> pos = nx.arf_layout(G)
| def arf_layout(
G,
pos=None,
scaling=1,
a=1.1,
etol=1e-6,
dt=1e-3,
max_iter=1000,
):
"""Arf layout for networkx
The attractive and repulsive forces (arf) layout [1]
improves the spring layout in three ways. First, it
prevents congestion of highly connected nodes due to
strong forcing between nodes. Second, it utilizes the
layout space more effectively by preventing large gaps
that spring layout tends to create. Lastly, the arf
layout represents symmetries in the layout better than
the default spring layout.
Parameters
----------
G : nx.Graph or nx.DiGraph
Networkx graph.
pos : dict
Initial position of the nodes. If set to None a
random layout will be used.
scaling : float
Scales the radius of the circular layout space.
a : float
Strength of springs between connected nodes. Should be larger than 1. The greater a, the clearer the separation ofunconnected sub clusters.
etol : float
Gradient sum of spring forces must be larger than `etol` before successful termination.
dt : float
Time step for force differential equation simulations.
max_iter : int
Max iterations before termination of the algorithm.
References
.. [1] "Self-Organization Applied to Dynamic Network Layout", M. Geipel,
International Journal of Modern Physics C, 2007, Vol 18, No 10, pp. 1537-1549.
https://doi.org/10.1142/S0129183107011558 https://arxiv.org/abs/0704.1748
Returns
-------
pos : dict
A dictionary of positions keyed by node.
Examples
--------
>>> G = nx.grid_graph((5, 5))
>>> pos = nx.arf_layout(G)
"""
import warnings
import numpy as np
if a <= 1:
msg = "The parameter a should be larger than 1"
raise ValueError(msg)
pos_tmp = nx.random_layout(G)
if pos is None:
pos = pos_tmp
else:
for node in G.nodes():
if node not in pos:
pos[node] = pos_tmp[node].copy()
# Initialize spring constant matrix
N = len(G)
# No nodes no computation
if N == 0:
return pos
# init force of springs
K = np.ones((N, N)) - np.eye(N)
node_order = {node: i for i, node in enumerate(G)}
for x, y in G.edges():
if x != y:
idx, jdx = (node_order[i] for i in (x, y))
K[idx, jdx] = a
# vectorize values
p = np.asarray(list(pos.values()))
# equation 10 in [1]
rho = scaling * np.sqrt(N)
# looping variables
error = etol + 1
n_iter = 0
while error > etol:
diff = p[:, np.newaxis] - p[np.newaxis]
A = np.linalg.norm(diff, axis=-1)[..., np.newaxis]
# attraction_force - repulsions force
# suppress nans due to division; caused by diagonal set to zero.
# Does not affect the computation due to nansum
with warnings.catch_warnings():
warnings.simplefilter("ignore")
change = K[..., np.newaxis] * diff - rho / A * diff
change = np.nansum(change, axis=0)
p += change * dt
error = np.linalg.norm(change, axis=-1).sum()
if n_iter > max_iter:
break
n_iter += 1
return dict(zip(G.nodes(), p))
| (G, pos=None, scaling=1, a=1.1, etol=1e-06, dt=0.001, max_iter=1000) | [
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|
30,403 | networkx.algorithms.connectivity.connectivity | average_node_connectivity | Returns the average connectivity of a graph G.
The average connectivity `\bar{\kappa}` of a graph G is the average
of local node connectivity over all pairs of nodes of G [1]_ .
.. math::
\bar{\kappa}(G) = \frac{\sum_{u,v} \kappa_{G}(u,v)}{{n \choose 2}}
Parameters
----------
G : NetworkX graph
Undirected graph
flow_func : function
A function for computing the maximum flow among a pair of nodes.
The function has to accept at least three parameters: a Digraph,
a source node, and a target node. And return a residual network
that follows NetworkX conventions (see :meth:`maximum_flow` for
details). If flow_func is None, the default maximum flow function
(:meth:`edmonds_karp`) is used. See :meth:`local_node_connectivity`
for details. The choice of the default function may change from
version to version and should not be relied on. Default value: None.
Returns
-------
K : float
Average node connectivity
See also
--------
:meth:`local_node_connectivity`
:meth:`node_connectivity`
:meth:`edge_connectivity`
:meth:`maximum_flow`
:meth:`edmonds_karp`
:meth:`preflow_push`
:meth:`shortest_augmenting_path`
References
----------
.. [1] Beineke, L., O. Oellermann, and R. Pippert (2002). The average
connectivity of a graph. Discrete mathematics 252(1-3), 31-45.
http://www.sciencedirect.com/science/article/pii/S0012365X01001807
| @nx._dispatchable
def edge_connectivity(G, s=None, t=None, flow_func=None, cutoff=None):
r"""Returns the edge connectivity of the graph or digraph G.
The edge connectivity is equal to the minimum number of edges that
must be removed to disconnect G or render it trivial. If source
and target nodes are provided, this function returns the local edge
connectivity: the minimum number of edges that must be removed to
break all paths from source to target in G.
Parameters
----------
G : NetworkX graph
Undirected or directed graph
s : node
Source node. Optional. Default value: None.
t : node
Target node. Optional. Default value: None.
flow_func : function
A function for computing the maximum flow among a pair of nodes.
The function has to accept at least three parameters: a Digraph,
a source node, and a target node. And return a residual network
that follows NetworkX conventions (see :meth:`maximum_flow` for
details). If flow_func is None, the default maximum flow function
(:meth:`edmonds_karp`) is used. See below for details. The
choice of the default function may change from version
to version and should not be relied on. Default value: None.
cutoff : integer, float, or None (default: None)
If specified, the maximum flow algorithm will terminate when the
flow value reaches or exceeds the cutoff. This only works for flows
that support the cutoff parameter (most do) and is ignored otherwise.
Returns
-------
K : integer
Edge connectivity for G, or local edge connectivity if source
and target were provided
Examples
--------
>>> # Platonic icosahedral graph is 5-edge-connected
>>> G = nx.icosahedral_graph()
>>> nx.edge_connectivity(G)
5
You can use alternative flow algorithms for the underlying
maximum flow computation. In dense networks the algorithm
:meth:`shortest_augmenting_path` will usually perform better
than the default :meth:`edmonds_karp`, which is faster for
sparse networks with highly skewed degree distributions.
Alternative flow functions have to be explicitly imported
from the flow package.
>>> from networkx.algorithms.flow import shortest_augmenting_path
>>> nx.edge_connectivity(G, flow_func=shortest_augmenting_path)
5
If you specify a pair of nodes (source and target) as parameters,
this function returns the value of local edge connectivity.
>>> nx.edge_connectivity(G, 3, 7)
5
If you need to perform several local computations among different
pairs of nodes on the same graph, it is recommended that you reuse
the data structures used in the maximum flow computations. See
:meth:`local_edge_connectivity` for details.
Notes
-----
This is a flow based implementation of global edge connectivity.
For undirected graphs the algorithm works by finding a 'small'
dominating set of nodes of G (see algorithm 7 in [1]_ ) and
computing local maximum flow (see :meth:`local_edge_connectivity`)
between an arbitrary node in the dominating set and the rest of
nodes in it. This is an implementation of algorithm 6 in [1]_ .
For directed graphs, the algorithm does n calls to the maximum
flow function. This is an implementation of algorithm 8 in [1]_ .
See also
--------
:meth:`local_edge_connectivity`
:meth:`local_node_connectivity`
:meth:`node_connectivity`
:meth:`maximum_flow`
:meth:`edmonds_karp`
:meth:`preflow_push`
:meth:`shortest_augmenting_path`
:meth:`k_edge_components`
:meth:`k_edge_subgraphs`
References
----------
.. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
"""
if (s is not None and t is None) or (s is None and t is not None):
raise nx.NetworkXError("Both source and target must be specified.")
# Local edge connectivity
if s is not None and t is not None:
if s not in G:
raise nx.NetworkXError(f"node {s} not in graph")
if t not in G:
raise nx.NetworkXError(f"node {t} not in graph")
return local_edge_connectivity(G, s, t, flow_func=flow_func, cutoff=cutoff)
# Global edge connectivity
# reuse auxiliary digraph and residual network
H = build_auxiliary_edge_connectivity(G)
R = build_residual_network(H, "capacity")
kwargs = {"flow_func": flow_func, "auxiliary": H, "residual": R}
if G.is_directed():
# Algorithm 8 in [1]
if not nx.is_weakly_connected(G):
return 0
# initial value for \lambda is minimum degree
L = min(d for n, d in G.degree())
nodes = list(G)
n = len(nodes)
if cutoff is not None:
L = min(cutoff, L)
for i in range(n):
kwargs["cutoff"] = L
try:
L = min(L, local_edge_connectivity(G, nodes[i], nodes[i + 1], **kwargs))
except IndexError: # last node!
L = min(L, local_edge_connectivity(G, nodes[i], nodes[0], **kwargs))
return L
else: # undirected
# Algorithm 6 in [1]
if not nx.is_connected(G):
return 0
# initial value for \lambda is minimum degree
L = min(d for n, d in G.degree())
if cutoff is not None:
L = min(cutoff, L)
# A dominating set is \lambda-covering
# We need a dominating set with at least two nodes
for node in G:
D = nx.dominating_set(G, start_with=node)
v = D.pop()
if D:
break
else:
# in complete graphs the dominating sets will always be of one node
# thus we return min degree
return L
for w in D:
kwargs["cutoff"] = L
L = min(L, local_edge_connectivity(G, v, w, **kwargs))
return L
| (G, flow_func=None, *, backend=None, **backend_kwargs) | [
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|
30,405 | networkx.generators.classic | balanced_tree | Returns the perfectly balanced `r`-ary tree of height `h`.
.. plot::
>>> nx.draw(nx.balanced_tree(2, 3))
Parameters
----------
r : int
Branching factor of the tree; each node will have `r`
children.
h : int
Height of the tree.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Returns
-------
G : NetworkX graph
A balanced `r`-ary tree of height `h`.
Notes
-----
This is the rooted tree where all leaves are at distance `h` from
the root. The root has degree `r` and all other internal nodes
have degree `r + 1`.
Node labels are integers, starting from zero.
A balanced tree is also known as a *complete r-ary tree*.
| def star_graph(n, create_using=None):
"""Return the star graph
The star graph consists of one center node connected to n outer nodes.
.. plot::
>>> nx.draw(nx.star_graph(6))
Parameters
----------
n : int or iterable
If an integer, node labels are 0 to n with center 0.
If an iterable of nodes, the center is the first.
Warning: n is not checked for duplicates and if present the
resulting graph may not be as desired. Make sure you have no duplicates.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Notes
-----
The graph has n+1 nodes for integer n.
So star_graph(3) is the same as star_graph(range(4)).
"""
n, nodes = n
if isinstance(n, numbers.Integral):
nodes.append(int(n)) # there should be n+1 nodes
G = empty_graph(nodes, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
if len(nodes) > 1:
hub, *spokes = nodes
G.add_edges_from((hub, node) for node in spokes)
return G
| (r, h, create_using=None, *, backend=None, **backend_kwargs) | [
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|
30,406 | networkx.generators.random_graphs | barabasi_albert_graph | Returns a random graph using Barabási–Albert preferential attachment
A graph of $n$ nodes is grown by attaching new nodes each with $m$
edges that are preferentially attached to existing nodes with high degree.
Parameters
----------
n : int
Number of nodes
m : int
Number of edges to attach from a new node to existing nodes
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
initial_graph : Graph or None (default)
Initial network for Barabási–Albert algorithm.
It should be a connected graph for most use cases.
A copy of `initial_graph` is used.
If None, starts from a star graph on (m+1) nodes.
Returns
-------
G : Graph
Raises
------
NetworkXError
If `m` does not satisfy ``1 <= m < n``, or
the initial graph number of nodes m0 does not satisfy ``m <= m0 <= n``.
References
----------
.. [1] A. L. Barabási and R. Albert "Emergence of scaling in
random networks", Science 286, pp 509-512, 1999.
| def dual_barabasi_albert_graph(n, m1, m2, p, seed=None, initial_graph=None):
"""Returns a random graph using dual Barabási–Albert preferential attachment
A graph of $n$ nodes is grown by attaching new nodes each with either $m_1$
edges (with probability $p$) or $m_2$ edges (with probability $1-p$) that
are preferentially attached to existing nodes with high degree.
Parameters
----------
n : int
Number of nodes
m1 : int
Number of edges to link each new node to existing nodes with probability $p$
m2 : int
Number of edges to link each new node to existing nodes with probability $1-p$
p : float
The probability of attaching $m_1$ edges (as opposed to $m_2$ edges)
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
initial_graph : Graph or None (default)
Initial network for Barabási–Albert algorithm.
A copy of `initial_graph` is used.
It should be connected for most use cases.
If None, starts from an star graph on max(m1, m2) + 1 nodes.
Returns
-------
G : Graph
Raises
------
NetworkXError
If `m1` and `m2` do not satisfy ``1 <= m1,m2 < n``, or
`p` does not satisfy ``0 <= p <= 1``, or
the initial graph number of nodes m0 does not satisfy m1, m2 <= m0 <= n.
References
----------
.. [1] N. Moshiri "The dual-Barabasi-Albert model", arXiv:1810.10538.
"""
if m1 < 1 or m1 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m1 >= 1 and m1 < n, m1 = {m1}, n = {n}"
)
if m2 < 1 or m2 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m2 >= 1 and m2 < n, m2 = {m2}, n = {n}"
)
if p < 0 or p > 1:
raise nx.NetworkXError(
f"Dual Barabási–Albert network must have 0 <= p <= 1, p = {p}"
)
# For simplicity, if p == 0 or 1, just return BA
if p == 1:
return barabasi_albert_graph(n, m1, seed)
elif p == 0:
return barabasi_albert_graph(n, m2, seed)
if initial_graph is None:
# Default initial graph : empty graph on max(m1, m2) nodes
G = star_graph(max(m1, m2))
else:
if len(initial_graph) < max(m1, m2) or len(initial_graph) > n:
raise nx.NetworkXError(
f"Barabási–Albert initial graph must have between "
f"max(m1, m2) = {max(m1, m2)} and n = {n} nodes"
)
G = initial_graph.copy()
# Target nodes for new edges
targets = list(G)
# List of existing nodes, with nodes repeated once for each adjacent edge
repeated_nodes = [n for n, d in G.degree() for _ in range(d)]
# Start adding the remaining nodes.
source = len(G)
while source < n:
# Pick which m to use (m1 or m2)
if seed.random() < p:
m = m1
else:
m = m2
# Now choose m unique nodes from the existing nodes
# Pick uniformly from repeated_nodes (preferential attachment)
targets = _random_subset(repeated_nodes, m, seed)
# Add edges to m nodes from the source.
G.add_edges_from(zip([source] * m, targets))
# Add one node to the list for each new edge just created.
repeated_nodes.extend(targets)
# And the new node "source" has m edges to add to the list.
repeated_nodes.extend([source] * m)
source += 1
return G
| (n, m, seed=None, initial_graph=None, *, backend=None, **backend_kwargs) | [
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|
30,407 | networkx.generators.classic | barbell_graph | Returns the Barbell Graph: two complete graphs connected by a path.
.. plot::
>>> nx.draw(nx.barbell_graph(4, 2))
Parameters
----------
m1 : int
Size of the left and right barbells, must be greater than 2.
m2 : int
Length of the path connecting the barbells.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Only undirected Graphs are supported.
Returns
-------
G : NetworkX graph
A barbell graph.
Notes
-----
Two identical complete graphs $K_{m1}$ form the left and right bells,
and are connected by a path $P_{m2}$.
The `2*m1+m2` nodes are numbered
`0, ..., m1-1` for the left barbell,
`m1, ..., m1+m2-1` for the path,
and `m1+m2, ..., 2*m1+m2-1` for the right barbell.
The 3 subgraphs are joined via the edges `(m1-1, m1)` and
`(m1+m2-1, m1+m2)`. If `m2=0`, this is merely two complete
graphs joined together.
This graph is an extremal example in David Aldous
and Jim Fill's e-text on Random Walks on Graphs.
| def star_graph(n, create_using=None):
"""Return the star graph
The star graph consists of one center node connected to n outer nodes.
.. plot::
>>> nx.draw(nx.star_graph(6))
Parameters
----------
n : int or iterable
If an integer, node labels are 0 to n with center 0.
If an iterable of nodes, the center is the first.
Warning: n is not checked for duplicates and if present the
resulting graph may not be as desired. Make sure you have no duplicates.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Notes
-----
The graph has n+1 nodes for integer n.
So star_graph(3) is the same as star_graph(range(4)).
"""
n, nodes = n
if isinstance(n, numbers.Integral):
nodes.append(int(n)) # there should be n+1 nodes
G = empty_graph(nodes, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
if len(nodes) > 1:
hub, *spokes = nodes
G.add_edges_from((hub, node) for node in spokes)
return G
| (m1, m2, create_using=None, *, backend=None, **backend_kwargs) | [
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|
30,408 | networkx.algorithms.distance_measures | barycenter | Calculate barycenter of a connected graph, optionally with edge weights.
The :dfn:`barycenter` a
:func:`connected <networkx.algorithms.components.is_connected>` graph
:math:`G` is the subgraph induced by the set of its nodes :math:`v`
minimizing the objective function
.. math::
\sum_{u \in V(G)} d_G(u, v),
where :math:`d_G` is the (possibly weighted) :func:`path length
<networkx.algorithms.shortest_paths.generic.shortest_path_length>`.
The barycenter is also called the :dfn:`median`. See [West01]_, p. 78.
Parameters
----------
G : :class:`networkx.Graph`
The connected graph :math:`G`.
weight : :class:`str`, optional
Passed through to
:func:`~networkx.algorithms.shortest_paths.generic.shortest_path_length`.
attr : :class:`str`, optional
If given, write the value of the objective function to each node's
`attr` attribute. Otherwise do not store the value.
sp : dict of dicts, optional
All pairs shortest path lengths as a dictionary of dictionaries
Returns
-------
list
Nodes of `G` that induce the barycenter of `G`.
Raises
------
NetworkXNoPath
If `G` is disconnected. `G` may appear disconnected to
:func:`barycenter` if `sp` is given but is missing shortest path
lengths for any pairs.
ValueError
If `sp` and `weight` are both given.
Examples
--------
>>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
>>> nx.barycenter(G)
[1, 3, 4]
See Also
--------
center
periphery
| def effective_graph_resistance(G, weight=None, invert_weight=True):
"""Returns the Effective graph resistance of G.
Also known as the Kirchhoff index.
The effective graph resistance is defined as the sum
of the resistance distance of every node pair in G [1]_.
If weight is not provided, then a weight of 1 is used for all edges.
The effective graph resistance of a disconnected graph is infinite.
Parameters
----------
G : NetworkX graph
A graph
weight : string or None, optional (default=None)
The edge data key used to compute the effective graph resistance.
If None, then each edge has weight 1.
invert_weight : boolean (default=True)
Proper calculation of resistance distance requires building the
Laplacian matrix with the reciprocal of the weight. Not required
if the weight is already inverted. Weight cannot be zero.
Returns
-------
RG : float
The effective graph resistance of `G`.
Raises
------
NetworkXNotImplemented
If `G` is a directed graph.
NetworkXError
If `G` does not contain any nodes.
Examples
--------
>>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
>>> round(nx.effective_graph_resistance(G), 10)
10.25
Notes
-----
The implementation is based on Theorem 2.2 in [2]_. Self-loops are ignored.
Multi-edges are contracted in one edge with weight equal to the harmonic sum of the weights.
References
----------
.. [1] Wolfram
"Kirchhoff Index."
https://mathworld.wolfram.com/KirchhoffIndex.html
.. [2] W. Ellens, F. M. Spieksma, P. Van Mieghem, A. Jamakovic, R. E. Kooij.
Effective graph resistance.
Lin. Alg. Appl. 435:2491-2506, 2011.
"""
import numpy as np
if len(G) == 0:
raise nx.NetworkXError("Graph G must contain at least one node.")
# Disconnected graphs have infinite Effective graph resistance
if not nx.is_connected(G):
return float("inf")
# Invert weights
G = G.copy()
if invert_weight and weight is not None:
if G.is_multigraph():
for u, v, k, d in G.edges(keys=True, data=True):
d[weight] = 1 / d[weight]
else:
for u, v, d in G.edges(data=True):
d[weight] = 1 / d[weight]
# Get Laplacian eigenvalues
mu = np.sort(nx.laplacian_spectrum(G, weight=weight))
# Compute Effective graph resistance based on spectrum of the Laplacian
# Self-loops are ignored
return float(np.sum(1 / mu[1:]) * G.number_of_nodes())
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|
30,410 | networkx.algorithms.shortest_paths.weighted | bellman_ford_path | Returns the shortest path from source to target in a weighted graph G.
Parameters
----------
G : NetworkX graph
source : node
Starting node
target : node
Ending node
weight : string or function (default="weight")
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number.
Returns
-------
path : list
List of nodes in a shortest path.
Raises
------
NodeNotFound
If `source` is not in `G`.
NetworkXNoPath
If no path exists between source and target.
Examples
--------
>>> G = nx.path_graph(5)
>>> nx.bellman_ford_path(G, 0, 4)
[0, 1, 2, 3, 4]
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
See Also
--------
dijkstra_path, bellman_ford_path_length
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
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|
30,411 | networkx.algorithms.shortest_paths.weighted | bellman_ford_path_length | Returns the shortest path length from source to target
in a weighted graph.
Parameters
----------
G : NetworkX graph
source : node label
starting node for path
target : node label
ending node for path
weight : string or function (default="weight")
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number.
Returns
-------
length : number
Shortest path length.
Raises
------
NodeNotFound
If `source` is not in `G`.
NetworkXNoPath
If no path exists between source and target.
Examples
--------
>>> G = nx.path_graph(5)
>>> nx.bellman_ford_path_length(G, 0, 4)
4
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
See Also
--------
dijkstra_path_length, bellman_ford_path
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
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|
30,412 | networkx.algorithms.shortest_paths.weighted | bellman_ford_predecessor_and_distance | Compute shortest path lengths and predecessors on shortest paths
in weighted graphs.
The algorithm has a running time of $O(mn)$ where $n$ is the number of
nodes and $m$ is the number of edges. It is slower than Dijkstra but
can handle negative edge weights.
If a negative cycle is detected, you can use :func:`find_negative_cycle`
to return the cycle and examine it. Shortest paths are not defined when
a negative cycle exists because once reached, the path can cycle forever
to build up arbitrarily low weights.
Parameters
----------
G : NetworkX graph
The algorithm works for all types of graphs, including directed
graphs and multigraphs.
source: node label
Starting node for path
target : node label, optional
Ending node for path
weight : string or function
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number.
heuristic : bool
Determines whether to use a heuristic to early detect negative
cycles at a hopefully negligible cost.
Returns
-------
pred, dist : dictionaries
Returns two dictionaries keyed by node to predecessor in the
path and to the distance from the source respectively.
Raises
------
NodeNotFound
If `source` is not in `G`.
NetworkXUnbounded
If the (di)graph contains a negative (di)cycle, the
algorithm raises an exception to indicate the presence of the
negative (di)cycle. Note: any negative weight edge in an
undirected graph is a negative cycle.
Examples
--------
>>> G = nx.path_graph(5, create_using=nx.DiGraph())
>>> pred, dist = nx.bellman_ford_predecessor_and_distance(G, 0)
>>> sorted(pred.items())
[(0, []), (1, [0]), (2, [1]), (3, [2]), (4, [3])]
>>> sorted(dist.items())
[(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)]
>>> pred, dist = nx.bellman_ford_predecessor_and_distance(G, 0, 1)
>>> sorted(pred.items())
[(0, []), (1, [0]), (2, [1]), (3, [2]), (4, [3])]
>>> sorted(dist.items())
[(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)]
>>> G = nx.cycle_graph(5, create_using=nx.DiGraph())
>>> G[1][2]["weight"] = -7
>>> nx.bellman_ford_predecessor_and_distance(G, 0)
Traceback (most recent call last):
...
networkx.exception.NetworkXUnbounded: Negative cycle detected.
See Also
--------
find_negative_cycle
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
The dictionaries returned only have keys for nodes reachable from
the source.
In the case where the (di)graph is not connected, if a component
not containing the source contains a negative (di)cycle, it
will not be detected.
In NetworkX v2.1 and prior, the source node had predecessor `[None]`.
In NetworkX v2.2 this changed to the source node having predecessor `[]`
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
| (G, source, target=None, weight='weight', heuristic=False, *, backend=None, **backend_kwargs) | [
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|
30,424 | networkx.drawing.layout | bfs_layout | Position nodes according to breadth-first search algorithm.
Parameters
----------
G : NetworkX graph
A position will be assigned to every node in G.
start : node in `G`
Starting node for bfs
center : array-like or None
Coordinate pair around which to center the layout.
Returns
-------
pos : dict
A dictionary of positions keyed by node.
Examples
--------
>>> G = nx.path_graph(4)
>>> pos = nx.bfs_layout(G, 0)
Notes
-----
This algorithm currently only works in two dimensions and does not
try to minimize edge crossings.
| def bfs_layout(G, start, *, align="vertical", scale=1, center=None):
"""Position nodes according to breadth-first search algorithm.
Parameters
----------
G : NetworkX graph
A position will be assigned to every node in G.
start : node in `G`
Starting node for bfs
center : array-like or None
Coordinate pair around which to center the layout.
Returns
-------
pos : dict
A dictionary of positions keyed by node.
Examples
--------
>>> G = nx.path_graph(4)
>>> pos = nx.bfs_layout(G, 0)
Notes
-----
This algorithm currently only works in two dimensions and does not
try to minimize edge crossings.
"""
G, center = _process_params(G, center, 2)
# Compute layers with BFS
layers = dict(enumerate(nx.bfs_layers(G, start)))
if len(G) != sum(len(nodes) for nodes in layers.values()):
raise nx.NetworkXError(
"bfs_layout didn't include all nodes. Perhaps use input graph:\n"
" G.subgraph(nx.node_connected_component(G, start))"
)
# Compute node positions with multipartite_layout
return multipartite_layout(
G, subset_key=layers, align=align, scale=scale, center=center
)
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|
30,431 | networkx.algorithms.shortest_paths.weighted | bidirectional_dijkstra | Dijkstra's algorithm for shortest paths using bidirectional search.
Parameters
----------
G : NetworkX graph
source : node
Starting node.
target : node
Ending node.
weight : string or function
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number or None to indicate a hidden edge.
Returns
-------
length, path : number and list
length is the distance from source to target.
path is a list of nodes on a path from source to target.
Raises
------
NodeNotFound
If either `source` or `target` is not in `G`.
NetworkXNoPath
If no path exists between source and target.
Examples
--------
>>> G = nx.path_graph(5)
>>> length, path = nx.bidirectional_dijkstra(G, 0, 4)
>>> print(length)
4
>>> print(path)
[0, 1, 2, 3, 4]
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
The weight function can be used to hide edges by returning None.
So ``weight = lambda u, v, d: 1 if d['color']=="red" else None``
will find the shortest red path.
In practice bidirectional Dijkstra is much more than twice as fast as
ordinary Dijkstra.
Ordinary Dijkstra expands nodes in a sphere-like manner from the
source. The radius of this sphere will eventually be the length
of the shortest path. Bidirectional Dijkstra will expand nodes
from both the source and the target, making two spheres of half
this radius. Volume of the first sphere is `\pi*r*r` while the
others are `2*\pi*r/2*r/2`, making up half the volume.
This algorithm is not guaranteed to work if edge weights
are negative or are floating point numbers
(overflows and roundoff errors can cause problems).
See Also
--------
shortest_path
shortest_path_length
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
| (G, source, target, weight='weight', *, backend=None, **backend_kwargs) | [
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|
30,434 | networkx.generators.random_graphs | gnp_random_graph | Returns a $G_{n,p}$ random graph, also known as an Erdős-Rényi graph
or a binomial graph.
The $G_{n,p}$ model chooses each of the possible edges with probability $p$.
Parameters
----------
n : int
The number of nodes.
p : float
Probability for edge creation.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
directed : bool, optional (default=False)
If True, this function returns a directed graph.
See Also
--------
fast_gnp_random_graph
Notes
-----
This algorithm [2]_ runs in $O(n^2)$ time. For sparse graphs (that is, for
small values of $p$), :func:`fast_gnp_random_graph` is a faster algorithm.
:func:`binomial_graph` and :func:`erdos_renyi_graph` are
aliases for :func:`gnp_random_graph`.
>>> nx.binomial_graph is nx.gnp_random_graph
True
>>> nx.erdos_renyi_graph is nx.gnp_random_graph
True
References
----------
.. [1] P. Erdős and A. Rényi, On Random Graphs, Publ. Math. 6, 290 (1959).
.. [2] E. N. Gilbert, Random Graphs, Ann. Math. Stat., 30, 1141 (1959).
| def dual_barabasi_albert_graph(n, m1, m2, p, seed=None, initial_graph=None):
"""Returns a random graph using dual Barabási–Albert preferential attachment
A graph of $n$ nodes is grown by attaching new nodes each with either $m_1$
edges (with probability $p$) or $m_2$ edges (with probability $1-p$) that
are preferentially attached to existing nodes with high degree.
Parameters
----------
n : int
Number of nodes
m1 : int
Number of edges to link each new node to existing nodes with probability $p$
m2 : int
Number of edges to link each new node to existing nodes with probability $1-p$
p : float
The probability of attaching $m_1$ edges (as opposed to $m_2$ edges)
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
initial_graph : Graph or None (default)
Initial network for Barabási–Albert algorithm.
A copy of `initial_graph` is used.
It should be connected for most use cases.
If None, starts from an star graph on max(m1, m2) + 1 nodes.
Returns
-------
G : Graph
Raises
------
NetworkXError
If `m1` and `m2` do not satisfy ``1 <= m1,m2 < n``, or
`p` does not satisfy ``0 <= p <= 1``, or
the initial graph number of nodes m0 does not satisfy m1, m2 <= m0 <= n.
References
----------
.. [1] N. Moshiri "The dual-Barabasi-Albert model", arXiv:1810.10538.
"""
if m1 < 1 or m1 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m1 >= 1 and m1 < n, m1 = {m1}, n = {n}"
)
if m2 < 1 or m2 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m2 >= 1 and m2 < n, m2 = {m2}, n = {n}"
)
if p < 0 or p > 1:
raise nx.NetworkXError(
f"Dual Barabási–Albert network must have 0 <= p <= 1, p = {p}"
)
# For simplicity, if p == 0 or 1, just return BA
if p == 1:
return barabasi_albert_graph(n, m1, seed)
elif p == 0:
return barabasi_albert_graph(n, m2, seed)
if initial_graph is None:
# Default initial graph : empty graph on max(m1, m2) nodes
G = star_graph(max(m1, m2))
else:
if len(initial_graph) < max(m1, m2) or len(initial_graph) > n:
raise nx.NetworkXError(
f"Barabási–Albert initial graph must have between "
f"max(m1, m2) = {max(m1, m2)} and n = {n} nodes"
)
G = initial_graph.copy()
# Target nodes for new edges
targets = list(G)
# List of existing nodes, with nodes repeated once for each adjacent edge
repeated_nodes = [n for n, d in G.degree() for _ in range(d)]
# Start adding the remaining nodes.
source = len(G)
while source < n:
# Pick which m to use (m1 or m2)
if seed.random() < p:
m = m1
else:
m = m2
# Now choose m unique nodes from the existing nodes
# Pick uniformly from repeated_nodes (preferential attachment)
targets = _random_subset(repeated_nodes, m, seed)
# Add edges to m nodes from the source.
G.add_edges_from(zip([source] * m, targets))
# Add one node to the list for each new edge just created.
repeated_nodes.extend(targets)
# And the new node "source" has m edges to add to the list.
repeated_nodes.extend([source] * m)
source += 1
return G
| (n, p, seed=None, directed=False, *, backend=None, **backend_kwargs) | [
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|
30,435 | networkx.generators.classic | binomial_tree | Returns the Binomial Tree of order n.
The binomial tree of order 0 consists of a single node. A binomial tree of order k
is defined recursively by linking two binomial trees of order k-1: the root of one is
the leftmost child of the root of the other.
.. plot::
>>> nx.draw(nx.binomial_tree(3))
Parameters
----------
n : int
Order of the binomial tree.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Returns
-------
G : NetworkX graph
A binomial tree of $2^n$ nodes and $2^n - 1$ edges.
| def star_graph(n, create_using=None):
"""Return the star graph
The star graph consists of one center node connected to n outer nodes.
.. plot::
>>> nx.draw(nx.star_graph(6))
Parameters
----------
n : int or iterable
If an integer, node labels are 0 to n with center 0.
If an iterable of nodes, the center is the first.
Warning: n is not checked for duplicates and if present the
resulting graph may not be as desired. Make sure you have no duplicates.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Notes
-----
The graph has n+1 nodes for integer n.
So star_graph(3) is the same as star_graph(range(4)).
"""
n, nodes = n
if isinstance(n, numbers.Integral):
nodes.append(int(n)) # there should be n+1 nodes
G = empty_graph(nodes, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
if len(nodes) > 1:
hub, *spokes = nodes
G.add_edges_from((hub, node) for node in spokes)
return G
| (n, create_using=None, *, backend=None, **backend_kwargs) | [
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|
30,437 | networkx.drawing.layout | bipartite_layout | Position nodes in two straight lines.
Parameters
----------
G : NetworkX graph or list of nodes
A position will be assigned to every node in G.
nodes : list or container
Nodes in one node set of the bipartite graph.
This set will be placed on left or top.
align : string (default='vertical')
The alignment of nodes. Vertical or horizontal.
scale : number (default: 1)
Scale factor for positions.
center : array-like or None
Coordinate pair around which to center the layout.
aspect_ratio : number (default=4/3):
The ratio of the width to the height of the layout.
Returns
-------
pos : dict
A dictionary of positions keyed by node.
Examples
--------
>>> G = nx.bipartite.gnmk_random_graph(3, 5, 10, seed=123)
>>> top = nx.bipartite.sets(G)[0]
>>> pos = nx.bipartite_layout(G, top)
Notes
-----
This algorithm currently only works in two dimensions and does not
try to minimize edge crossings.
| def bipartite_layout(
G, nodes, align="vertical", scale=1, center=None, aspect_ratio=4 / 3
):
"""Position nodes in two straight lines.
Parameters
----------
G : NetworkX graph or list of nodes
A position will be assigned to every node in G.
nodes : list or container
Nodes in one node set of the bipartite graph.
This set will be placed on left or top.
align : string (default='vertical')
The alignment of nodes. Vertical or horizontal.
scale : number (default: 1)
Scale factor for positions.
center : array-like or None
Coordinate pair around which to center the layout.
aspect_ratio : number (default=4/3):
The ratio of the width to the height of the layout.
Returns
-------
pos : dict
A dictionary of positions keyed by node.
Examples
--------
>>> G = nx.bipartite.gnmk_random_graph(3, 5, 10, seed=123)
>>> top = nx.bipartite.sets(G)[0]
>>> pos = nx.bipartite_layout(G, top)
Notes
-----
This algorithm currently only works in two dimensions and does not
try to minimize edge crossings.
"""
import numpy as np
if align not in ("vertical", "horizontal"):
msg = "align must be either vertical or horizontal."
raise ValueError(msg)
G, center = _process_params(G, center=center, dim=2)
if len(G) == 0:
return {}
height = 1
width = aspect_ratio * height
offset = (width / 2, height / 2)
top = dict.fromkeys(nodes)
bottom = [v for v in G if v not in top]
nodes = list(top) + bottom
left_xs = np.repeat(0, len(top))
right_xs = np.repeat(width, len(bottom))
left_ys = np.linspace(0, height, len(top))
right_ys = np.linspace(0, height, len(bottom))
top_pos = np.column_stack([left_xs, left_ys]) - offset
bottom_pos = np.column_stack([right_xs, right_ys]) - offset
pos = np.concatenate([top_pos, bottom_pos])
pos = rescale_layout(pos, scale=scale) + center
if align == "horizontal":
pos = pos[:, ::-1] # swap x and y coords
pos = dict(zip(nodes, pos))
return pos
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|
30,443 | networkx.generators.small | bull_graph |
Returns the Bull Graph
The Bull Graph has 5 nodes and 5 edges. It is a planar undirected
graph in the form of a triangle with two disjoint pendant edges [1]_
The name comes from the triangle and pendant edges representing
respectively the body and legs of a bull.
Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Returns
-------
G : networkx Graph
A bull graph with 5 nodes
References
----------
.. [1] https://en.wikipedia.org/wiki/Bull_graph.
| def _raise_on_directed(func):
"""
A decorator which inspects the `create_using` argument and raises a
NetworkX exception when `create_using` is a DiGraph (class or instance) for
graph generators that do not support directed outputs.
"""
@wraps(func)
def wrapper(*args, **kwargs):
if kwargs.get("create_using") is not None:
G = nx.empty_graph(create_using=kwargs["create_using"])
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
return func(*args, **kwargs)
return wrapper
| (create_using=None, *, backend=None, **backend_kwargs) | [
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|
30,446 | networkx.generators.community | caveman_graph | Returns a caveman graph of `l` cliques of size `k`.
Parameters
----------
l : int
Number of cliques
k : int
Size of cliques
Returns
-------
G : NetworkX Graph
caveman graph
Notes
-----
This returns an undirected graph, it can be converted to a directed
graph using :func:`nx.to_directed`, or a multigraph using
``nx.MultiGraph(nx.caveman_graph(l, k))``. Only the undirected version is
described in [1]_ and it is unclear which of the directed
generalizations is most useful.
Examples
--------
>>> G = nx.caveman_graph(3, 3)
See also
--------
connected_caveman_graph
References
----------
.. [1] Watts, D. J. 'Networks, Dynamics, and the Small-World Phenomenon.'
Amer. J. Soc. 105, 493-527, 1999.
| def _generate_communities(degree_seq, community_sizes, mu, max_iters, seed):
"""Returns a list of sets, each of which represents a community.
``degree_seq`` is the degree sequence that must be met by the
graph.
``community_sizes`` is the community size distribution that must be
met by the generated list of sets.
``mu`` is a float in the interval [0, 1] indicating the fraction of
intra-community edges incident to each node.
``max_iters`` is the number of times to try to add a node to a
community. This must be greater than the length of
``degree_seq``, otherwise this function will always fail. If
the number of iterations exceeds this value,
:exc:`~networkx.exception.ExceededMaxIterations` is raised.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
The communities returned by this are sets of integers in the set {0,
..., *n* - 1}, where *n* is the length of ``degree_seq``.
"""
# This assumes the nodes in the graph will be natural numbers.
result = [set() for _ in community_sizes]
n = len(degree_seq)
free = list(range(n))
for i in range(max_iters):
v = free.pop()
c = seed.choice(range(len(community_sizes)))
# s = int(degree_seq[v] * (1 - mu) + 0.5)
s = round(degree_seq[v] * (1 - mu))
# If the community is large enough, add the node to the chosen
# community. Otherwise, return it to the list of unaffiliated
# nodes.
if s < community_sizes[c]:
result[c].add(v)
else:
free.append(v)
# If the community is too big, remove a node from it.
if len(result[c]) > community_sizes[c]:
free.append(result[c].pop())
if not free:
return result
msg = "Could not assign communities; try increasing min_community"
raise nx.ExceededMaxIterations(msg)
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|
30,448 | networkx.algorithms.distance_measures | center | Returns the center of the graph G.
The center is the set of nodes with eccentricity equal to radius.
Parameters
----------
G : NetworkX graph
A graph
e : eccentricity dictionary, optional
A precomputed dictionary of eccentricities.
weight : string, function, or None
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number.
If this is None, every edge has weight/distance/cost 1.
Weights stored as floating point values can lead to small round-off
errors in distances. Use integer weights to avoid this.
Weights should be positive, since they are distances.
Returns
-------
c : list
List of nodes in center
Examples
--------
>>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
>>> list(nx.center(G))
[1, 3, 4]
See Also
--------
barycenter
periphery
| def effective_graph_resistance(G, weight=None, invert_weight=True):
"""Returns the Effective graph resistance of G.
Also known as the Kirchhoff index.
The effective graph resistance is defined as the sum
of the resistance distance of every node pair in G [1]_.
If weight is not provided, then a weight of 1 is used for all edges.
The effective graph resistance of a disconnected graph is infinite.
Parameters
----------
G : NetworkX graph
A graph
weight : string or None, optional (default=None)
The edge data key used to compute the effective graph resistance.
If None, then each edge has weight 1.
invert_weight : boolean (default=True)
Proper calculation of resistance distance requires building the
Laplacian matrix with the reciprocal of the weight. Not required
if the weight is already inverted. Weight cannot be zero.
Returns
-------
RG : float
The effective graph resistance of `G`.
Raises
------
NetworkXNotImplemented
If `G` is a directed graph.
NetworkXError
If `G` does not contain any nodes.
Examples
--------
>>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
>>> round(nx.effective_graph_resistance(G), 10)
10.25
Notes
-----
The implementation is based on Theorem 2.2 in [2]_. Self-loops are ignored.
Multi-edges are contracted in one edge with weight equal to the harmonic sum of the weights.
References
----------
.. [1] Wolfram
"Kirchhoff Index."
https://mathworld.wolfram.com/KirchhoffIndex.html
.. [2] W. Ellens, F. M. Spieksma, P. Van Mieghem, A. Jamakovic, R. E. Kooij.
Effective graph resistance.
Lin. Alg. Appl. 435:2491-2506, 2011.
"""
import numpy as np
if len(G) == 0:
raise nx.NetworkXError("Graph G must contain at least one node.")
# Disconnected graphs have infinite Effective graph resistance
if not nx.is_connected(G):
return float("inf")
# Invert weights
G = G.copy()
if invert_weight and weight is not None:
if G.is_multigraph():
for u, v, k, d in G.edges(keys=True, data=True):
d[weight] = 1 / d[weight]
else:
for u, v, d in G.edges(data=True):
d[weight] = 1 / d[weight]
# Get Laplacian eigenvalues
mu = np.sort(nx.laplacian_spectrum(G, weight=weight))
# Compute Effective graph resistance based on spectrum of the Laplacian
# Self-loops are ignored
return float(np.sum(1 / mu[1:]) * G.number_of_nodes())
| (G, e=None, usebounds=False, weight=None, *, backend=None, **backend_kwargs) | [
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|
30,452 | networkx.algorithms.planarity | check_planarity | Check if a graph is planar and return a counterexample or an embedding.
A graph is planar iff it can be drawn in a plane without
any edge intersections.
Parameters
----------
G : NetworkX graph
counterexample : bool
A Kuratowski subgraph (to proof non planarity) is only returned if set
to true.
Returns
-------
(is_planar, certificate) : (bool, NetworkX graph) tuple
is_planar is true if the graph is planar.
If the graph is planar `certificate` is a PlanarEmbedding
otherwise it is a Kuratowski subgraph.
Examples
--------
>>> G = nx.Graph([(0, 1), (0, 2)])
>>> is_planar, P = nx.check_planarity(G)
>>> print(is_planar)
True
When `G` is planar, a `PlanarEmbedding` instance is returned:
>>> P.get_data()
{0: [1, 2], 1: [0], 2: [0]}
Notes
-----
A (combinatorial) embedding consists of cyclic orderings of the incident
edges at each vertex. Given such an embedding there are multiple approaches
discussed in literature to drawing the graph (subject to various
constraints, e.g. integer coordinates), see e.g. [2].
The planarity check algorithm and extraction of the combinatorial embedding
is based on the Left-Right Planarity Test [1].
A counterexample is only generated if the corresponding parameter is set,
because the complexity of the counterexample generation is higher.
See also
--------
is_planar :
Check for planarity without creating a `PlanarEmbedding` or counterexample.
References
----------
.. [1] Ulrik Brandes:
The Left-Right Planarity Test
2009
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.9208
.. [2] Takao Nishizeki, Md Saidur Rahman:
Planar graph drawing
Lecture Notes Series on Computing: Volume 12
2004
| def sign_recursive(self, e):
"""Recursive version of :meth:`sign`."""
if self.ref[e] is not None:
self.side[e] = self.side[e] * self.sign_recursive(self.ref[e])
self.ref[e] = None
return self.side[e]
| (G, counterexample=False, *, backend=None, **backend_kwargs) | [
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|
30,457 | networkx.algorithms.cycles | chordless_cycles | Find simple chordless cycles of a graph.
A `simple cycle` is a closed path where no node appears twice. In a simple
cycle, a `chord` is an additional edge between two nodes in the cycle. A
`chordless cycle` is a simple cycle without chords. Said differently, a
chordless cycle is a cycle C in a graph G where the number of edges in the
induced graph G[C] is equal to the length of `C`.
Note that some care must be taken in the case that G is not a simple graph
nor a simple digraph. Some authors limit the definition of chordless cycles
to have a prescribed minimum length; we do not.
1. We interpret self-loops to be chordless cycles, except in multigraphs
with multiple loops in parallel. Likewise, in a chordless cycle of
length greater than 1, there can be no nodes with self-loops.
2. We interpret directed two-cycles to be chordless cycles, except in
multi-digraphs when any edge in a two-cycle has a parallel copy.
3. We interpret parallel pairs of undirected edges as two-cycles, except
when a third (or more) parallel edge exists between the two nodes.
4. Generalizing the above, edges with parallel clones may not occur in
chordless cycles.
In a directed graph, two chordless cycles are distinct if they are not
cyclic permutations of each other. In an undirected graph, two chordless
cycles are distinct if they are not cyclic permutations of each other nor of
the other's reversal.
Optionally, the cycles are bounded in length.
We use an algorithm strongly inspired by that of Dias et al [1]_. It has
been modified in the following ways:
1. Recursion is avoided, per Python's limitations
2. The labeling function is not necessary, because the starting paths
are chosen (and deleted from the host graph) to prevent multiple
occurrences of the same path
3. The search is optionally bounded at a specified length
4. Support for directed graphs is provided by extending cycles along
forward edges, and blocking nodes along forward and reverse edges
5. Support for multigraphs is provided by omitting digons from the set
of forward edges
Parameters
----------
G : NetworkX DiGraph
A directed graph
length_bound : int or None, optional (default=None)
If length_bound is an int, generate all simple cycles of G with length at
most length_bound. Otherwise, generate all simple cycles of G.
Yields
------
list of nodes
Each cycle is represented by a list of nodes along the cycle.
Examples
--------
>>> sorted(list(nx.chordless_cycles(nx.complete_graph(4))))
[[1, 0, 2], [1, 0, 3], [2, 0, 3], [2, 1, 3]]
Notes
-----
When length_bound is None, and the graph is simple, the time complexity is
$O((n+e)(c+1))$ for $n$ nodes, $e$ edges and $c$ chordless cycles.
Raises
------
ValueError
when length_bound < 0.
References
----------
.. [1] Efficient enumeration of chordless cycles
E. Dias and D. Castonguay and H. Longo and W.A.R. Jradi
https://arxiv.org/abs/1309.1051
See Also
--------
simple_cycles
| def recursive_simple_cycles(G):
"""Find simple cycles (elementary circuits) of a directed graph.
A `simple cycle`, or `elementary circuit`, is a closed path where
no node appears twice. Two elementary circuits are distinct if they
are not cyclic permutations of each other.
This version uses a recursive algorithm to build a list of cycles.
You should probably use the iterator version called simple_cycles().
Warning: This recursive version uses lots of RAM!
It appears in NetworkX for pedagogical value.
Parameters
----------
G : NetworkX DiGraph
A directed graph
Returns
-------
A list of cycles, where each cycle is represented by a list of nodes
along the cycle.
Example:
>>> edges = [(0, 0), (0, 1), (0, 2), (1, 2), (2, 0), (2, 1), (2, 2)]
>>> G = nx.DiGraph(edges)
>>> nx.recursive_simple_cycles(G)
[[0], [2], [0, 1, 2], [0, 2], [1, 2]]
Notes
-----
The implementation follows pp. 79-80 in [1]_.
The time complexity is $O((n+e)(c+1))$ for $n$ nodes, $e$ edges and $c$
elementary circuits.
References
----------
.. [1] Finding all the elementary circuits of a directed graph.
D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975.
https://doi.org/10.1137/0204007
See Also
--------
simple_cycles, cycle_basis
"""
# Jon Olav Vik, 2010-08-09
def _unblock(thisnode):
"""Recursively unblock and remove nodes from B[thisnode]."""
if blocked[thisnode]:
blocked[thisnode] = False
while B[thisnode]:
_unblock(B[thisnode].pop())
def circuit(thisnode, startnode, component):
closed = False # set to True if elementary path is closed
path.append(thisnode)
blocked[thisnode] = True
for nextnode in component[thisnode]: # direct successors of thisnode
if nextnode == startnode:
result.append(path[:])
closed = True
elif not blocked[nextnode]:
if circuit(nextnode, startnode, component):
closed = True
if closed:
_unblock(thisnode)
else:
for nextnode in component[thisnode]:
if thisnode not in B[nextnode]: # TODO: use set for speedup?
B[nextnode].append(thisnode)
path.pop() # remove thisnode from path
return closed
path = [] # stack of nodes in current path
blocked = defaultdict(bool) # vertex: blocked from search?
B = defaultdict(list) # graph portions that yield no elementary circuit
result = [] # list to accumulate the circuits found
# Johnson's algorithm exclude self cycle edges like (v, v)
# To be backward compatible, we record those cycles in advance
# and then remove from subG
for v in G:
if G.has_edge(v, v):
result.append([v])
G.remove_edge(v, v)
# Johnson's algorithm requires some ordering of the nodes.
# They might not be sortable so we assign an arbitrary ordering.
ordering = dict(zip(G, range(len(G))))
for s in ordering:
# Build the subgraph induced by s and following nodes in the ordering
subgraph = G.subgraph(node for node in G if ordering[node] >= ordering[s])
# Find the strongly connected component in the subgraph
# that contains the least node according to the ordering
strongcomp = nx.strongly_connected_components(subgraph)
mincomp = min(strongcomp, key=lambda ns: min(ordering[n] for n in ns))
component = G.subgraph(mincomp)
if len(component) > 1:
# smallest node in the component according to the ordering
startnode = min(component, key=ordering.__getitem__)
for node in component:
blocked[node] = False
B[node][:] = []
dummy = circuit(startnode, startnode, component)
return result
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|
30,459 | networkx.generators.small | chvatal_graph |
Returns the Chvátal Graph
The Chvátal Graph is an undirected graph with 12 nodes and 24 edges [1]_.
It has 370 distinct (directed) Hamiltonian cycles, giving a unique generalized
LCF notation of order 4, two of order 6 , and 43 of order 1 [2]_.
Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Returns
-------
G : networkx Graph
The Chvátal graph with 12 nodes and 24 edges
References
----------
.. [1] https://en.wikipedia.org/wiki/Chv%C3%A1tal_graph
.. [2] https://mathworld.wolfram.com/ChvatalGraph.html
| def _raise_on_directed(func):
"""
A decorator which inspects the `create_using` argument and raises a
NetworkX exception when `create_using` is a DiGraph (class or instance) for
graph generators that do not support directed outputs.
"""
@wraps(func)
def wrapper(*args, **kwargs):
if kwargs.get("create_using") is not None:
G = nx.empty_graph(create_using=kwargs["create_using"])
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
return func(*args, **kwargs)
return wrapper
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|
30,460 | networkx.generators.classic | circulant_graph | Returns the circulant graph $Ci_n(x_1, x_2, ..., x_m)$ with $n$ nodes.
The circulant graph $Ci_n(x_1, ..., x_m)$ consists of $n$ nodes $0, ..., n-1$
such that node $i$ is connected to nodes $(i + x) \mod n$ and $(i - x) \mod n$
for all $x$ in $x_1, ..., x_m$. Thus $Ci_n(1)$ is a cycle graph.
.. plot::
>>> nx.draw(nx.circulant_graph(10, [1]))
Parameters
----------
n : integer
The number of nodes in the graph.
offsets : list of integers
A list of node offsets, $x_1$ up to $x_m$, as described above.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Returns
-------
NetworkX Graph of type create_using
Examples
--------
Many well-known graph families are subfamilies of the circulant graphs;
for example, to create the cycle graph on n points, we connect every
node to nodes on either side (with offset plus or minus one). For n = 10,
>>> G = nx.circulant_graph(10, [1])
>>> edges = [
... (0, 9),
... (0, 1),
... (1, 2),
... (2, 3),
... (3, 4),
... (4, 5),
... (5, 6),
... (6, 7),
... (7, 8),
... (8, 9),
... ]
>>> sorted(edges) == sorted(G.edges())
True
Similarly, we can create the complete graph
on 5 points with the set of offsets [1, 2]:
>>> G = nx.circulant_graph(5, [1, 2])
>>> edges = [
... (0, 1),
... (0, 2),
... (0, 3),
... (0, 4),
... (1, 2),
... (1, 3),
... (1, 4),
... (2, 3),
... (2, 4),
... (3, 4),
... ]
>>> sorted(edges) == sorted(G.edges())
True
| def star_graph(n, create_using=None):
"""Return the star graph
The star graph consists of one center node connected to n outer nodes.
.. plot::
>>> nx.draw(nx.star_graph(6))
Parameters
----------
n : int or iterable
If an integer, node labels are 0 to n with center 0.
If an iterable of nodes, the center is the first.
Warning: n is not checked for duplicates and if present the
resulting graph may not be as desired. Make sure you have no duplicates.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Notes
-----
The graph has n+1 nodes for integer n.
So star_graph(3) is the same as star_graph(range(4)).
"""
n, nodes = n
if isinstance(n, numbers.Integral):
nodes.append(int(n)) # there should be n+1 nodes
G = empty_graph(nodes, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
if len(nodes) > 1:
hub, *spokes = nodes
G.add_edges_from((hub, node) for node in spokes)
return G
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|
30,461 | networkx.generators.classic | circular_ladder_graph | Returns the circular ladder graph $CL_n$ of length n.
$CL_n$ consists of two concentric n-cycles in which
each of the n pairs of concentric nodes are joined by an edge.
Node labels are the integers 0 to n-1
.. plot::
>>> nx.draw(nx.circular_ladder_graph(5))
| def star_graph(n, create_using=None):
"""Return the star graph
The star graph consists of one center node connected to n outer nodes.
.. plot::
>>> nx.draw(nx.star_graph(6))
Parameters
----------
n : int or iterable
If an integer, node labels are 0 to n with center 0.
If an iterable of nodes, the center is the first.
Warning: n is not checked for duplicates and if present the
resulting graph may not be as desired. Make sure you have no duplicates.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Notes
-----
The graph has n+1 nodes for integer n.
So star_graph(3) is the same as star_graph(range(4)).
"""
n, nodes = n
if isinstance(n, numbers.Integral):
nodes.append(int(n)) # there should be n+1 nodes
G = empty_graph(nodes, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
if len(nodes) > 1:
hub, *spokes = nodes
G.add_edges_from((hub, node) for node in spokes)
return G
| (n, create_using=None, *, backend=None, **backend_kwargs) | [
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|
30,462 | networkx.drawing.layout | circular_layout | Position nodes on a circle.
Parameters
----------
G : NetworkX graph or list of nodes
A position will be assigned to every node in G.
scale : number (default: 1)
Scale factor for positions.
center : array-like or None
Coordinate pair around which to center the layout.
dim : int
Dimension of layout.
If dim>2, the remaining dimensions are set to zero
in the returned positions.
If dim<2, a ValueError is raised.
Returns
-------
pos : dict
A dictionary of positions keyed by node
Raises
------
ValueError
If dim < 2
Examples
--------
>>> G = nx.path_graph(4)
>>> pos = nx.circular_layout(G)
Notes
-----
This algorithm currently only works in two dimensions and does not
try to minimize edge crossings.
| def circular_layout(G, scale=1, center=None, dim=2):
# dim=2 only
"""Position nodes on a circle.
Parameters
----------
G : NetworkX graph or list of nodes
A position will be assigned to every node in G.
scale : number (default: 1)
Scale factor for positions.
center : array-like or None
Coordinate pair around which to center the layout.
dim : int
Dimension of layout.
If dim>2, the remaining dimensions are set to zero
in the returned positions.
If dim<2, a ValueError is raised.
Returns
-------
pos : dict
A dictionary of positions keyed by node
Raises
------
ValueError
If dim < 2
Examples
--------
>>> G = nx.path_graph(4)
>>> pos = nx.circular_layout(G)
Notes
-----
This algorithm currently only works in two dimensions and does not
try to minimize edge crossings.
"""
import numpy as np
if dim < 2:
raise ValueError("cannot handle dimensions < 2")
G, center = _process_params(G, center, dim)
paddims = max(0, (dim - 2))
if len(G) == 0:
pos = {}
elif len(G) == 1:
pos = {nx.utils.arbitrary_element(G): center}
else:
# Discard the extra angle since it matches 0 radians.
theta = np.linspace(0, 1, len(G) + 1)[:-1] * 2 * np.pi
theta = theta.astype(np.float32)
pos = np.column_stack(
[np.cos(theta), np.sin(theta), np.zeros((len(G), paddims))]
)
pos = rescale_layout(pos, scale=scale) + center
pos = dict(zip(G, pos))
return pos
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|
30,474 | networkx.algorithms.planar_drawing | combinatorial_embedding_to_pos | Assigns every node a (x, y) position based on the given embedding
The algorithm iteratively inserts nodes of the input graph in a certain
order and rearranges previously inserted nodes so that the planar drawing
stays valid. This is done efficiently by only maintaining relative
positions during the node placements and calculating the absolute positions
at the end. For more information see [1]_.
Parameters
----------
embedding : nx.PlanarEmbedding
This defines the order of the edges
fully_triangulate : bool
If set to True the algorithm adds edges to a copy of the input
embedding and makes it chordal.
Returns
-------
pos : dict
Maps each node to a tuple that defines the (x, y) position
References
----------
.. [1] M. Chrobak and T.H. Payne:
A Linear-time Algorithm for Drawing a Planar Graph on a Grid 1989
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.6677
| def combinatorial_embedding_to_pos(embedding, fully_triangulate=False):
"""Assigns every node a (x, y) position based on the given embedding
The algorithm iteratively inserts nodes of the input graph in a certain
order and rearranges previously inserted nodes so that the planar drawing
stays valid. This is done efficiently by only maintaining relative
positions during the node placements and calculating the absolute positions
at the end. For more information see [1]_.
Parameters
----------
embedding : nx.PlanarEmbedding
This defines the order of the edges
fully_triangulate : bool
If set to True the algorithm adds edges to a copy of the input
embedding and makes it chordal.
Returns
-------
pos : dict
Maps each node to a tuple that defines the (x, y) position
References
----------
.. [1] M. Chrobak and T.H. Payne:
A Linear-time Algorithm for Drawing a Planar Graph on a Grid 1989
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.6677
"""
if len(embedding.nodes()) < 4:
# Position the node in any triangle
default_positions = [(0, 0), (2, 0), (1, 1)]
pos = {}
for i, v in enumerate(embedding.nodes()):
pos[v] = default_positions[i]
return pos
embedding, outer_face = triangulate_embedding(embedding, fully_triangulate)
# The following dicts map a node to another node
# If a node is not in the key set it means that the node is not yet in G_k
# If a node maps to None then the corresponding subtree does not exist
left_t_child = {}
right_t_child = {}
# The following dicts map a node to an integer
delta_x = {}
y_coordinate = {}
node_list = get_canonical_ordering(embedding, outer_face)
# 1. Phase: Compute relative positions
# Initialization
v1, v2, v3 = node_list[0][0], node_list[1][0], node_list[2][0]
delta_x[v1] = 0
y_coordinate[v1] = 0
right_t_child[v1] = v3
left_t_child[v1] = None
delta_x[v2] = 1
y_coordinate[v2] = 0
right_t_child[v2] = None
left_t_child[v2] = None
delta_x[v3] = 1
y_coordinate[v3] = 1
right_t_child[v3] = v2
left_t_child[v3] = None
for k in range(3, len(node_list)):
vk, contour_nbrs = node_list[k]
wp = contour_nbrs[0]
wp1 = contour_nbrs[1]
wq = contour_nbrs[-1]
wq1 = contour_nbrs[-2]
adds_mult_tri = len(contour_nbrs) > 2
# Stretch gaps:
delta_x[wp1] += 1
delta_x[wq] += 1
delta_x_wp_wq = sum(delta_x[x] for x in contour_nbrs[1:])
# Adjust offsets
delta_x[vk] = (-y_coordinate[wp] + delta_x_wp_wq + y_coordinate[wq]) // 2
y_coordinate[vk] = (y_coordinate[wp] + delta_x_wp_wq + y_coordinate[wq]) // 2
delta_x[wq] = delta_x_wp_wq - delta_x[vk]
if adds_mult_tri:
delta_x[wp1] -= delta_x[vk]
# Install v_k:
right_t_child[wp] = vk
right_t_child[vk] = wq
if adds_mult_tri:
left_t_child[vk] = wp1
right_t_child[wq1] = None
else:
left_t_child[vk] = None
# 2. Phase: Set absolute positions
pos = {}
pos[v1] = (0, y_coordinate[v1])
remaining_nodes = [v1]
while remaining_nodes:
parent_node = remaining_nodes.pop()
# Calculate position for left child
set_position(
parent_node, left_t_child, remaining_nodes, delta_x, y_coordinate, pos
)
# Calculate position for right child
set_position(
parent_node, right_t_child, remaining_nodes, delta_x, y_coordinate, pos
)
return pos
| (embedding, fully_triangulate=False) | [
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|
30,476 | networkx.classes.function | common_neighbors | Returns the common neighbors of two nodes in a graph.
Parameters
----------
G : graph
A NetworkX undirected graph.
u, v : nodes
Nodes in the graph.
Returns
-------
cnbors : set
Set of common neighbors of u and v in the graph.
Raises
------
NetworkXError
If u or v is not a node in the graph.
Examples
--------
>>> G = nx.complete_graph(5)
>>> sorted(nx.common_neighbors(G, 0, 1))
[2, 3, 4]
| def set_edge_attributes(G, values, name=None):
"""Sets edge attributes from a given value or dictionary of values.
.. Warning:: The call order of arguments `values` and `name`
switched between v1.x & v2.x.
Parameters
----------
G : NetworkX Graph
values : scalar value, dict-like
What the edge attribute should be set to. If `values` is
not a dictionary, then it is treated as a single attribute value
that is then applied to every edge in `G`. This means that if
you provide a mutable object, like a list, updates to that object
will be reflected in the edge attribute for each edge. The attribute
name will be `name`.
If `values` is a dict or a dict of dict, it should be keyed
by edge tuple to either an attribute value or a dict of attribute
key/value pairs used to update the edge's attributes.
For multigraphs, the edge tuples must be of the form ``(u, v, key)``,
where `u` and `v` are nodes and `key` is the edge key.
For non-multigraphs, the keys must be tuples of the form ``(u, v)``.
name : string (optional, default=None)
Name of the edge attribute to set if values is a scalar.
Examples
--------
After computing some property of the edges of a graph, you may want
to assign a edge attribute to store the value of that property for
each edge::
>>> G = nx.path_graph(3)
>>> bb = nx.edge_betweenness_centrality(G, normalized=False)
>>> nx.set_edge_attributes(G, bb, "betweenness")
>>> G.edges[1, 2]["betweenness"]
2.0
If you provide a list as the second argument, updates to the list
will be reflected in the edge attribute for each edge::
>>> labels = []
>>> nx.set_edge_attributes(G, labels, "labels")
>>> labels.append("foo")
>>> G.edges[0, 1]["labels"]
['foo']
>>> G.edges[1, 2]["labels"]
['foo']
If you provide a dictionary of dictionaries as the second argument,
the entire dictionary will be used to update edge attributes::
>>> G = nx.path_graph(3)
>>> attrs = {(0, 1): {"attr1": 20, "attr2": "nothing"}, (1, 2): {"attr2": 3}}
>>> nx.set_edge_attributes(G, attrs)
>>> G[0][1]["attr1"]
20
>>> G[0][1]["attr2"]
'nothing'
>>> G[1][2]["attr2"]
3
The attributes of one Graph can be used to set those of another.
>>> H = nx.path_graph(3)
>>> nx.set_edge_attributes(H, G.edges)
Note that if the dict contains edges that are not in `G`, they are
silently ignored::
>>> G = nx.Graph([(0, 1)])
>>> nx.set_edge_attributes(G, {(1, 2): {"weight": 2.0}})
>>> (1, 2) in G.edges()
False
For multigraphs, the `values` dict is expected to be keyed by 3-tuples
including the edge key::
>>> MG = nx.MultiGraph()
>>> edges = [(0, 1), (0, 1)]
>>> MG.add_edges_from(edges) # Returns list of edge keys
[0, 1]
>>> attributes = {(0, 1, 0): {"cost": 21}, (0, 1, 1): {"cost": 7}}
>>> nx.set_edge_attributes(MG, attributes)
>>> MG[0][1][0]["cost"]
21
>>> MG[0][1][1]["cost"]
7
If MultiGraph attributes are desired for a Graph, you must convert the 3-tuple
multiedge to a 2-tuple edge and the last multiedge's attribute value will
overwrite the previous values. Continuing from the previous case we get::
>>> H = nx.path_graph([0, 1, 2])
>>> nx.set_edge_attributes(H, {(u, v): ed for u, v, ed in MG.edges.data()})
>>> nx.get_edge_attributes(H, "cost")
{(0, 1): 7}
"""
if name is not None:
# `values` does not contain attribute names
try:
# if `values` is a dict using `.items()` => {edge: value}
if G.is_multigraph():
for (u, v, key), value in values.items():
try:
G._adj[u][v][key][name] = value
except KeyError:
pass
else:
for (u, v), value in values.items():
try:
G._adj[u][v][name] = value
except KeyError:
pass
except AttributeError:
# treat `values` as a constant
for u, v, data in G.edges(data=True):
data[name] = values
else:
# `values` consists of doct-of-dict {edge: {attr: value}} shape
if G.is_multigraph():
for (u, v, key), d in values.items():
try:
G._adj[u][v][key].update(d)
except KeyError:
pass
else:
for (u, v), d in values.items():
try:
G._adj[u][v].update(d)
except KeyError:
pass
nx._clear_cache(G)
| (G, u, v) | [
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|
30,484 | networkx.generators.classic | complete_graph | Return the complete graph `K_n` with n nodes.
A complete graph on `n` nodes means that all pairs
of distinct nodes have an edge connecting them.
.. plot::
>>> nx.draw(nx.complete_graph(5))
Parameters
----------
n : int or iterable container of nodes
If n is an integer, nodes are from range(n).
If n is a container of nodes, those nodes appear in the graph.
Warning: n is not checked for duplicates and if present the
resulting graph may not be as desired. Make sure you have no duplicates.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Examples
--------
>>> G = nx.complete_graph(9)
>>> len(G)
9
>>> G.size()
36
>>> G = nx.complete_graph(range(11, 14))
>>> list(G.nodes())
[11, 12, 13]
>>> G = nx.complete_graph(4, nx.DiGraph())
>>> G.is_directed()
True
| def star_graph(n, create_using=None):
"""Return the star graph
The star graph consists of one center node connected to n outer nodes.
.. plot::
>>> nx.draw(nx.star_graph(6))
Parameters
----------
n : int or iterable
If an integer, node labels are 0 to n with center 0.
If an iterable of nodes, the center is the first.
Warning: n is not checked for duplicates and if present the
resulting graph may not be as desired. Make sure you have no duplicates.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Notes
-----
The graph has n+1 nodes for integer n.
So star_graph(3) is the same as star_graph(range(4)).
"""
n, nodes = n
if isinstance(n, numbers.Integral):
nodes.append(int(n)) # there should be n+1 nodes
G = empty_graph(nodes, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
if len(nodes) > 1:
hub, *spokes = nodes
G.add_edges_from((hub, node) for node in spokes)
return G
| (n, create_using=None, *, backend=None, **backend_kwargs) | [
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|
30,485 | networkx.generators.classic | complete_multipartite_graph | Returns the complete multipartite graph with the specified subset sizes.
.. plot::
>>> nx.draw(nx.complete_multipartite_graph(1, 2, 3))
Parameters
----------
subset_sizes : tuple of integers or tuple of node iterables
The arguments can either all be integer number of nodes or they
can all be iterables of nodes. If integers, they represent the
number of nodes in each subset of the multipartite graph.
If iterables, each is used to create the nodes for that subset.
The length of subset_sizes is the number of subsets.
Returns
-------
G : NetworkX Graph
Returns the complete multipartite graph with the specified subsets.
For each node, the node attribute 'subset' is an integer
indicating which subset contains the node.
Examples
--------
Creating a complete tripartite graph, with subsets of one, two, and three
nodes, respectively.
>>> G = nx.complete_multipartite_graph(1, 2, 3)
>>> [G.nodes[u]["subset"] for u in G]
[0, 1, 1, 2, 2, 2]
>>> list(G.edges(0))
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)]
>>> list(G.edges(2))
[(2, 0), (2, 3), (2, 4), (2, 5)]
>>> list(G.edges(4))
[(4, 0), (4, 1), (4, 2)]
>>> G = nx.complete_multipartite_graph("a", "bc", "def")
>>> [G.nodes[u]["subset"] for u in sorted(G)]
[0, 1, 1, 2, 2, 2]
Notes
-----
This function generalizes several other graph builder functions.
- If no subset sizes are given, this returns the null graph.
- If a single subset size `n` is given, this returns the empty graph on
`n` nodes.
- If two subset sizes `m` and `n` are given, this returns the complete
bipartite graph on `m + n` nodes.
- If subset sizes `1` and `n` are given, this returns the star graph on
`n + 1` nodes.
See also
--------
complete_bipartite_graph
| def star_graph(n, create_using=None):
"""Return the star graph
The star graph consists of one center node connected to n outer nodes.
.. plot::
>>> nx.draw(nx.star_graph(6))
Parameters
----------
n : int or iterable
If an integer, node labels are 0 to n with center 0.
If an iterable of nodes, the center is the first.
Warning: n is not checked for duplicates and if present the
resulting graph may not be as desired. Make sure you have no duplicates.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Notes
-----
The graph has n+1 nodes for integer n.
So star_graph(3) is the same as star_graph(range(4)).
"""
n, nodes = n
if isinstance(n, numbers.Integral):
nodes.append(int(n)) # there should be n+1 nodes
G = empty_graph(nodes, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
if len(nodes) > 1:
hub, *spokes = nodes
G.add_edges_from((hub, node) for node in spokes)
return G
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|
30,490 | networkx.algorithms.dag | compute_v_structures | Iterate through the graph to compute all v-structures.
V-structures are triples in the directed graph where
two parent nodes point to the same child and the two parent nodes
are not adjacent.
Parameters
----------
G : graph
A networkx DiGraph.
Returns
-------
vstructs : iterator of tuples
The v structures within the graph. Each v structure is a 3-tuple with the
parent, collider, and other parent.
Examples
--------
>>> G = nx.DiGraph()
>>> G.add_edges_from([(1, 2), (0, 5), (3, 1), (2, 4), (3, 1), (4, 5), (1, 5)])
>>> sorted(nx.compute_v_structures(G))
[(0, 5, 1), (0, 5, 4), (1, 5, 4)]
Notes
-----
`Wikipedia: Collider in causal graphs <https://en.wikipedia.org/wiki/Collider_(statistics)>`_
| def transitive_closure_dag(G, topo_order=None):
"""Returns the transitive closure of a directed acyclic graph.
This function is faster than the function `transitive_closure`, but fails
if the graph has a cycle.
The transitive closure of G = (V,E) is a graph G+ = (V,E+) such that
for all v, w in V there is an edge (v, w) in E+ if and only if there
is a non-null path from v to w in G.
Parameters
----------
G : NetworkX DiGraph
A directed acyclic graph (DAG)
topo_order: list or tuple, optional
A topological order for G (if None, the function will compute one)
Returns
-------
NetworkX DiGraph
The transitive closure of `G`
Raises
------
NetworkXNotImplemented
If `G` is not directed
NetworkXUnfeasible
If `G` has a cycle
Examples
--------
>>> DG = nx.DiGraph([(1, 2), (2, 3)])
>>> TC = nx.transitive_closure_dag(DG)
>>> TC.edges()
OutEdgeView([(1, 2), (1, 3), (2, 3)])
Notes
-----
This algorithm is probably simple enough to be well-known but I didn't find
a mention in the literature.
"""
if topo_order is None:
topo_order = list(topological_sort(G))
TC = G.copy()
# idea: traverse vertices following a reverse topological order, connecting
# each vertex to its descendants at distance 2 as we go
for v in reversed(topo_order):
TC.add_edges_from((v, u) for u in nx.descendants_at_distance(TC, v, 2))
return TC
| (G, *, backend=None, **backend_kwargs) | [
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|
30,493 | networkx.generators.degree_seq | configuration_model | Returns a random graph with the given degree sequence.
The configuration model generates a random pseudograph (graph with
parallel edges and self loops) by randomly assigning edges to
match the given degree sequence.
Parameters
----------
deg_sequence : list of nonnegative integers
Each list entry corresponds to the degree of a node.
create_using : NetworkX graph constructor, optional (default MultiGraph)
Graph type to create. If graph instance, then cleared before populated.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
Returns
-------
G : MultiGraph
A graph with the specified degree sequence.
Nodes are labeled starting at 0 with an index
corresponding to the position in deg_sequence.
Raises
------
NetworkXError
If the degree sequence does not have an even sum.
See Also
--------
is_graphical
Notes
-----
As described by Newman [1]_.
A non-graphical degree sequence (not realizable by some simple
graph) is allowed since this function returns graphs with self
loops and parallel edges. An exception is raised if the degree
sequence does not have an even sum.
This configuration model construction process can lead to
duplicate edges and loops. You can remove the self-loops and
parallel edges (see below) which will likely result in a graph
that doesn't have the exact degree sequence specified.
The density of self-loops and parallel edges tends to decrease as
the number of nodes increases. However, typically the number of
self-loops will approach a Poisson distribution with a nonzero mean,
and similarly for the number of parallel edges. Consider a node
with *k* stubs. The probability of being joined to another stub of
the same node is basically (*k* - *1*) / *N*, where *k* is the
degree and *N* is the number of nodes. So the probability of a
self-loop scales like *c* / *N* for some constant *c*. As *N* grows,
this means we expect *c* self-loops. Similarly for parallel edges.
References
----------
.. [1] M.E.J. Newman, "The structure and function of complex networks",
SIAM REVIEW 45-2, pp 167-256, 2003.
Examples
--------
You can create a degree sequence following a particular distribution
by using the one of the distribution functions in
:mod:`~networkx.utils.random_sequence` (or one of your own). For
example, to create an undirected multigraph on one hundred nodes
with degree sequence chosen from the power law distribution:
>>> sequence = nx.random_powerlaw_tree_sequence(100, tries=5000)
>>> G = nx.configuration_model(sequence)
>>> len(G)
100
>>> actual_degrees = [d for v, d in G.degree()]
>>> actual_degrees == sequence
True
The returned graph is a multigraph, which may have parallel
edges. To remove any parallel edges from the returned graph:
>>> G = nx.Graph(G)
Similarly, to remove self-loops:
>>> G.remove_edges_from(nx.selfloop_edges(G))
| def generate(self):
# remaining_degree is mapping from int->remaining degree
self.remaining_degree = dict(enumerate(self.degree))
# add all nodes to make sure we get isolated nodes
self.graph = nx.Graph()
self.graph.add_nodes_from(self.remaining_degree)
# remove zero degree nodes
for n, d in list(self.remaining_degree.items()):
if d == 0:
del self.remaining_degree[n]
if len(self.remaining_degree) > 0:
# build graph in three phases according to how many unmatched edges
self.phase1()
self.phase2()
self.phase3()
return self.graph
| (deg_sequence, create_using=None, seed=None, *, backend=None, **backend_kwargs) | [
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|
30,495 | networkx.generators.community | connected_caveman_graph | Returns a connected caveman graph of `l` cliques of size `k`.
The connected caveman graph is formed by creating `n` cliques of size
`k`, then a single edge in each clique is rewired to a node in an
adjacent clique.
Parameters
----------
l : int
number of cliques
k : int
size of cliques (k at least 2 or NetworkXError is raised)
Returns
-------
G : NetworkX Graph
connected caveman graph
Raises
------
NetworkXError
If the size of cliques `k` is smaller than 2.
Notes
-----
This returns an undirected graph, it can be converted to a directed
graph using :func:`nx.to_directed`, or a multigraph using
``nx.MultiGraph(nx.caveman_graph(l, k))``. Only the undirected version is
described in [1]_ and it is unclear which of the directed
generalizations is most useful.
Examples
--------
>>> G = nx.connected_caveman_graph(3, 3)
References
----------
.. [1] Watts, D. J. 'Networks, Dynamics, and the Small-World Phenomenon.'
Amer. J. Soc. 105, 493-527, 1999.
| def _generate_communities(degree_seq, community_sizes, mu, max_iters, seed):
"""Returns a list of sets, each of which represents a community.
``degree_seq`` is the degree sequence that must be met by the
graph.
``community_sizes`` is the community size distribution that must be
met by the generated list of sets.
``mu`` is a float in the interval [0, 1] indicating the fraction of
intra-community edges incident to each node.
``max_iters`` is the number of times to try to add a node to a
community. This must be greater than the length of
``degree_seq``, otherwise this function will always fail. If
the number of iterations exceeds this value,
:exc:`~networkx.exception.ExceededMaxIterations` is raised.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
The communities returned by this are sets of integers in the set {0,
..., *n* - 1}, where *n* is the length of ``degree_seq``.
"""
# This assumes the nodes in the graph will be natural numbers.
result = [set() for _ in community_sizes]
n = len(degree_seq)
free = list(range(n))
for i in range(max_iters):
v = free.pop()
c = seed.choice(range(len(community_sizes)))
# s = int(degree_seq[v] * (1 - mu) + 0.5)
s = round(degree_seq[v] * (1 - mu))
# If the community is large enough, add the node to the chosen
# community. Otherwise, return it to the list of unaffiliated
# nodes.
if s < community_sizes[c]:
result[c].add(v)
else:
free.append(v)
# If the community is too big, remove a node from it.
if len(result[c]) > community_sizes[c]:
free.append(result[c].pop())
if not free:
return result
msg = "Could not assign communities; try increasing min_community"
raise nx.ExceededMaxIterations(msg)
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|
30,498 | networkx.generators.random_graphs | connected_watts_strogatz_graph | Returns a connected Watts–Strogatz small-world graph.
Attempts to generate a connected graph by repeated generation of
Watts–Strogatz small-world graphs. An exception is raised if the maximum
number of tries is exceeded.
Parameters
----------
n : int
The number of nodes
k : int
Each node is joined with its `k` nearest neighbors in a ring
topology.
p : float
The probability of rewiring each edge
tries : int
Number of attempts to generate a connected graph.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
Notes
-----
First create a ring over $n$ nodes [1]_. Then each node in the ring is joined
to its $k$ nearest neighbors (or $k - 1$ neighbors if $k$ is odd).
Then shortcuts are created by replacing some edges as follows: for each
edge $(u, v)$ in the underlying "$n$-ring with $k$ nearest neighbors"
with probability $p$ replace it with a new edge $(u, w)$ with uniformly
random choice of existing node $w$.
The entire process is repeated until a connected graph results.
See Also
--------
newman_watts_strogatz_graph
watts_strogatz_graph
References
----------
.. [1] Duncan J. Watts and Steven H. Strogatz,
Collective dynamics of small-world networks,
Nature, 393, pp. 440--442, 1998.
| def dual_barabasi_albert_graph(n, m1, m2, p, seed=None, initial_graph=None):
"""Returns a random graph using dual Barabási–Albert preferential attachment
A graph of $n$ nodes is grown by attaching new nodes each with either $m_1$
edges (with probability $p$) or $m_2$ edges (with probability $1-p$) that
are preferentially attached to existing nodes with high degree.
Parameters
----------
n : int
Number of nodes
m1 : int
Number of edges to link each new node to existing nodes with probability $p$
m2 : int
Number of edges to link each new node to existing nodes with probability $1-p$
p : float
The probability of attaching $m_1$ edges (as opposed to $m_2$ edges)
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
initial_graph : Graph or None (default)
Initial network for Barabási–Albert algorithm.
A copy of `initial_graph` is used.
It should be connected for most use cases.
If None, starts from an star graph on max(m1, m2) + 1 nodes.
Returns
-------
G : Graph
Raises
------
NetworkXError
If `m1` and `m2` do not satisfy ``1 <= m1,m2 < n``, or
`p` does not satisfy ``0 <= p <= 1``, or
the initial graph number of nodes m0 does not satisfy m1, m2 <= m0 <= n.
References
----------
.. [1] N. Moshiri "The dual-Barabasi-Albert model", arXiv:1810.10538.
"""
if m1 < 1 or m1 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m1 >= 1 and m1 < n, m1 = {m1}, n = {n}"
)
if m2 < 1 or m2 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m2 >= 1 and m2 < n, m2 = {m2}, n = {n}"
)
if p < 0 or p > 1:
raise nx.NetworkXError(
f"Dual Barabási–Albert network must have 0 <= p <= 1, p = {p}"
)
# For simplicity, if p == 0 or 1, just return BA
if p == 1:
return barabasi_albert_graph(n, m1, seed)
elif p == 0:
return barabasi_albert_graph(n, m2, seed)
if initial_graph is None:
# Default initial graph : empty graph on max(m1, m2) nodes
G = star_graph(max(m1, m2))
else:
if len(initial_graph) < max(m1, m2) or len(initial_graph) > n:
raise nx.NetworkXError(
f"Barabási–Albert initial graph must have between "
f"max(m1, m2) = {max(m1, m2)} and n = {n} nodes"
)
G = initial_graph.copy()
# Target nodes for new edges
targets = list(G)
# List of existing nodes, with nodes repeated once for each adjacent edge
repeated_nodes = [n for n, d in G.degree() for _ in range(d)]
# Start adding the remaining nodes.
source = len(G)
while source < n:
# Pick which m to use (m1 or m2)
if seed.random() < p:
m = m1
else:
m = m2
# Now choose m unique nodes from the existing nodes
# Pick uniformly from repeated_nodes (preferential attachment)
targets = _random_subset(repeated_nodes, m, seed)
# Add edges to m nodes from the source.
G.add_edges_from(zip([source] * m, targets))
# Add one node to the list for each new edge just created.
repeated_nodes.extend(targets)
# And the new node "source" has m edges to add to the list.
repeated_nodes.extend([source] * m)
source += 1
return G
| (n, k, p, tries=100, seed=None, *, backend=None, **backend_kwargs) | [
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|
30,514 | networkx.classes.function | create_empty_copy | Returns a copy of the graph G with all of the edges removed.
Parameters
----------
G : graph
A NetworkX graph
with_data : bool (default=True)
Propagate Graph and Nodes data to the new graph.
See Also
--------
empty_graph
| def create_empty_copy(G, with_data=True):
"""Returns a copy of the graph G with all of the edges removed.
Parameters
----------
G : graph
A NetworkX graph
with_data : bool (default=True)
Propagate Graph and Nodes data to the new graph.
See Also
--------
empty_graph
"""
H = G.__class__()
H.add_nodes_from(G.nodes(data=with_data))
if with_data:
H.graph.update(G.graph)
return H
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|
30,515 | networkx.generators.small | cubical_graph |
Returns the 3-regular Platonic Cubical Graph
The skeleton of the cube (the nodes and edges) form a graph, with 8
nodes, and 12 edges. It is a special case of the hypercube graph.
It is one of 5 Platonic graphs, each a skeleton of its
Platonic solid [1]_.
Such graphs arise in parallel processing in computers.
Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Returns
-------
G : networkx Graph
A cubical graph with 8 nodes and 12 edges
References
----------
.. [1] https://en.wikipedia.org/wiki/Cube#Cubical_graph
| def _raise_on_directed(func):
"""
A decorator which inspects the `create_using` argument and raises a
NetworkX exception when `create_using` is a DiGraph (class or instance) for
graph generators that do not support directed outputs.
"""
@wraps(func)
def wrapper(*args, **kwargs):
if kwargs.get("create_using") is not None:
G = nx.empty_graph(create_using=kwargs["create_using"])
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
return func(*args, **kwargs)
return wrapper
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|
30,524 | networkx.algorithms.cycles | cycle_basis | Returns a list of cycles which form a basis for cycles of G.
A basis for cycles of a network is a minimal collection of
cycles such that any cycle in the network can be written
as a sum of cycles in the basis. Here summation of cycles
is defined as "exclusive or" of the edges. Cycle bases are
useful, e.g. when deriving equations for electric circuits
using Kirchhoff's Laws.
Parameters
----------
G : NetworkX Graph
root : node, optional
Specify starting node for basis.
Returns
-------
A list of cycle lists. Each cycle list is a list of nodes
which forms a cycle (loop) in G.
Examples
--------
>>> G = nx.Graph()
>>> nx.add_cycle(G, [0, 1, 2, 3])
>>> nx.add_cycle(G, [0, 3, 4, 5])
>>> nx.cycle_basis(G, 0)
[[3, 4, 5, 0], [1, 2, 3, 0]]
Notes
-----
This is adapted from algorithm CACM 491 [1]_.
References
----------
.. [1] Paton, K. An algorithm for finding a fundamental set of
cycles of a graph. Comm. ACM 12, 9 (Sept 1969), 514-518.
See Also
--------
simple_cycles
minimum_cycle_basis
| def recursive_simple_cycles(G):
"""Find simple cycles (elementary circuits) of a directed graph.
A `simple cycle`, or `elementary circuit`, is a closed path where
no node appears twice. Two elementary circuits are distinct if they
are not cyclic permutations of each other.
This version uses a recursive algorithm to build a list of cycles.
You should probably use the iterator version called simple_cycles().
Warning: This recursive version uses lots of RAM!
It appears in NetworkX for pedagogical value.
Parameters
----------
G : NetworkX DiGraph
A directed graph
Returns
-------
A list of cycles, where each cycle is represented by a list of nodes
along the cycle.
Example:
>>> edges = [(0, 0), (0, 1), (0, 2), (1, 2), (2, 0), (2, 1), (2, 2)]
>>> G = nx.DiGraph(edges)
>>> nx.recursive_simple_cycles(G)
[[0], [2], [0, 1, 2], [0, 2], [1, 2]]
Notes
-----
The implementation follows pp. 79-80 in [1]_.
The time complexity is $O((n+e)(c+1))$ for $n$ nodes, $e$ edges and $c$
elementary circuits.
References
----------
.. [1] Finding all the elementary circuits of a directed graph.
D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975.
https://doi.org/10.1137/0204007
See Also
--------
simple_cycles, cycle_basis
"""
# Jon Olav Vik, 2010-08-09
def _unblock(thisnode):
"""Recursively unblock and remove nodes from B[thisnode]."""
if blocked[thisnode]:
blocked[thisnode] = False
while B[thisnode]:
_unblock(B[thisnode].pop())
def circuit(thisnode, startnode, component):
closed = False # set to True if elementary path is closed
path.append(thisnode)
blocked[thisnode] = True
for nextnode in component[thisnode]: # direct successors of thisnode
if nextnode == startnode:
result.append(path[:])
closed = True
elif not blocked[nextnode]:
if circuit(nextnode, startnode, component):
closed = True
if closed:
_unblock(thisnode)
else:
for nextnode in component[thisnode]:
if thisnode not in B[nextnode]: # TODO: use set for speedup?
B[nextnode].append(thisnode)
path.pop() # remove thisnode from path
return closed
path = [] # stack of nodes in current path
blocked = defaultdict(bool) # vertex: blocked from search?
B = defaultdict(list) # graph portions that yield no elementary circuit
result = [] # list to accumulate the circuits found
# Johnson's algorithm exclude self cycle edges like (v, v)
# To be backward compatible, we record those cycles in advance
# and then remove from subG
for v in G:
if G.has_edge(v, v):
result.append([v])
G.remove_edge(v, v)
# Johnson's algorithm requires some ordering of the nodes.
# They might not be sortable so we assign an arbitrary ordering.
ordering = dict(zip(G, range(len(G))))
for s in ordering:
# Build the subgraph induced by s and following nodes in the ordering
subgraph = G.subgraph(node for node in G if ordering[node] >= ordering[s])
# Find the strongly connected component in the subgraph
# that contains the least node according to the ordering
strongcomp = nx.strongly_connected_components(subgraph)
mincomp = min(strongcomp, key=lambda ns: min(ordering[n] for n in ns))
component = G.subgraph(mincomp)
if len(component) > 1:
# smallest node in the component according to the ordering
startnode = min(component, key=ordering.__getitem__)
for node in component:
blocked[node] = False
B[node][:] = []
dummy = circuit(startnode, startnode, component)
return result
| (G, root=None, *, backend=None, **backend_kwargs) | [
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|
30,525 | networkx.generators.classic | cycle_graph | Returns the cycle graph $C_n$ of cyclically connected nodes.
$C_n$ is a path with its two end-nodes connected.
.. plot::
>>> nx.draw(nx.cycle_graph(5))
Parameters
----------
n : int or iterable container of nodes
If n is an integer, nodes are from `range(n)`.
If n is a container of nodes, those nodes appear in the graph.
Warning: n is not checked for duplicates and if present the
resulting graph may not be as desired. Make sure you have no duplicates.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Notes
-----
If create_using is directed, the direction is in increasing order.
| def star_graph(n, create_using=None):
"""Return the star graph
The star graph consists of one center node connected to n outer nodes.
.. plot::
>>> nx.draw(nx.star_graph(6))
Parameters
----------
n : int or iterable
If an integer, node labels are 0 to n with center 0.
If an iterable of nodes, the center is the first.
Warning: n is not checked for duplicates and if present the
resulting graph may not be as desired. Make sure you have no duplicates.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Notes
-----
The graph has n+1 nodes for integer n.
So star_graph(3) is the same as star_graph(range(4)).
"""
n, nodes = n
if isinstance(n, numbers.Integral):
nodes.append(int(n)) # there should be n+1 nodes
G = empty_graph(nodes, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
if len(nodes) > 1:
hub, *spokes = nodes
G.add_edges_from((hub, node) for node in spokes)
return G
| (n, create_using=None, *, backend=None, **backend_kwargs) | [
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|
30,528 | networkx.readwrite.json_graph.cytoscape | cytoscape_data | Returns data in Cytoscape JSON format (cyjs).
Parameters
----------
G : NetworkX Graph
The graph to convert to cytoscape format
name : string
A string which is mapped to the 'name' node element in cyjs format.
Must not have the same value as `ident`.
ident : string
A string which is mapped to the 'id' node element in cyjs format.
Must not have the same value as `name`.
Returns
-------
data: dict
A dictionary with cyjs formatted data.
Raises
------
NetworkXError
If the values for `name` and `ident` are identical.
See Also
--------
cytoscape_graph: convert a dictionary in cyjs format to a graph
References
----------
.. [1] Cytoscape user's manual:
http://manual.cytoscape.org/en/stable/index.html
Examples
--------
>>> G = nx.path_graph(2)
>>> nx.cytoscape_data(G) # doctest: +SKIP
{'data': [],
'directed': False,
'multigraph': False,
'elements': {'nodes': [{'data': {'id': '0', 'value': 0, 'name': '0'}},
{'data': {'id': '1', 'value': 1, 'name': '1'}}],
'edges': [{'data': {'source': 0, 'target': 1}}]}}
| def cytoscape_data(G, name="name", ident="id"):
"""Returns data in Cytoscape JSON format (cyjs).
Parameters
----------
G : NetworkX Graph
The graph to convert to cytoscape format
name : string
A string which is mapped to the 'name' node element in cyjs format.
Must not have the same value as `ident`.
ident : string
A string which is mapped to the 'id' node element in cyjs format.
Must not have the same value as `name`.
Returns
-------
data: dict
A dictionary with cyjs formatted data.
Raises
------
NetworkXError
If the values for `name` and `ident` are identical.
See Also
--------
cytoscape_graph: convert a dictionary in cyjs format to a graph
References
----------
.. [1] Cytoscape user's manual:
http://manual.cytoscape.org/en/stable/index.html
Examples
--------
>>> G = nx.path_graph(2)
>>> nx.cytoscape_data(G) # doctest: +SKIP
{'data': [],
'directed': False,
'multigraph': False,
'elements': {'nodes': [{'data': {'id': '0', 'value': 0, 'name': '0'}},
{'data': {'id': '1', 'value': 1, 'name': '1'}}],
'edges': [{'data': {'source': 0, 'target': 1}}]}}
"""
if name == ident:
raise nx.NetworkXError("name and ident must be different.")
jsondata = {"data": list(G.graph.items())}
jsondata["directed"] = G.is_directed()
jsondata["multigraph"] = G.is_multigraph()
jsondata["elements"] = {"nodes": [], "edges": []}
nodes = jsondata["elements"]["nodes"]
edges = jsondata["elements"]["edges"]
for i, j in G.nodes.items():
n = {"data": j.copy()}
n["data"]["id"] = j.get(ident) or str(i)
n["data"]["value"] = i
n["data"]["name"] = j.get(name) or str(i)
nodes.append(n)
if G.is_multigraph():
for e in G.edges(keys=True):
n = {"data": G.adj[e[0]][e[1]][e[2]].copy()}
n["data"]["source"] = e[0]
n["data"]["target"] = e[1]
n["data"]["key"] = e[2]
edges.append(n)
else:
for e in G.edges():
n = {"data": G.adj[e[0]][e[1]].copy()}
n["data"]["source"] = e[0]
n["data"]["target"] = e[1]
edges.append(n)
return jsondata
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|
30,530 | networkx.algorithms.d_separation | d_separated | Return whether nodes sets ``x`` and ``y`` are d-separated by ``z``.
.. deprecated:: 3.3
This function is deprecated and will be removed in NetworkX v3.5.
Please use `is_d_separator(G, x, y, z)`.
| def d_separated(G, x, y, z):
"""Return whether nodes sets ``x`` and ``y`` are d-separated by ``z``.
.. deprecated:: 3.3
This function is deprecated and will be removed in NetworkX v3.5.
Please use `is_d_separator(G, x, y, z)`.
"""
import warnings
warnings.warn(
"d_separated is deprecated and will be removed in NetworkX v3.5."
"Please use `is_d_separator(G, x, y, z)`.",
category=DeprecationWarning,
stacklevel=2,
)
return nx.is_d_separator(G, x, y, z)
| (G, x, y, z) | [
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|
30,533 | networkx.algorithms.dag | dag_longest_path | Returns the longest path in a directed acyclic graph (DAG).
If `G` has edges with `weight` attribute the edge data are used as
weight values.
Parameters
----------
G : NetworkX DiGraph
A directed acyclic graph (DAG)
weight : str, optional
Edge data key to use for weight
default_weight : int, optional
The weight of edges that do not have a weight attribute
topo_order: list or tuple, optional
A topological order for `G` (if None, the function will compute one)
Returns
-------
list
Longest path
Raises
------
NetworkXNotImplemented
If `G` is not directed
Examples
--------
>>> DG = nx.DiGraph([(0, 1, {"cost": 1}), (1, 2, {"cost": 1}), (0, 2, {"cost": 42})])
>>> list(nx.all_simple_paths(DG, 0, 2))
[[0, 1, 2], [0, 2]]
>>> nx.dag_longest_path(DG)
[0, 1, 2]
>>> nx.dag_longest_path(DG, weight="cost")
[0, 2]
In the case where multiple valid topological orderings exist, `topo_order`
can be used to specify a specific ordering:
>>> DG = nx.DiGraph([(0, 1), (0, 2)])
>>> sorted(nx.all_topological_sorts(DG)) # Valid topological orderings
[[0, 1, 2], [0, 2, 1]]
>>> nx.dag_longest_path(DG, topo_order=[0, 1, 2])
[0, 1]
>>> nx.dag_longest_path(DG, topo_order=[0, 2, 1])
[0, 2]
See also
--------
dag_longest_path_length
| def transitive_closure_dag(G, topo_order=None):
"""Returns the transitive closure of a directed acyclic graph.
This function is faster than the function `transitive_closure`, but fails
if the graph has a cycle.
The transitive closure of G = (V,E) is a graph G+ = (V,E+) such that
for all v, w in V there is an edge (v, w) in E+ if and only if there
is a non-null path from v to w in G.
Parameters
----------
G : NetworkX DiGraph
A directed acyclic graph (DAG)
topo_order: list or tuple, optional
A topological order for G (if None, the function will compute one)
Returns
-------
NetworkX DiGraph
The transitive closure of `G`
Raises
------
NetworkXNotImplemented
If `G` is not directed
NetworkXUnfeasible
If `G` has a cycle
Examples
--------
>>> DG = nx.DiGraph([(1, 2), (2, 3)])
>>> TC = nx.transitive_closure_dag(DG)
>>> TC.edges()
OutEdgeView([(1, 2), (1, 3), (2, 3)])
Notes
-----
This algorithm is probably simple enough to be well-known but I didn't find
a mention in the literature.
"""
if topo_order is None:
topo_order = list(topological_sort(G))
TC = G.copy()
# idea: traverse vertices following a reverse topological order, connecting
# each vertex to its descendants at distance 2 as we go
for v in reversed(topo_order):
TC.add_edges_from((v, u) for u in nx.descendants_at_distance(TC, v, 2))
return TC
| (G, weight='weight', default_weight=1, topo_order=None, *, backend=None, **backend_kwargs) | [
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|
30,534 | networkx.algorithms.dag | dag_longest_path_length | Returns the longest path length in a DAG
Parameters
----------
G : NetworkX DiGraph
A directed acyclic graph (DAG)
weight : string, optional
Edge data key to use for weight
default_weight : int, optional
The weight of edges that do not have a weight attribute
Returns
-------
int
Longest path length
Raises
------
NetworkXNotImplemented
If `G` is not directed
Examples
--------
>>> DG = nx.DiGraph([(0, 1, {"cost": 1}), (1, 2, {"cost": 1}), (0, 2, {"cost": 42})])
>>> list(nx.all_simple_paths(DG, 0, 2))
[[0, 1, 2], [0, 2]]
>>> nx.dag_longest_path_length(DG)
2
>>> nx.dag_longest_path_length(DG, weight="cost")
42
See also
--------
dag_longest_path
| def transitive_closure_dag(G, topo_order=None):
"""Returns the transitive closure of a directed acyclic graph.
This function is faster than the function `transitive_closure`, but fails
if the graph has a cycle.
The transitive closure of G = (V,E) is a graph G+ = (V,E+) such that
for all v, w in V there is an edge (v, w) in E+ if and only if there
is a non-null path from v to w in G.
Parameters
----------
G : NetworkX DiGraph
A directed acyclic graph (DAG)
topo_order: list or tuple, optional
A topological order for G (if None, the function will compute one)
Returns
-------
NetworkX DiGraph
The transitive closure of `G`
Raises
------
NetworkXNotImplemented
If `G` is not directed
NetworkXUnfeasible
If `G` has a cycle
Examples
--------
>>> DG = nx.DiGraph([(1, 2), (2, 3)])
>>> TC = nx.transitive_closure_dag(DG)
>>> TC.edges()
OutEdgeView([(1, 2), (1, 3), (2, 3)])
Notes
-----
This algorithm is probably simple enough to be well-known but I didn't find
a mention in the literature.
"""
if topo_order is None:
topo_order = list(topological_sort(G))
TC = G.copy()
# idea: traverse vertices following a reverse topological order, connecting
# each vertex to its descendants at distance 2 as we go
for v in reversed(topo_order):
TC.add_edges_from((v, u) for u in nx.descendants_at_distance(TC, v, 2))
return TC
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|
30,535 | networkx.algorithms.dag | dag_to_branching | Returns a branching representing all (overlapping) paths from
root nodes to leaf nodes in the given directed acyclic graph.
As described in :mod:`networkx.algorithms.tree.recognition`, a
*branching* is a directed forest in which each node has at most one
parent. In other words, a branching is a disjoint union of
*arborescences*. For this function, each node of in-degree zero in
`G` becomes a root of one of the arborescences, and there will be
one leaf node for each distinct path from that root to a leaf node
in `G`.
Each node `v` in `G` with *k* parents becomes *k* distinct nodes in
the returned branching, one for each parent, and the sub-DAG rooted
at `v` is duplicated for each copy. The algorithm then recurses on
the children of each copy of `v`.
Parameters
----------
G : NetworkX graph
A directed acyclic graph.
Returns
-------
DiGraph
The branching in which there is a bijection between root-to-leaf
paths in `G` (in which multiple paths may share the same leaf)
and root-to-leaf paths in the branching (in which there is a
unique path from a root to a leaf).
Each node has an attribute 'source' whose value is the original
node to which this node corresponds. No other graph, node, or
edge attributes are copied into this new graph.
Raises
------
NetworkXNotImplemented
If `G` is not directed, or if `G` is a multigraph.
HasACycle
If `G` is not acyclic.
Examples
--------
To examine which nodes in the returned branching were produced by
which original node in the directed acyclic graph, we can collect
the mapping from source node to new nodes into a dictionary. For
example, consider the directed diamond graph::
>>> from collections import defaultdict
>>> from operator import itemgetter
>>>
>>> G = nx.DiGraph(nx.utils.pairwise("abd"))
>>> G.add_edges_from(nx.utils.pairwise("acd"))
>>> B = nx.dag_to_branching(G)
>>>
>>> sources = defaultdict(set)
>>> for v, source in B.nodes(data="source"):
... sources[source].add(v)
>>> len(sources["a"])
1
>>> len(sources["d"])
2
To copy node attributes from the original graph to the new graph,
you can use a dictionary like the one constructed in the above
example::
>>> for source, nodes in sources.items():
... for v in nodes:
... B.nodes[v].update(G.nodes[source])
Notes
-----
This function is not idempotent in the sense that the node labels in
the returned branching may be uniquely generated each time the
function is invoked. In fact, the node labels may not be integers;
in order to relabel the nodes to be more readable, you can use the
:func:`networkx.convert_node_labels_to_integers` function.
The current implementation of this function uses
:func:`networkx.prefix_tree`, so it is subject to the limitations of
that function.
| def transitive_closure_dag(G, topo_order=None):
"""Returns the transitive closure of a directed acyclic graph.
This function is faster than the function `transitive_closure`, but fails
if the graph has a cycle.
The transitive closure of G = (V,E) is a graph G+ = (V,E+) such that
for all v, w in V there is an edge (v, w) in E+ if and only if there
is a non-null path from v to w in G.
Parameters
----------
G : NetworkX DiGraph
A directed acyclic graph (DAG)
topo_order: list or tuple, optional
A topological order for G (if None, the function will compute one)
Returns
-------
NetworkX DiGraph
The transitive closure of `G`
Raises
------
NetworkXNotImplemented
If `G` is not directed
NetworkXUnfeasible
If `G` has a cycle
Examples
--------
>>> DG = nx.DiGraph([(1, 2), (2, 3)])
>>> TC = nx.transitive_closure_dag(DG)
>>> TC.edges()
OutEdgeView([(1, 2), (1, 3), (2, 3)])
Notes
-----
This algorithm is probably simple enough to be well-known but I didn't find
a mention in the literature.
"""
if topo_order is None:
topo_order = list(topological_sort(G))
TC = G.copy()
# idea: traverse vertices following a reverse topological order, connecting
# each vertex to its descendants at distance 2 as we go
for v in reversed(topo_order):
TC.add_edges_from((v, u) for u in nx.descendants_at_distance(TC, v, 2))
return TC
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|
30,538 | networkx.classes.function | degree | Returns a degree view of single node or of nbunch of nodes.
If nbunch is omitted, then return degrees of *all* nodes.
This function wraps the :func:`G.degree <networkx.Graph.degree>` property.
| def degree(G, nbunch=None, weight=None):
"""Returns a degree view of single node or of nbunch of nodes.
If nbunch is omitted, then return degrees of *all* nodes.
This function wraps the :func:`G.degree <networkx.Graph.degree>` property.
"""
return G.degree(nbunch, weight)
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|
30,542 | networkx.classes.function | degree_histogram | Returns a list of the frequency of each degree value.
Parameters
----------
G : Networkx graph
A graph
Returns
-------
hist : list
A list of frequencies of degrees.
The degree values are the index in the list.
Notes
-----
Note: the bins are width one, hence len(list) can be large
(Order(number_of_edges))
| def degree_histogram(G):
"""Returns a list of the frequency of each degree value.
Parameters
----------
G : Networkx graph
A graph
Returns
-------
hist : list
A list of frequencies of degrees.
The degree values are the index in the list.
Notes
-----
Note: the bins are width one, hence len(list) can be large
(Order(number_of_edges))
"""
counts = Counter(d for n, d in G.degree())
return [counts.get(i, 0) for i in range(max(counts) + 1 if counts else 0)]
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|
30,547 | networkx.generators.degree_seq | degree_sequence_tree | Make a tree for the given degree sequence.
A tree has #nodes-#edges=1 so
the degree sequence must have
len(deg_sequence)-sum(deg_sequence)/2=1
| def generate(self):
# remaining_degree is mapping from int->remaining degree
self.remaining_degree = dict(enumerate(self.degree))
# add all nodes to make sure we get isolated nodes
self.graph = nx.Graph()
self.graph.add_nodes_from(self.remaining_degree)
# remove zero degree nodes
for n, d in list(self.remaining_degree.items()):
if d == 0:
del self.remaining_degree[n]
if len(self.remaining_degree) > 0:
# build graph in three phases according to how many unmatched edges
self.phase1()
self.phase2()
self.phase3()
return self.graph
| (deg_sequence, create_using=None, *, backend=None, **backend_kwargs) | [
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|
30,549 | networkx.generators.random_graphs | dense_gnm_random_graph | Returns a $G_{n,m}$ random graph.
In the $G_{n,m}$ model, a graph is chosen uniformly at random from the set
of all graphs with $n$ nodes and $m$ edges.
This algorithm should be faster than :func:`gnm_random_graph` for dense
graphs.
Parameters
----------
n : int
The number of nodes.
m : int
The number of edges.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
See Also
--------
gnm_random_graph
Notes
-----
Algorithm by Keith M. Briggs Mar 31, 2006.
Inspired by Knuth's Algorithm S (Selection sampling technique),
in section 3.4.2 of [1]_.
References
----------
.. [1] Donald E. Knuth, The Art of Computer Programming,
Volume 2/Seminumerical algorithms, Third Edition, Addison-Wesley, 1997.
| def dual_barabasi_albert_graph(n, m1, m2, p, seed=None, initial_graph=None):
"""Returns a random graph using dual Barabási–Albert preferential attachment
A graph of $n$ nodes is grown by attaching new nodes each with either $m_1$
edges (with probability $p$) or $m_2$ edges (with probability $1-p$) that
are preferentially attached to existing nodes with high degree.
Parameters
----------
n : int
Number of nodes
m1 : int
Number of edges to link each new node to existing nodes with probability $p$
m2 : int
Number of edges to link each new node to existing nodes with probability $1-p$
p : float
The probability of attaching $m_1$ edges (as opposed to $m_2$ edges)
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
initial_graph : Graph or None (default)
Initial network for Barabási–Albert algorithm.
A copy of `initial_graph` is used.
It should be connected for most use cases.
If None, starts from an star graph on max(m1, m2) + 1 nodes.
Returns
-------
G : Graph
Raises
------
NetworkXError
If `m1` and `m2` do not satisfy ``1 <= m1,m2 < n``, or
`p` does not satisfy ``0 <= p <= 1``, or
the initial graph number of nodes m0 does not satisfy m1, m2 <= m0 <= n.
References
----------
.. [1] N. Moshiri "The dual-Barabasi-Albert model", arXiv:1810.10538.
"""
if m1 < 1 or m1 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m1 >= 1 and m1 < n, m1 = {m1}, n = {n}"
)
if m2 < 1 or m2 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m2 >= 1 and m2 < n, m2 = {m2}, n = {n}"
)
if p < 0 or p > 1:
raise nx.NetworkXError(
f"Dual Barabási–Albert network must have 0 <= p <= 1, p = {p}"
)
# For simplicity, if p == 0 or 1, just return BA
if p == 1:
return barabasi_albert_graph(n, m1, seed)
elif p == 0:
return barabasi_albert_graph(n, m2, seed)
if initial_graph is None:
# Default initial graph : empty graph on max(m1, m2) nodes
G = star_graph(max(m1, m2))
else:
if len(initial_graph) < max(m1, m2) or len(initial_graph) > n:
raise nx.NetworkXError(
f"Barabási–Albert initial graph must have between "
f"max(m1, m2) = {max(m1, m2)} and n = {n} nodes"
)
G = initial_graph.copy()
# Target nodes for new edges
targets = list(G)
# List of existing nodes, with nodes repeated once for each adjacent edge
repeated_nodes = [n for n, d in G.degree() for _ in range(d)]
# Start adding the remaining nodes.
source = len(G)
while source < n:
# Pick which m to use (m1 or m2)
if seed.random() < p:
m = m1
else:
m = m2
# Now choose m unique nodes from the existing nodes
# Pick uniformly from repeated_nodes (preferential attachment)
targets = _random_subset(repeated_nodes, m, seed)
# Add edges to m nodes from the source.
G.add_edges_from(zip([source] * m, targets))
# Add one node to the list for each new edge just created.
repeated_nodes.extend(targets)
# And the new node "source" has m edges to add to the list.
repeated_nodes.extend([source] * m)
source += 1
return G
| (n, m, seed=None, *, backend=None, **backend_kwargs) | [
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|
30,550 | networkx.classes.function | density | Returns the density of a graph.
The density for undirected graphs is
.. math::
d = \frac{2m}{n(n-1)},
and for directed graphs is
.. math::
d = \frac{m}{n(n-1)},
where `n` is the number of nodes and `m` is the number of edges in `G`.
Notes
-----
The density is 0 for a graph without edges and 1 for a complete graph.
The density of multigraphs can be higher than 1.
Self loops are counted in the total number of edges so graphs with self
loops can have density higher than 1.
| def density(G):
r"""Returns the density of a graph.
The density for undirected graphs is
.. math::
d = \frac{2m}{n(n-1)},
and for directed graphs is
.. math::
d = \frac{m}{n(n-1)},
where `n` is the number of nodes and `m` is the number of edges in `G`.
Notes
-----
The density is 0 for a graph without edges and 1 for a complete graph.
The density of multigraphs can be higher than 1.
Self loops are counted in the total number of edges so graphs with self
loops can have density higher than 1.
"""
n = number_of_nodes(G)
m = number_of_edges(G)
if m == 0 or n <= 1:
return 0
d = m / (n * (n - 1))
if not G.is_directed():
d *= 2
return d
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|
30,552 | networkx.generators.small | desargues_graph |
Returns the Desargues Graph
The Desargues Graph is a non-planar, distance-transitive cubic graph
with 20 nodes and 30 edges [1]_.
It is a symmetric graph. It can be represented in LCF notation
as [5,-5,9,-9]^5 [2]_.
Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Returns
-------
G : networkx Graph
Desargues Graph with 20 nodes and 30 edges
References
----------
.. [1] https://en.wikipedia.org/wiki/Desargues_graph
.. [2] https://mathworld.wolfram.com/DesarguesGraph.html
| def sedgewick_maze_graph(create_using=None):
"""
Return a small maze with a cycle.
This is the maze used in Sedgewick, 3rd Edition, Part 5, Graph
Algorithms, Chapter 18, e.g. Figure 18.2 and following [1]_.
Nodes are numbered 0,..,7
Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Returns
-------
G : networkx Graph
Small maze with a cycle
References
----------
.. [1] Figure 18.2, Chapter 18, Graph Algorithms (3rd Ed), Sedgewick
"""
G = empty_graph(0, create_using)
G.add_nodes_from(range(8))
G.add_edges_from([[0, 2], [0, 7], [0, 5]])
G.add_edges_from([[1, 7], [2, 6]])
G.add_edges_from([[3, 4], [3, 5]])
G.add_edges_from([[4, 5], [4, 7], [4, 6]])
G.name = "Sedgewick Maze"
return G
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|
30,553 | networkx.algorithms.dag | descendants | Returns all nodes reachable from `source` in `G`.
Parameters
----------
G : NetworkX Graph
source : node in `G`
Returns
-------
set()
The descendants of `source` in `G`
Raises
------
NetworkXError
If node `source` is not in `G`.
Examples
--------
>>> DG = nx.path_graph(5, create_using=nx.DiGraph)
>>> sorted(nx.descendants(DG, 2))
[3, 4]
The `source` node is not a descendant of itself, but can be included manually:
>>> sorted(nx.descendants(DG, 2) | {2})
[2, 3, 4]
See also
--------
ancestors
| def transitive_closure_dag(G, topo_order=None):
"""Returns the transitive closure of a directed acyclic graph.
This function is faster than the function `transitive_closure`, but fails
if the graph has a cycle.
The transitive closure of G = (V,E) is a graph G+ = (V,E+) such that
for all v, w in V there is an edge (v, w) in E+ if and only if there
is a non-null path from v to w in G.
Parameters
----------
G : NetworkX DiGraph
A directed acyclic graph (DAG)
topo_order: list or tuple, optional
A topological order for G (if None, the function will compute one)
Returns
-------
NetworkX DiGraph
The transitive closure of `G`
Raises
------
NetworkXNotImplemented
If `G` is not directed
NetworkXUnfeasible
If `G` has a cycle
Examples
--------
>>> DG = nx.DiGraph([(1, 2), (2, 3)])
>>> TC = nx.transitive_closure_dag(DG)
>>> TC.edges()
OutEdgeView([(1, 2), (1, 3), (2, 3)])
Notes
-----
This algorithm is probably simple enough to be well-known but I didn't find
a mention in the literature.
"""
if topo_order is None:
topo_order = list(topological_sort(G))
TC = G.copy()
# idea: traverse vertices following a reverse topological order, connecting
# each vertex to its descendants at distance 2 as we go
for v in reversed(topo_order):
TC.add_edges_from((v, u) for u in nx.descendants_at_distance(TC, v, 2))
return TC
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|
30,562 | networkx.algorithms.distance_measures | diameter | Returns the diameter of the graph G.
The diameter is the maximum eccentricity.
Parameters
----------
G : NetworkX graph
A graph
e : eccentricity dictionary, optional
A precomputed dictionary of eccentricities.
weight : string, function, or None
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number.
If this is None, every edge has weight/distance/cost 1.
Weights stored as floating point values can lead to small round-off
errors in distances. Use integer weights to avoid this.
Weights should be positive, since they are distances.
Returns
-------
d : integer
Diameter of graph
Examples
--------
>>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
>>> nx.diameter(G)
3
See Also
--------
eccentricity
| def effective_graph_resistance(G, weight=None, invert_weight=True):
"""Returns the Effective graph resistance of G.
Also known as the Kirchhoff index.
The effective graph resistance is defined as the sum
of the resistance distance of every node pair in G [1]_.
If weight is not provided, then a weight of 1 is used for all edges.
The effective graph resistance of a disconnected graph is infinite.
Parameters
----------
G : NetworkX graph
A graph
weight : string or None, optional (default=None)
The edge data key used to compute the effective graph resistance.
If None, then each edge has weight 1.
invert_weight : boolean (default=True)
Proper calculation of resistance distance requires building the
Laplacian matrix with the reciprocal of the weight. Not required
if the weight is already inverted. Weight cannot be zero.
Returns
-------
RG : float
The effective graph resistance of `G`.
Raises
------
NetworkXNotImplemented
If `G` is a directed graph.
NetworkXError
If `G` does not contain any nodes.
Examples
--------
>>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
>>> round(nx.effective_graph_resistance(G), 10)
10.25
Notes
-----
The implementation is based on Theorem 2.2 in [2]_. Self-loops are ignored.
Multi-edges are contracted in one edge with weight equal to the harmonic sum of the weights.
References
----------
.. [1] Wolfram
"Kirchhoff Index."
https://mathworld.wolfram.com/KirchhoffIndex.html
.. [2] W. Ellens, F. M. Spieksma, P. Van Mieghem, A. Jamakovic, R. E. Kooij.
Effective graph resistance.
Lin. Alg. Appl. 435:2491-2506, 2011.
"""
import numpy as np
if len(G) == 0:
raise nx.NetworkXError("Graph G must contain at least one node.")
# Disconnected graphs have infinite Effective graph resistance
if not nx.is_connected(G):
return float("inf")
# Invert weights
G = G.copy()
if invert_weight and weight is not None:
if G.is_multigraph():
for u, v, k, d in G.edges(keys=True, data=True):
d[weight] = 1 / d[weight]
else:
for u, v, d in G.edges(data=True):
d[weight] = 1 / d[weight]
# Get Laplacian eigenvalues
mu = np.sort(nx.laplacian_spectrum(G, weight=weight))
# Compute Effective graph resistance based on spectrum of the Laplacian
# Self-loops are ignored
return float(np.sum(1 / mu[1:]) * G.number_of_nodes())
| (G, e=None, usebounds=False, weight=None, *, backend=None, **backend_kwargs) | [
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|
30,563 | networkx.generators.small | diamond_graph |
Returns the Diamond graph
The Diamond Graph is planar undirected graph with 4 nodes and 5 edges.
It is also sometimes known as the double triangle graph or kite graph [1]_.
Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Returns
-------
G : networkx Graph
Diamond Graph with 4 nodes and 5 edges
References
----------
.. [1] https://mathworld.wolfram.com/DiamondGraph.html
| def _raise_on_directed(func):
"""
A decorator which inspects the `create_using` argument and raises a
NetworkX exception when `create_using` is a DiGraph (class or instance) for
graph generators that do not support directed outputs.
"""
@wraps(func)
def wrapper(*args, **kwargs):
if kwargs.get("create_using") is not None:
G = nx.empty_graph(create_using=kwargs["create_using"])
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
return func(*args, **kwargs)
return wrapper
| (create_using=None, *, backend=None, **backend_kwargs) | [
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|
30,566 | networkx.algorithms.shortest_paths.weighted | dijkstra_path | Returns the shortest weighted path from source to target in G.
Uses Dijkstra's Method to compute the shortest weighted path
between two nodes in a graph.
Parameters
----------
G : NetworkX graph
source : node
Starting node
target : node
Ending node
weight : string or function
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number or None to indicate a hidden edge.
Returns
-------
path : list
List of nodes in a shortest path.
Raises
------
NodeNotFound
If `source` is not in `G`.
NetworkXNoPath
If no path exists between source and target.
Examples
--------
>>> G = nx.path_graph(5)
>>> print(nx.dijkstra_path(G, 0, 4))
[0, 1, 2, 3, 4]
Find edges of shortest path in Multigraph
>>> G = nx.MultiDiGraph()
>>> G.add_weighted_edges_from([(1, 2, 0.75), (1, 2, 0.5), (2, 3, 0.5), (1, 3, 1.5)])
>>> nodes = nx.dijkstra_path(G, 1, 3)
>>> edges = nx.utils.pairwise(nodes)
>>> list(
... (u, v, min(G[u][v], key=lambda k: G[u][v][k].get("weight", 1)))
... for u, v in edges
... )
[(1, 2, 1), (2, 3, 0)]
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
The weight function can be used to hide edges by returning None.
So ``weight = lambda u, v, d: 1 if d['color']=="red" else None``
will find the shortest red path.
The weight function can be used to include node weights.
>>> def func(u, v, d):
... node_u_wt = G.nodes[u].get("node_weight", 1)
... node_v_wt = G.nodes[v].get("node_weight", 1)
... edge_wt = d.get("weight", 1)
... return node_u_wt / 2 + node_v_wt / 2 + edge_wt
In this example we take the average of start and end node
weights of an edge and add it to the weight of the edge.
The function :func:`single_source_dijkstra` computes both
path and length-of-path if you need both, use that.
See Also
--------
bidirectional_dijkstra
bellman_ford_path
single_source_dijkstra
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
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|
30,567 | networkx.algorithms.shortest_paths.weighted | dijkstra_path_length | Returns the shortest weighted path length in G from source to target.
Uses Dijkstra's Method to compute the shortest weighted path length
between two nodes in a graph.
Parameters
----------
G : NetworkX graph
source : node label
starting node for path
target : node label
ending node for path
weight : string or function
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number or None to indicate a hidden edge.
Returns
-------
length : number
Shortest path length.
Raises
------
NodeNotFound
If `source` is not in `G`.
NetworkXNoPath
If no path exists between source and target.
Examples
--------
>>> G = nx.path_graph(5)
>>> nx.dijkstra_path_length(G, 0, 4)
4
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
The weight function can be used to hide edges by returning None.
So ``weight = lambda u, v, d: 1 if d['color']=="red" else None``
will find the shortest red path.
The function :func:`single_source_dijkstra` computes both
path and length-of-path if you need both, use that.
See Also
--------
bidirectional_dijkstra
bellman_ford_path_length
single_source_dijkstra
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
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|
30,568 | networkx.algorithms.shortest_paths.weighted | dijkstra_predecessor_and_distance | Compute weighted shortest path length and predecessors.
Uses Dijkstra's Method to obtain the shortest weighted paths
and return dictionaries of predecessors for each node and
distance for each node from the `source`.
Parameters
----------
G : NetworkX graph
source : node label
Starting node for path
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
weight : string or function
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number or None to indicate a hidden edge.
Returns
-------
pred, distance : dictionaries
Returns two dictionaries representing a list of predecessors
of a node and the distance to each node.
Raises
------
NodeNotFound
If `source` is not in `G`.
Notes
-----
Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.
The list of predecessors contains more than one element only when
there are more than one shortest paths to the key node.
Examples
--------
>>> G = nx.path_graph(5, create_using=nx.DiGraph())
>>> pred, dist = nx.dijkstra_predecessor_and_distance(G, 0)
>>> sorted(pred.items())
[(0, []), (1, [0]), (2, [1]), (3, [2]), (4, [3])]
>>> sorted(dist.items())
[(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)]
>>> pred, dist = nx.dijkstra_predecessor_and_distance(G, 0, 1)
>>> sorted(pred.items())
[(0, []), (1, [0])]
>>> sorted(dist.items())
[(0, 0), (1, 1)]
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
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|
30,571 | networkx.generators.degree_seq | directed_configuration_model | Returns a directed_random graph with the given degree sequences.
The configuration model generates a random directed pseudograph
(graph with parallel edges and self loops) by randomly assigning
edges to match the given degree sequences.
Parameters
----------
in_degree_sequence : list of nonnegative integers
Each list entry corresponds to the in-degree of a node.
out_degree_sequence : list of nonnegative integers
Each list entry corresponds to the out-degree of a node.
create_using : NetworkX graph constructor, optional (default MultiDiGraph)
Graph type to create. If graph instance, then cleared before populated.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
Returns
-------
G : MultiDiGraph
A graph with the specified degree sequences.
Nodes are labeled starting at 0 with an index
corresponding to the position in deg_sequence.
Raises
------
NetworkXError
If the degree sequences do not have the same sum.
See Also
--------
configuration_model
Notes
-----
Algorithm as described by Newman [1]_.
A non-graphical degree sequence (not realizable by some simple
graph) is allowed since this function returns graphs with self
loops and parallel edges. An exception is raised if the degree
sequences does not have the same sum.
This configuration model construction process can lead to
duplicate edges and loops. You can remove the self-loops and
parallel edges (see below) which will likely result in a graph
that doesn't have the exact degree sequence specified. This
"finite-size effect" decreases as the size of the graph increases.
References
----------
.. [1] Newman, M. E. J. and Strogatz, S. H. and Watts, D. J.
Random graphs with arbitrary degree distributions and their applications
Phys. Rev. E, 64, 026118 (2001)
Examples
--------
One can modify the in- and out-degree sequences from an existing
directed graph in order to create a new directed graph. For example,
here we modify the directed path graph:
>>> D = nx.DiGraph([(0, 1), (1, 2), (2, 3)])
>>> din = list(d for n, d in D.in_degree())
>>> dout = list(d for n, d in D.out_degree())
>>> din.append(1)
>>> dout[0] = 2
>>> # We now expect an edge from node 0 to a new node, node 3.
... D = nx.directed_configuration_model(din, dout)
The returned graph is a directed multigraph, which may have parallel
edges. To remove any parallel edges from the returned graph:
>>> D = nx.DiGraph(D)
Similarly, to remove self-loops:
>>> D.remove_edges_from(nx.selfloop_edges(D))
| def generate(self):
# remaining_degree is mapping from int->remaining degree
self.remaining_degree = dict(enumerate(self.degree))
# add all nodes to make sure we get isolated nodes
self.graph = nx.Graph()
self.graph.add_nodes_from(self.remaining_degree)
# remove zero degree nodes
for n, d in list(self.remaining_degree.items()):
if d == 0:
del self.remaining_degree[n]
if len(self.remaining_degree) > 0:
# build graph in three phases according to how many unmatched edges
self.phase1()
self.phase2()
self.phase3()
return self.graph
| (in_degree_sequence, out_degree_sequence, create_using=None, seed=None, *, backend=None, **backend_kwargs) | [
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|
30,573 | networkx.generators.degree_seq | directed_havel_hakimi_graph | Returns a directed graph with the given degree sequences.
Parameters
----------
in_deg_sequence : list of integers
Each list entry corresponds to the in-degree of a node.
out_deg_sequence : list of integers
Each list entry corresponds to the out-degree of a node.
create_using : NetworkX graph constructor, optional (default DiGraph)
Graph type to create. If graph instance, then cleared before populated.
Returns
-------
G : DiGraph
A graph with the specified degree sequences.
Nodes are labeled starting at 0 with an index
corresponding to the position in deg_sequence
Raises
------
NetworkXError
If the degree sequences are not digraphical.
See Also
--------
configuration_model
Notes
-----
Algorithm as described by Kleitman and Wang [1]_.
References
----------
.. [1] D.J. Kleitman and D.L. Wang
Algorithms for Constructing Graphs and Digraphs with Given Valences
and Factors Discrete Mathematics, 6(1), pp. 79-88 (1973)
| def generate(self):
# remaining_degree is mapping from int->remaining degree
self.remaining_degree = dict(enumerate(self.degree))
# add all nodes to make sure we get isolated nodes
self.graph = nx.Graph()
self.graph.add_nodes_from(self.remaining_degree)
# remove zero degree nodes
for n, d in list(self.remaining_degree.items()):
if d == 0:
del self.remaining_degree[n]
if len(self.remaining_degree) > 0:
# build graph in three phases according to how many unmatched edges
self.phase1()
self.phase2()
self.phase3()
return self.graph
| (in_deg_sequence, out_deg_sequence, create_using=None, *, backend=None, **backend_kwargs) | [
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|
30,582 | networkx.generators.small | dodecahedral_graph |
Returns the Platonic Dodecahedral graph.
The dodecahedral graph has 20 nodes and 30 edges. The skeleton of the
dodecahedron forms a graph. It is one of 5 Platonic graphs [1]_.
It can be described in LCF notation as:
``[10, 7, 4, -4, -7, 10, -4, 7, -7, 4]^2`` [2]_.
Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Returns
-------
G : networkx Graph
Dodecahedral Graph with 20 nodes and 30 edges
References
----------
.. [1] https://en.wikipedia.org/wiki/Regular_dodecahedron#Dodecahedral_graph
.. [2] https://mathworld.wolfram.com/DodecahedralGraph.html
| def sedgewick_maze_graph(create_using=None):
"""
Return a small maze with a cycle.
This is the maze used in Sedgewick, 3rd Edition, Part 5, Graph
Algorithms, Chapter 18, e.g. Figure 18.2 and following [1]_.
Nodes are numbered 0,..,7
Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Returns
-------
G : networkx Graph
Small maze with a cycle
References
----------
.. [1] Figure 18.2, Chapter 18, Graph Algorithms (3rd Ed), Sedgewick
"""
G = empty_graph(0, create_using)
G.add_nodes_from(range(8))
G.add_edges_from([[0, 2], [0, 7], [0, 5]])
G.add_edges_from([[1, 7], [2, 6]])
G.add_edges_from([[3, 4], [3, 5]])
G.add_edges_from([[4, 5], [4, 7], [4, 6]])
G.name = "Sedgewick Maze"
return G
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|
30,587 | networkx.generators.classic | dorogovtsev_goltsev_mendes_graph | Returns the hierarchically constructed Dorogovtsev-Goltsev-Mendes graph.
The Dorogovtsev-Goltsev-Mendes [1]_ procedure produces a scale-free graph
deterministically with the following properties for a given `n`:
- Total number of nodes = ``3 * (3**n + 1) / 2``
- Total number of edges = ``3 ** (n + 1)``
.. plot::
>>> nx.draw(nx.dorogovtsev_goltsev_mendes_graph(3))
Parameters
----------
n : integer
The generation number.
create_using : NetworkX Graph, optional
Graph type to be returned. Directed graphs and multi graphs are not
supported.
Returns
-------
G : NetworkX Graph
Examples
--------
>>> G = nx.dorogovtsev_goltsev_mendes_graph(3)
>>> G.number_of_nodes()
15
>>> G.number_of_edges()
27
>>> nx.is_planar(G)
True
References
----------
.. [1] S. N. Dorogovtsev, A. V. Goltsev and J. F. F. Mendes,
"Pseudofractal scale-free web", Physical Review E 65, 066122, 2002.
https://arxiv.org/pdf/cond-mat/0112143.pdf
| def star_graph(n, create_using=None):
"""Return the star graph
The star graph consists of one center node connected to n outer nodes.
.. plot::
>>> nx.draw(nx.star_graph(6))
Parameters
----------
n : int or iterable
If an integer, node labels are 0 to n with center 0.
If an iterable of nodes, the center is the first.
Warning: n is not checked for duplicates and if present the
resulting graph may not be as desired. Make sure you have no duplicates.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Notes
-----
The graph has n+1 nodes for integer n.
So star_graph(3) is the same as star_graph(range(4)).
"""
n, nodes = n
if isinstance(n, numbers.Integral):
nodes.append(int(n)) # there should be n+1 nodes
G = empty_graph(nodes, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
if len(nodes) > 1:
hub, *spokes = nodes
G.add_edges_from((hub, node) for node in spokes)
return G
| (n, create_using=None, *, backend=None, **backend_kwargs) | [
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|
30,589 | networkx.drawing.nx_pylab | draw | Draw the graph G with Matplotlib.
Draw the graph as a simple representation with no node
labels or edge labels and using the full Matplotlib figure area
and no axis labels by default. See draw_networkx() for more
full-featured drawing that allows title, axis labels etc.
Parameters
----------
G : graph
A networkx graph
pos : dictionary, optional
A dictionary with nodes as keys and positions as values.
If not specified a spring layout positioning will be computed.
See :py:mod:`networkx.drawing.layout` for functions that
compute node positions.
ax : Matplotlib Axes object, optional
Draw the graph in specified Matplotlib axes.
kwds : optional keywords
See networkx.draw_networkx() for a description of optional keywords.
Examples
--------
>>> G = nx.dodecahedral_graph()
>>> nx.draw(G)
>>> nx.draw(G, pos=nx.spring_layout(G)) # use spring layout
See Also
--------
draw_networkx
draw_networkx_nodes
draw_networkx_edges
draw_networkx_labels
draw_networkx_edge_labels
Notes
-----
This function has the same name as pylab.draw and pyplot.draw
so beware when using `from networkx import *`
since you might overwrite the pylab.draw function.
With pyplot use
>>> import matplotlib.pyplot as plt
>>> G = nx.dodecahedral_graph()
>>> nx.draw(G) # networkx draw()
>>> plt.draw() # pyplot draw()
Also see the NetworkX drawing examples at
https://networkx.org/documentation/latest/auto_examples/index.html
| def draw(G, pos=None, ax=None, **kwds):
"""Draw the graph G with Matplotlib.
Draw the graph as a simple representation with no node
labels or edge labels and using the full Matplotlib figure area
and no axis labels by default. See draw_networkx() for more
full-featured drawing that allows title, axis labels etc.
Parameters
----------
G : graph
A networkx graph
pos : dictionary, optional
A dictionary with nodes as keys and positions as values.
If not specified a spring layout positioning will be computed.
See :py:mod:`networkx.drawing.layout` for functions that
compute node positions.
ax : Matplotlib Axes object, optional
Draw the graph in specified Matplotlib axes.
kwds : optional keywords
See networkx.draw_networkx() for a description of optional keywords.
Examples
--------
>>> G = nx.dodecahedral_graph()
>>> nx.draw(G)
>>> nx.draw(G, pos=nx.spring_layout(G)) # use spring layout
See Also
--------
draw_networkx
draw_networkx_nodes
draw_networkx_edges
draw_networkx_labels
draw_networkx_edge_labels
Notes
-----
This function has the same name as pylab.draw and pyplot.draw
so beware when using `from networkx import *`
since you might overwrite the pylab.draw function.
With pyplot use
>>> import matplotlib.pyplot as plt
>>> G = nx.dodecahedral_graph()
>>> nx.draw(G) # networkx draw()
>>> plt.draw() # pyplot draw()
Also see the NetworkX drawing examples at
https://networkx.org/documentation/latest/auto_examples/index.html
"""
import matplotlib.pyplot as plt
if ax is None:
cf = plt.gcf()
else:
cf = ax.get_figure()
cf.set_facecolor("w")
if ax is None:
if cf.axes:
ax = cf.gca()
else:
ax = cf.add_axes((0, 0, 1, 1))
if "with_labels" not in kwds:
kwds["with_labels"] = "labels" in kwds
draw_networkx(G, pos=pos, ax=ax, **kwds)
ax.set_axis_off()
plt.draw_if_interactive()
return
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|
30,590 | networkx.drawing.nx_pylab | draw_circular | Draw the graph `G` with a circular layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.circular_layout(G), **kwargs)
Parameters
----------
G : graph
A networkx graph
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Notes
-----
The layout is computed each time this function is called. For
repeated drawing it is much more efficient to call
`~networkx.drawing.layout.circular_layout` directly and reuse the result::
>>> G = nx.complete_graph(5)
>>> pos = nx.circular_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.path_graph(5)
>>> nx.draw_circular(G)
See Also
--------
:func:`~networkx.drawing.layout.circular_layout`
| def draw_circular(G, **kwargs):
"""Draw the graph `G` with a circular layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.circular_layout(G), **kwargs)
Parameters
----------
G : graph
A networkx graph
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Notes
-----
The layout is computed each time this function is called. For
repeated drawing it is much more efficient to call
`~networkx.drawing.layout.circular_layout` directly and reuse the result::
>>> G = nx.complete_graph(5)
>>> pos = nx.circular_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.path_graph(5)
>>> nx.draw_circular(G)
See Also
--------
:func:`~networkx.drawing.layout.circular_layout`
"""
draw(G, circular_layout(G), **kwargs)
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|
30,591 | networkx.drawing.nx_pylab | draw_kamada_kawai | Draw the graph `G` with a Kamada-Kawai force-directed layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.kamada_kawai_layout(G), **kwargs)
Parameters
----------
G : graph
A networkx graph
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Notes
-----
The layout is computed each time this function is called.
For repeated drawing it is much more efficient to call
`~networkx.drawing.layout.kamada_kawai_layout` directly and reuse the
result::
>>> G = nx.complete_graph(5)
>>> pos = nx.kamada_kawai_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.path_graph(5)
>>> nx.draw_kamada_kawai(G)
See Also
--------
:func:`~networkx.drawing.layout.kamada_kawai_layout`
| def draw_kamada_kawai(G, **kwargs):
"""Draw the graph `G` with a Kamada-Kawai force-directed layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.kamada_kawai_layout(G), **kwargs)
Parameters
----------
G : graph
A networkx graph
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Notes
-----
The layout is computed each time this function is called.
For repeated drawing it is much more efficient to call
`~networkx.drawing.layout.kamada_kawai_layout` directly and reuse the
result::
>>> G = nx.complete_graph(5)
>>> pos = nx.kamada_kawai_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.path_graph(5)
>>> nx.draw_kamada_kawai(G)
See Also
--------
:func:`~networkx.drawing.layout.kamada_kawai_layout`
"""
draw(G, kamada_kawai_layout(G), **kwargs)
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|
30,592 | networkx.drawing.nx_pylab | draw_networkx | Draw the graph G using Matplotlib.
Draw the graph with Matplotlib with options for node positions,
labeling, titles, and many other drawing features.
See draw() for simple drawing without labels or axes.
Parameters
----------
G : graph
A networkx graph
pos : dictionary, optional
A dictionary with nodes as keys and positions as values.
If not specified a spring layout positioning will be computed.
See :py:mod:`networkx.drawing.layout` for functions that
compute node positions.
arrows : bool or None, optional (default=None)
If `None`, directed graphs draw arrowheads with
`~matplotlib.patches.FancyArrowPatch`, while undirected graphs draw edges
via `~matplotlib.collections.LineCollection` for speed.
If `True`, draw arrowheads with FancyArrowPatches (bendable and stylish).
If `False`, draw edges using LineCollection (linear and fast).
For directed graphs, if True draw arrowheads.
Note: Arrows will be the same color as edges.
arrowstyle : str (default='-\|>' for directed graphs)
For directed graphs, choose the style of the arrowsheads.
For undirected graphs default to '-'
See `matplotlib.patches.ArrowStyle` for more options.
arrowsize : int or list (default=10)
For directed graphs, choose the size of the arrow head's length and
width. A list of values can be passed in to assign a different size for arrow head's length and width.
See `matplotlib.patches.FancyArrowPatch` for attribute `mutation_scale`
for more info.
with_labels : bool (default=True)
Set to True to draw labels on the nodes.
ax : Matplotlib Axes object, optional
Draw the graph in the specified Matplotlib axes.
nodelist : list (default=list(G))
Draw only specified nodes
edgelist : list (default=list(G.edges()))
Draw only specified edges
node_size : scalar or array (default=300)
Size of nodes. If an array is specified it must be the
same length as nodelist.
node_color : color or array of colors (default='#1f78b4')
Node color. Can be a single color or a sequence of colors with the same
length as nodelist. Color can be string or rgb (or rgba) tuple of
floats from 0-1. If numeric values are specified they will be
mapped to colors using the cmap and vmin,vmax parameters. See
matplotlib.scatter for more details.
node_shape : string (default='o')
The shape of the node. Specification is as matplotlib.scatter
marker, one of 'so^>v<dph8'.
alpha : float or None (default=None)
The node and edge transparency
cmap : Matplotlib colormap, optional
Colormap for mapping intensities of nodes
vmin,vmax : float, optional
Minimum and maximum for node colormap scaling
linewidths : scalar or sequence (default=1.0)
Line width of symbol border
width : float or array of floats (default=1.0)
Line width of edges
edge_color : color or array of colors (default='k')
Edge color. Can be a single color or a sequence of colors with the same
length as edgelist. Color can be string or rgb (or rgba) tuple of
floats from 0-1. If numeric values are specified they will be
mapped to colors using the edge_cmap and edge_vmin,edge_vmax parameters.
edge_cmap : Matplotlib colormap, optional
Colormap for mapping intensities of edges
edge_vmin,edge_vmax : floats, optional
Minimum and maximum for edge colormap scaling
style : string (default=solid line)
Edge line style e.g.: '-', '--', '-.', ':'
or words like 'solid' or 'dashed'.
(See `matplotlib.patches.FancyArrowPatch`: `linestyle`)
labels : dictionary (default=None)
Node labels in a dictionary of text labels keyed by node
font_size : int (default=12 for nodes, 10 for edges)
Font size for text labels
font_color : color (default='k' black)
Font color string. Color can be string or rgb (or rgba) tuple of
floats from 0-1.
font_weight : string (default='normal')
Font weight
font_family : string (default='sans-serif')
Font family
label : string, optional
Label for graph legend
hide_ticks : bool, optional
Hide ticks of axes. When `True` (the default), ticks and ticklabels
are removed from the axes. To set ticks and tick labels to the pyplot default,
use ``hide_ticks=False``.
kwds : optional keywords
See networkx.draw_networkx_nodes(), networkx.draw_networkx_edges(), and
networkx.draw_networkx_labels() for a description of optional keywords.
Notes
-----
For directed graphs, arrows are drawn at the head end. Arrows can be
turned off with keyword arrows=False.
Examples
--------
>>> G = nx.dodecahedral_graph()
>>> nx.draw(G)
>>> nx.draw(G, pos=nx.spring_layout(G)) # use spring layout
>>> import matplotlib.pyplot as plt
>>> limits = plt.axis("off") # turn off axis
Also see the NetworkX drawing examples at
https://networkx.org/documentation/latest/auto_examples/index.html
See Also
--------
draw
draw_networkx_nodes
draw_networkx_edges
draw_networkx_labels
draw_networkx_edge_labels
| def draw_networkx(G, pos=None, arrows=None, with_labels=True, **kwds):
r"""Draw the graph G using Matplotlib.
Draw the graph with Matplotlib with options for node positions,
labeling, titles, and many other drawing features.
See draw() for simple drawing without labels or axes.
Parameters
----------
G : graph
A networkx graph
pos : dictionary, optional
A dictionary with nodes as keys and positions as values.
If not specified a spring layout positioning will be computed.
See :py:mod:`networkx.drawing.layout` for functions that
compute node positions.
arrows : bool or None, optional (default=None)
If `None`, directed graphs draw arrowheads with
`~matplotlib.patches.FancyArrowPatch`, while undirected graphs draw edges
via `~matplotlib.collections.LineCollection` for speed.
If `True`, draw arrowheads with FancyArrowPatches (bendable and stylish).
If `False`, draw edges using LineCollection (linear and fast).
For directed graphs, if True draw arrowheads.
Note: Arrows will be the same color as edges.
arrowstyle : str (default='-\|>' for directed graphs)
For directed graphs, choose the style of the arrowsheads.
For undirected graphs default to '-'
See `matplotlib.patches.ArrowStyle` for more options.
arrowsize : int or list (default=10)
For directed graphs, choose the size of the arrow head's length and
width. A list of values can be passed in to assign a different size for arrow head's length and width.
See `matplotlib.patches.FancyArrowPatch` for attribute `mutation_scale`
for more info.
with_labels : bool (default=True)
Set to True to draw labels on the nodes.
ax : Matplotlib Axes object, optional
Draw the graph in the specified Matplotlib axes.
nodelist : list (default=list(G))
Draw only specified nodes
edgelist : list (default=list(G.edges()))
Draw only specified edges
node_size : scalar or array (default=300)
Size of nodes. If an array is specified it must be the
same length as nodelist.
node_color : color or array of colors (default='#1f78b4')
Node color. Can be a single color or a sequence of colors with the same
length as nodelist. Color can be string or rgb (or rgba) tuple of
floats from 0-1. If numeric values are specified they will be
mapped to colors using the cmap and vmin,vmax parameters. See
matplotlib.scatter for more details.
node_shape : string (default='o')
The shape of the node. Specification is as matplotlib.scatter
marker, one of 'so^>v<dph8'.
alpha : float or None (default=None)
The node and edge transparency
cmap : Matplotlib colormap, optional
Colormap for mapping intensities of nodes
vmin,vmax : float, optional
Minimum and maximum for node colormap scaling
linewidths : scalar or sequence (default=1.0)
Line width of symbol border
width : float or array of floats (default=1.0)
Line width of edges
edge_color : color or array of colors (default='k')
Edge color. Can be a single color or a sequence of colors with the same
length as edgelist. Color can be string or rgb (or rgba) tuple of
floats from 0-1. If numeric values are specified they will be
mapped to colors using the edge_cmap and edge_vmin,edge_vmax parameters.
edge_cmap : Matplotlib colormap, optional
Colormap for mapping intensities of edges
edge_vmin,edge_vmax : floats, optional
Minimum and maximum for edge colormap scaling
style : string (default=solid line)
Edge line style e.g.: '-', '--', '-.', ':'
or words like 'solid' or 'dashed'.
(See `matplotlib.patches.FancyArrowPatch`: `linestyle`)
labels : dictionary (default=None)
Node labels in a dictionary of text labels keyed by node
font_size : int (default=12 for nodes, 10 for edges)
Font size for text labels
font_color : color (default='k' black)
Font color string. Color can be string or rgb (or rgba) tuple of
floats from 0-1.
font_weight : string (default='normal')
Font weight
font_family : string (default='sans-serif')
Font family
label : string, optional
Label for graph legend
hide_ticks : bool, optional
Hide ticks of axes. When `True` (the default), ticks and ticklabels
are removed from the axes. To set ticks and tick labels to the pyplot default,
use ``hide_ticks=False``.
kwds : optional keywords
See networkx.draw_networkx_nodes(), networkx.draw_networkx_edges(), and
networkx.draw_networkx_labels() for a description of optional keywords.
Notes
-----
For directed graphs, arrows are drawn at the head end. Arrows can be
turned off with keyword arrows=False.
Examples
--------
>>> G = nx.dodecahedral_graph()
>>> nx.draw(G)
>>> nx.draw(G, pos=nx.spring_layout(G)) # use spring layout
>>> import matplotlib.pyplot as plt
>>> limits = plt.axis("off") # turn off axis
Also see the NetworkX drawing examples at
https://networkx.org/documentation/latest/auto_examples/index.html
See Also
--------
draw
draw_networkx_nodes
draw_networkx_edges
draw_networkx_labels
draw_networkx_edge_labels
"""
from inspect import signature
import matplotlib.pyplot as plt
# Get all valid keywords by inspecting the signatures of draw_networkx_nodes,
# draw_networkx_edges, draw_networkx_labels
valid_node_kwds = signature(draw_networkx_nodes).parameters.keys()
valid_edge_kwds = signature(draw_networkx_edges).parameters.keys()
valid_label_kwds = signature(draw_networkx_labels).parameters.keys()
# Create a set with all valid keywords across the three functions and
# remove the arguments of this function (draw_networkx)
valid_kwds = (valid_node_kwds | valid_edge_kwds | valid_label_kwds) - {
"G",
"pos",
"arrows",
"with_labels",
}
if any(k not in valid_kwds for k in kwds):
invalid_args = ", ".join([k for k in kwds if k not in valid_kwds])
raise ValueError(f"Received invalid argument(s): {invalid_args}")
node_kwds = {k: v for k, v in kwds.items() if k in valid_node_kwds}
edge_kwds = {k: v for k, v in kwds.items() if k in valid_edge_kwds}
label_kwds = {k: v for k, v in kwds.items() if k in valid_label_kwds}
if pos is None:
pos = nx.drawing.spring_layout(G) # default to spring layout
draw_networkx_nodes(G, pos, **node_kwds)
draw_networkx_edges(G, pos, arrows=arrows, **edge_kwds)
if with_labels:
draw_networkx_labels(G, pos, **label_kwds)
plt.draw_if_interactive()
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|
30,593 | networkx.drawing.nx_pylab | draw_networkx_edge_labels | Draw edge labels.
Parameters
----------
G : graph
A networkx graph
pos : dictionary
A dictionary with nodes as keys and positions as values.
Positions should be sequences of length 2.
edge_labels : dictionary (default=None)
Edge labels in a dictionary of labels keyed by edge two-tuple.
Only labels for the keys in the dictionary are drawn.
label_pos : float (default=0.5)
Position of edge label along edge (0=head, 0.5=center, 1=tail)
font_size : int (default=10)
Font size for text labels
font_color : color (default='k' black)
Font color string. Color can be string or rgb (or rgba) tuple of
floats from 0-1.
font_weight : string (default='normal')
Font weight
font_family : string (default='sans-serif')
Font family
alpha : float or None (default=None)
The text transparency
bbox : Matplotlib bbox, optional
Specify text box properties (e.g. shape, color etc.) for edge labels.
Default is {boxstyle='round', ec=(1.0, 1.0, 1.0), fc=(1.0, 1.0, 1.0)}.
horizontalalignment : string (default='center')
Horizontal alignment {'center', 'right', 'left'}
verticalalignment : string (default='center')
Vertical alignment {'center', 'top', 'bottom', 'baseline', 'center_baseline'}
ax : Matplotlib Axes object, optional
Draw the graph in the specified Matplotlib axes.
rotate : bool (default=True)
Rotate edge labels to lie parallel to edges
clip_on : bool (default=True)
Turn on clipping of edge labels at axis boundaries
node_size : scalar or array (default=300)
Size of nodes. If an array it must be the same length as nodelist.
nodelist : list, optional (default=G.nodes())
This provides the node order for the `node_size` array (if it is an array).
connectionstyle : string or iterable of strings (default="arc3")
Pass the connectionstyle parameter to create curved arc of rounding
radius rad. For example, connectionstyle='arc3,rad=0.2'.
See `matplotlib.patches.ConnectionStyle` and
`matplotlib.patches.FancyArrowPatch` for more info.
If Iterable, index indicates i'th edge key of MultiGraph
hide_ticks : bool, optional
Hide ticks of axes. When `True` (the default), ticks and ticklabels
are removed from the axes. To set ticks and tick labels to the pyplot default,
use ``hide_ticks=False``.
Returns
-------
dict
`dict` of labels keyed by edge
Examples
--------
>>> G = nx.dodecahedral_graph()
>>> edge_labels = nx.draw_networkx_edge_labels(G, pos=nx.spring_layout(G))
Also see the NetworkX drawing examples at
https://networkx.org/documentation/latest/auto_examples/index.html
See Also
--------
draw
draw_networkx
draw_networkx_nodes
draw_networkx_edges
draw_networkx_labels
| def draw_networkx_edge_labels(
G,
pos,
edge_labels=None,
label_pos=0.5,
font_size=10,
font_color="k",
font_family="sans-serif",
font_weight="normal",
alpha=None,
bbox=None,
horizontalalignment="center",
verticalalignment="center",
ax=None,
rotate=True,
clip_on=True,
node_size=300,
nodelist=None,
connectionstyle="arc3",
hide_ticks=True,
):
"""Draw edge labels.
Parameters
----------
G : graph
A networkx graph
pos : dictionary
A dictionary with nodes as keys and positions as values.
Positions should be sequences of length 2.
edge_labels : dictionary (default=None)
Edge labels in a dictionary of labels keyed by edge two-tuple.
Only labels for the keys in the dictionary are drawn.
label_pos : float (default=0.5)
Position of edge label along edge (0=head, 0.5=center, 1=tail)
font_size : int (default=10)
Font size for text labels
font_color : color (default='k' black)
Font color string. Color can be string or rgb (or rgba) tuple of
floats from 0-1.
font_weight : string (default='normal')
Font weight
font_family : string (default='sans-serif')
Font family
alpha : float or None (default=None)
The text transparency
bbox : Matplotlib bbox, optional
Specify text box properties (e.g. shape, color etc.) for edge labels.
Default is {boxstyle='round', ec=(1.0, 1.0, 1.0), fc=(1.0, 1.0, 1.0)}.
horizontalalignment : string (default='center')
Horizontal alignment {'center', 'right', 'left'}
verticalalignment : string (default='center')
Vertical alignment {'center', 'top', 'bottom', 'baseline', 'center_baseline'}
ax : Matplotlib Axes object, optional
Draw the graph in the specified Matplotlib axes.
rotate : bool (default=True)
Rotate edge labels to lie parallel to edges
clip_on : bool (default=True)
Turn on clipping of edge labels at axis boundaries
node_size : scalar or array (default=300)
Size of nodes. If an array it must be the same length as nodelist.
nodelist : list, optional (default=G.nodes())
This provides the node order for the `node_size` array (if it is an array).
connectionstyle : string or iterable of strings (default="arc3")
Pass the connectionstyle parameter to create curved arc of rounding
radius rad. For example, connectionstyle='arc3,rad=0.2'.
See `matplotlib.patches.ConnectionStyle` and
`matplotlib.patches.FancyArrowPatch` for more info.
If Iterable, index indicates i'th edge key of MultiGraph
hide_ticks : bool, optional
Hide ticks of axes. When `True` (the default), ticks and ticklabels
are removed from the axes. To set ticks and tick labels to the pyplot default,
use ``hide_ticks=False``.
Returns
-------
dict
`dict` of labels keyed by edge
Examples
--------
>>> G = nx.dodecahedral_graph()
>>> edge_labels = nx.draw_networkx_edge_labels(G, pos=nx.spring_layout(G))
Also see the NetworkX drawing examples at
https://networkx.org/documentation/latest/auto_examples/index.html
See Also
--------
draw
draw_networkx
draw_networkx_nodes
draw_networkx_edges
draw_networkx_labels
"""
import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
class CurvedArrowText(mpl.text.Text):
def __init__(
self,
arrow,
*args,
label_pos=0.5,
labels_horizontal=False,
ax=None,
**kwargs,
):
# Bind to FancyArrowPatch
self.arrow = arrow
# how far along the text should be on the curve,
# 0 is at start, 1 is at end etc.
self.label_pos = label_pos
self.labels_horizontal = labels_horizontal
if ax is None:
ax = plt.gca()
self.ax = ax
self.x, self.y, self.angle = self._update_text_pos_angle(arrow)
# Create text object
super().__init__(self.x, self.y, *args, rotation=self.angle, **kwargs)
# Bind to axis
self.ax.add_artist(self)
def _get_arrow_path_disp(self, arrow):
"""
This is part of FancyArrowPatch._get_path_in_displaycoord
It omits the second part of the method where path is converted
to polygon based on width
The transform is taken from ax, not the object, as the object
has not been added yet, and doesn't have transform
"""
dpi_cor = arrow._dpi_cor
# trans_data = arrow.get_transform()
trans_data = self.ax.transData
if arrow._posA_posB is not None:
posA = arrow._convert_xy_units(arrow._posA_posB[0])
posB = arrow._convert_xy_units(arrow._posA_posB[1])
(posA, posB) = trans_data.transform((posA, posB))
_path = arrow.get_connectionstyle()(
posA,
posB,
patchA=arrow.patchA,
patchB=arrow.patchB,
shrinkA=arrow.shrinkA * dpi_cor,
shrinkB=arrow.shrinkB * dpi_cor,
)
else:
_path = trans_data.transform_path(arrow._path_original)
# Return is in display coordinates
return _path
def _update_text_pos_angle(self, arrow):
# Fractional label position
path_disp = self._get_arrow_path_disp(arrow)
(x1, y1), (cx, cy), (x2, y2) = path_disp.vertices
# Text position at a proportion t along the line in display coords
# default is 0.5 so text appears at the halfway point
t = self.label_pos
tt = 1 - t
x = tt**2 * x1 + 2 * t * tt * cx + t**2 * x2
y = tt**2 * y1 + 2 * t * tt * cy + t**2 * y2
if self.labels_horizontal:
# Horizontal text labels
angle = 0
else:
# Labels parallel to curve
change_x = 2 * tt * (cx - x1) + 2 * t * (x2 - cx)
change_y = 2 * tt * (cy - y1) + 2 * t * (y2 - cy)
angle = (np.arctan2(change_y, change_x) / (2 * np.pi)) * 360
# Text is "right way up"
if angle > 90:
angle -= 180
if angle < -90:
angle += 180
(x, y) = self.ax.transData.inverted().transform((x, y))
return x, y, angle
def draw(self, renderer):
# recalculate the text position and angle
self.x, self.y, self.angle = self._update_text_pos_angle(self.arrow)
self.set_position((self.x, self.y))
self.set_rotation(self.angle)
# redraw text
super().draw(renderer)
# use default box of white with white border
if bbox is None:
bbox = {"boxstyle": "round", "ec": (1.0, 1.0, 1.0), "fc": (1.0, 1.0, 1.0)}
if isinstance(connectionstyle, str):
connectionstyle = [connectionstyle]
elif np.iterable(connectionstyle):
connectionstyle = list(connectionstyle)
else:
raise nx.NetworkXError(
"draw_networkx_edges arg `connectionstyle` must be"
"string or iterable of strings"
)
if ax is None:
ax = plt.gca()
if edge_labels is None:
kwds = {"keys": True} if G.is_multigraph() else {}
edge_labels = {tuple(edge): d for *edge, d in G.edges(data=True, **kwds)}
# NOTHING TO PLOT
if not edge_labels:
return {}
edgelist, labels = zip(*edge_labels.items())
if nodelist is None:
nodelist = list(G.nodes())
# set edge positions
edge_pos = np.asarray([(pos[e[0]], pos[e[1]]) for e in edgelist])
if G.is_multigraph():
key_count = collections.defaultdict(lambda: itertools.count(0))
edge_indices = | (G, pos, edge_labels=None, label_pos=0.5, font_size=10, font_color='k', font_family='sans-serif', font_weight='normal', alpha=None, bbox=None, horizontalalignment='center', verticalalignment='center', ax=None, rotate=True, clip_on=True, node_size=300, nodelist=None, connectionstyle='arc3', hide_ticks=True) | [
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|
30,594 | networkx.drawing.nx_pylab | draw_networkx_edges | Draw the edges of the graph G.
This draws only the edges of the graph G.
Parameters
----------
G : graph
A networkx graph
pos : dictionary
A dictionary with nodes as keys and positions as values.
Positions should be sequences of length 2.
edgelist : collection of edge tuples (default=G.edges())
Draw only specified edges
width : float or array of floats (default=1.0)
Line width of edges
edge_color : color or array of colors (default='k')
Edge color. Can be a single color or a sequence of colors with the same
length as edgelist. Color can be string or rgb (or rgba) tuple of
floats from 0-1. If numeric values are specified they will be
mapped to colors using the edge_cmap and edge_vmin,edge_vmax parameters.
style : string or array of strings (default='solid')
Edge line style e.g.: '-', '--', '-.', ':'
or words like 'solid' or 'dashed'.
Can be a single style or a sequence of styles with the same
length as the edge list.
If less styles than edges are given the styles will cycle.
If more styles than edges are given the styles will be used sequentially
and not be exhausted.
Also, `(offset, onoffseq)` tuples can be used as style instead of a strings.
(See `matplotlib.patches.FancyArrowPatch`: `linestyle`)
alpha : float or array of floats (default=None)
The edge transparency. This can be a single alpha value,
in which case it will be applied to all specified edges. Otherwise,
if it is an array, the elements of alpha will be applied to the colors
in order (cycling through alpha multiple times if necessary).
edge_cmap : Matplotlib colormap, optional
Colormap for mapping intensities of edges
edge_vmin,edge_vmax : floats, optional
Minimum and maximum for edge colormap scaling
ax : Matplotlib Axes object, optional
Draw the graph in the specified Matplotlib axes.
arrows : bool or None, optional (default=None)
If `None`, directed graphs draw arrowheads with
`~matplotlib.patches.FancyArrowPatch`, while undirected graphs draw edges
via `~matplotlib.collections.LineCollection` for speed.
If `True`, draw arrowheads with FancyArrowPatches (bendable and stylish).
If `False`, draw edges using LineCollection (linear and fast).
Note: Arrowheads will be the same color as edges.
arrowstyle : str (default='-\|>' for directed graphs)
For directed graphs and `arrows==True` defaults to '-\|>',
For undirected graphs default to '-'.
See `matplotlib.patches.ArrowStyle` for more options.
arrowsize : int (default=10)
For directed graphs, choose the size of the arrow head's length and
width. See `matplotlib.patches.FancyArrowPatch` for attribute
`mutation_scale` for more info.
connectionstyle : string or iterable of strings (default="arc3")
Pass the connectionstyle parameter to create curved arc of rounding
radius rad. For example, connectionstyle='arc3,rad=0.2'.
See `matplotlib.patches.ConnectionStyle` and
`matplotlib.patches.FancyArrowPatch` for more info.
If Iterable, index indicates i'th edge key of MultiGraph
node_size : scalar or array (default=300)
Size of nodes. Though the nodes are not drawn with this function, the
node size is used in determining edge positioning.
nodelist : list, optional (default=G.nodes())
This provides the node order for the `node_size` array (if it is an array).
node_shape : string (default='o')
The marker used for nodes, used in determining edge positioning.
Specification is as a `matplotlib.markers` marker, e.g. one of 'so^>v<dph8'.
label : None or string
Label for legend
min_source_margin : int (default=0)
The minimum margin (gap) at the beginning of the edge at the source.
min_target_margin : int (default=0)
The minimum margin (gap) at the end of the edge at the target.
hide_ticks : bool, optional
Hide ticks of axes. When `True` (the default), ticks and ticklabels
are removed from the axes. To set ticks and tick labels to the pyplot default,
use ``hide_ticks=False``.
Returns
-------
matplotlib.collections.LineCollection or a list of matplotlib.patches.FancyArrowPatch
If ``arrows=True``, a list of FancyArrowPatches is returned.
If ``arrows=False``, a LineCollection is returned.
If ``arrows=None`` (the default), then a LineCollection is returned if
`G` is undirected, otherwise returns a list of FancyArrowPatches.
Notes
-----
For directed graphs, arrows are drawn at the head end. Arrows can be
turned off with keyword arrows=False or by passing an arrowstyle without
an arrow on the end.
Be sure to include `node_size` as a keyword argument; arrows are
drawn considering the size of nodes.
Self-loops are always drawn with `~matplotlib.patches.FancyArrowPatch`
regardless of the value of `arrows` or whether `G` is directed.
When ``arrows=False`` or ``arrows=None`` and `G` is undirected, the
FancyArrowPatches corresponding to the self-loops are not explicitly
returned. They should instead be accessed via the ``Axes.patches``
attribute (see examples).
Examples
--------
>>> G = nx.dodecahedral_graph()
>>> edges = nx.draw_networkx_edges(G, pos=nx.spring_layout(G))
>>> G = nx.DiGraph()
>>> G.add_edges_from([(1, 2), (1, 3), (2, 3)])
>>> arcs = nx.draw_networkx_edges(G, pos=nx.spring_layout(G))
>>> alphas = [0.3, 0.4, 0.5]
>>> for i, arc in enumerate(arcs): # change alpha values of arcs
... arc.set_alpha(alphas[i])
The FancyArrowPatches corresponding to self-loops are not always
returned, but can always be accessed via the ``patches`` attribute of the
`matplotlib.Axes` object.
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> G = nx.Graph([(0, 1), (0, 0)]) # Self-loop at node 0
>>> edge_collection = nx.draw_networkx_edges(G, pos=nx.circular_layout(G), ax=ax)
>>> self_loop_fap = ax.patches[0]
Also see the NetworkX drawing examples at
https://networkx.org/documentation/latest/auto_examples/index.html
See Also
--------
draw
draw_networkx
draw_networkx_nodes
draw_networkx_labels
draw_networkx_edge_labels
| def draw_networkx_edges(
G,
pos,
edgelist=None,
width=1.0,
edge_color="k",
style="solid",
alpha=None,
arrowstyle=None,
arrowsize=10,
edge_cmap=None,
edge_vmin=None,
edge_vmax=None,
ax=None,
arrows=None,
label=None,
node_size=300,
nodelist=None,
node_shape="o",
connectionstyle="arc3",
min_source_margin=0,
min_target_margin=0,
hide_ticks=True,
):
r"""Draw the edges of the graph G.
This draws only the edges of the graph G.
Parameters
----------
G : graph
A networkx graph
pos : dictionary
A dictionary with nodes as keys and positions as values.
Positions should be sequences of length 2.
edgelist : collection of edge tuples (default=G.edges())
Draw only specified edges
width : float or array of floats (default=1.0)
Line width of edges
edge_color : color or array of colors (default='k')
Edge color. Can be a single color or a sequence of colors with the same
length as edgelist. Color can be string or rgb (or rgba) tuple of
floats from 0-1. If numeric values are specified they will be
mapped to colors using the edge_cmap and edge_vmin,edge_vmax parameters.
style : string or array of strings (default='solid')
Edge line style e.g.: '-', '--', '-.', ':'
or words like 'solid' or 'dashed'.
Can be a single style or a sequence of styles with the same
length as the edge list.
If less styles than edges are given the styles will cycle.
If more styles than edges are given the styles will be used sequentially
and not be exhausted.
Also, `(offset, onoffseq)` tuples can be used as style instead of a strings.
(See `matplotlib.patches.FancyArrowPatch`: `linestyle`)
alpha : float or array of floats (default=None)
The edge transparency. This can be a single alpha value,
in which case it will be applied to all specified edges. Otherwise,
if it is an array, the elements of alpha will be applied to the colors
in order (cycling through alpha multiple times if necessary).
edge_cmap : Matplotlib colormap, optional
Colormap for mapping intensities of edges
edge_vmin,edge_vmax : floats, optional
Minimum and maximum for edge colormap scaling
ax : Matplotlib Axes object, optional
Draw the graph in the specified Matplotlib axes.
arrows : bool or None, optional (default=None)
If `None`, directed graphs draw arrowheads with
`~matplotlib.patches.FancyArrowPatch`, while undirected graphs draw edges
via `~matplotlib.collections.LineCollection` for speed.
If `True`, draw arrowheads with FancyArrowPatches (bendable and stylish).
If `False`, draw edges using LineCollection (linear and fast).
Note: Arrowheads will be the same color as edges.
arrowstyle : str (default='-\|>' for directed graphs)
For directed graphs and `arrows==True` defaults to '-\|>',
For undirected graphs default to '-'.
See `matplotlib.patches.ArrowStyle` for more options.
arrowsize : int (default=10)
For directed graphs, choose the size of the arrow head's length and
width. See `matplotlib.patches.FancyArrowPatch` for attribute
`mutation_scale` for more info.
connectionstyle : string or iterable of strings (default="arc3")
Pass the connectionstyle parameter to create curved arc of rounding
radius rad. For example, connectionstyle='arc3,rad=0.2'.
See `matplotlib.patches.ConnectionStyle` and
`matplotlib.patches.FancyArrowPatch` for more info.
If Iterable, index indicates i'th edge key of MultiGraph
node_size : scalar or array (default=300)
Size of nodes. Though the nodes are not drawn with this function, the
node size is used in determining edge positioning.
nodelist : list, optional (default=G.nodes())
This provides the node order for the `node_size` array (if it is an array).
node_shape : string (default='o')
The marker used for nodes, used in determining edge positioning.
Specification is as a `matplotlib.markers` marker, e.g. one of 'so^>v<dph8'.
label : None or string
Label for legend
min_source_margin : int (default=0)
The minimum margin (gap) at the beginning of the edge at the source.
min_target_margin : int (default=0)
The minimum margin (gap) at the end of the edge at the target.
hide_ticks : bool, optional
Hide ticks of axes. When `True` (the default), ticks and ticklabels
are removed from the axes. To set ticks and tick labels to the pyplot default,
use ``hide_ticks=False``.
Returns
-------
matplotlib.collections.LineCollection or a list of matplotlib.patches.FancyArrowPatch
If ``arrows=True``, a list of FancyArrowPatches is returned.
If ``arrows=False``, a LineCollection is returned.
If ``arrows=None`` (the default), then a LineCollection is returned if
`G` is undirected, otherwise returns a list of FancyArrowPatches.
Notes
-----
For directed graphs, arrows are drawn at the head end. Arrows can be
turned off with keyword arrows=False or by passing an arrowstyle without
an arrow on the end.
Be sure to include `node_size` as a keyword argument; arrows are
drawn considering the size of nodes.
Self-loops are always drawn with `~matplotlib.patches.FancyArrowPatch`
regardless of the value of `arrows` or whether `G` is directed.
When ``arrows=False`` or ``arrows=None`` and `G` is undirected, the
FancyArrowPatches corresponding to the self-loops are not explicitly
returned. They should instead be accessed via the ``Axes.patches``
attribute (see examples).
Examples
--------
>>> G = nx.dodecahedral_graph()
>>> edges = nx.draw_networkx_edges(G, pos=nx.spring_layout(G))
>>> G = nx.DiGraph()
>>> G.add_edges_from([(1, 2), (1, 3), (2, 3)])
>>> arcs = nx.draw_networkx_edges(G, pos=nx.spring_layout(G))
>>> alphas = [0.3, 0.4, 0.5]
>>> for i, arc in enumerate(arcs): # change alpha values of arcs
... arc.set_alpha(alphas[i])
The FancyArrowPatches corresponding to self-loops are not always
returned, but can always be accessed via the ``patches`` attribute of the
`matplotlib.Axes` object.
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> G = nx.Graph([(0, 1), (0, 0)]) # Self-loop at node 0
>>> edge_collection = nx.draw_networkx_edges(G, pos=nx.circular_layout(G), ax=ax)
>>> self_loop_fap = ax.patches[0]
Also see the NetworkX drawing examples at
https://networkx.org/documentation/latest/auto_examples/index.html
See Also
--------
draw
draw_networkx
draw_networkx_nodes
draw_networkx_labels
draw_networkx_edge_labels
"""
import warnings
import matplotlib as mpl
import matplotlib.collections # call as mpl.collections
import matplotlib.colors # call as mpl.colors
import matplotlib.pyplot as plt
import numpy as np
# The default behavior is to use LineCollection to draw edges for
# undirected graphs (for performance reasons) and use FancyArrowPatches
# for directed graphs.
# The `arrows` keyword can be used to override the default behavior
if arrows is None:
use_linecollection = not (G.is_directed() or G.is_multigraph())
else:
if not isinstance(arrows, bool):
raise TypeError("Argument `arrows` must be of type bool or None")
use_linecollection = not arrows
if isinstance(connectionstyle, str):
connectionstyle = [connectionstyle]
elif np.iterable(connectionstyle):
connectionstyle = list(connectionstyle)
else:
msg = "draw_networkx_edges arg `connectionstyle` must be str or iterable"
raise nx.NetworkXError(msg)
# Some kwargs only apply to FancyArrowPatches. Warn users when they use
# non-default values for these kwargs when LineC | (G, pos, edgelist=None, width=1.0, edge_color='k', style='solid', alpha=None, arrowstyle=None, arrowsize=10, edge_cmap=None, edge_vmin=None, edge_vmax=None, ax=None, arrows=None, label=None, node_size=300, nodelist=None, node_shape='o', connectionstyle='arc3', min_source_margin=0, min_target_margin=0, hide_ticks=True) | [
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|
30,595 | networkx.drawing.nx_pylab | draw_networkx_labels | Draw node labels on the graph G.
Parameters
----------
G : graph
A networkx graph
pos : dictionary
A dictionary with nodes as keys and positions as values.
Positions should be sequences of length 2.
labels : dictionary (default={n: n for n in G})
Node labels in a dictionary of text labels keyed by node.
Node-keys in labels should appear as keys in `pos`.
If needed use: `{n:lab for n,lab in labels.items() if n in pos}`
font_size : int (default=12)
Font size for text labels
font_color : color (default='k' black)
Font color string. Color can be string or rgb (or rgba) tuple of
floats from 0-1.
font_weight : string (default='normal')
Font weight
font_family : string (default='sans-serif')
Font family
alpha : float or None (default=None)
The text transparency
bbox : Matplotlib bbox, (default is Matplotlib's ax.text default)
Specify text box properties (e.g. shape, color etc.) for node labels.
horizontalalignment : string (default='center')
Horizontal alignment {'center', 'right', 'left'}
verticalalignment : string (default='center')
Vertical alignment {'center', 'top', 'bottom', 'baseline', 'center_baseline'}
ax : Matplotlib Axes object, optional
Draw the graph in the specified Matplotlib axes.
clip_on : bool (default=True)
Turn on clipping of node labels at axis boundaries
hide_ticks : bool, optional
Hide ticks of axes. When `True` (the default), ticks and ticklabels
are removed from the axes. To set ticks and tick labels to the pyplot default,
use ``hide_ticks=False``.
Returns
-------
dict
`dict` of labels keyed on the nodes
Examples
--------
>>> G = nx.dodecahedral_graph()
>>> labels = nx.draw_networkx_labels(G, pos=nx.spring_layout(G))
Also see the NetworkX drawing examples at
https://networkx.org/documentation/latest/auto_examples/index.html
See Also
--------
draw
draw_networkx
draw_networkx_nodes
draw_networkx_edges
draw_networkx_edge_labels
| def draw_networkx_labels(
G,
pos,
labels=None,
font_size=12,
font_color="k",
font_family="sans-serif",
font_weight="normal",
alpha=None,
bbox=None,
horizontalalignment="center",
verticalalignment="center",
ax=None,
clip_on=True,
hide_ticks=True,
):
"""Draw node labels on the graph G.
Parameters
----------
G : graph
A networkx graph
pos : dictionary
A dictionary with nodes as keys and positions as values.
Positions should be sequences of length 2.
labels : dictionary (default={n: n for n in G})
Node labels in a dictionary of text labels keyed by node.
Node-keys in labels should appear as keys in `pos`.
If needed use: `{n:lab for n,lab in labels.items() if n in pos}`
font_size : int (default=12)
Font size for text labels
font_color : color (default='k' black)
Font color string. Color can be string or rgb (or rgba) tuple of
floats from 0-1.
font_weight : string (default='normal')
Font weight
font_family : string (default='sans-serif')
Font family
alpha : float or None (default=None)
The text transparency
bbox : Matplotlib bbox, (default is Matplotlib's ax.text default)
Specify text box properties (e.g. shape, color etc.) for node labels.
horizontalalignment : string (default='center')
Horizontal alignment {'center', 'right', 'left'}
verticalalignment : string (default='center')
Vertical alignment {'center', 'top', 'bottom', 'baseline', 'center_baseline'}
ax : Matplotlib Axes object, optional
Draw the graph in the specified Matplotlib axes.
clip_on : bool (default=True)
Turn on clipping of node labels at axis boundaries
hide_ticks : bool, optional
Hide ticks of axes. When `True` (the default), ticks and ticklabels
are removed from the axes. To set ticks and tick labels to the pyplot default,
use ``hide_ticks=False``.
Returns
-------
dict
`dict` of labels keyed on the nodes
Examples
--------
>>> G = nx.dodecahedral_graph()
>>> labels = nx.draw_networkx_labels(G, pos=nx.spring_layout(G))
Also see the NetworkX drawing examples at
https://networkx.org/documentation/latest/auto_examples/index.html
See Also
--------
draw
draw_networkx
draw_networkx_nodes
draw_networkx_edges
draw_networkx_edge_labels
"""
import matplotlib.pyplot as plt
if ax is None:
ax = plt.gca()
if labels is None:
labels = {n: n for n in G.nodes()}
text_items = {} # there is no text collection so we'll fake one
for n, label in labels.items():
(x, y) = pos[n]
if not isinstance(label, str):
label = str(label) # this makes "1" and 1 labeled the same
t = ax.text(
x,
y,
label,
size=font_size,
color=font_color,
family=font_family,
weight=font_weight,
alpha=alpha,
horizontalalignment=horizontalalignment,
verticalalignment=verticalalignment,
transform=ax.transData,
bbox=bbox,
clip_on=clip_on,
)
text_items[n] = t
if hide_ticks:
ax.tick_params(
axis="both",
which="both",
bottom=False,
left=False,
labelbottom=False,
labelleft=False,
)
return text_items
| (G, pos, labels=None, font_size=12, font_color='k', font_family='sans-serif', font_weight='normal', alpha=None, bbox=None, horizontalalignment='center', verticalalignment='center', ax=None, clip_on=True, hide_ticks=True) | [
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|
30,596 | networkx.drawing.nx_pylab | draw_networkx_nodes | Draw the nodes of the graph G.
This draws only the nodes of the graph G.
Parameters
----------
G : graph
A networkx graph
pos : dictionary
A dictionary with nodes as keys and positions as values.
Positions should be sequences of length 2.
ax : Matplotlib Axes object, optional
Draw the graph in the specified Matplotlib axes.
nodelist : list (default list(G))
Draw only specified nodes
node_size : scalar or array (default=300)
Size of nodes. If an array it must be the same length as nodelist.
node_color : color or array of colors (default='#1f78b4')
Node color. Can be a single color or a sequence of colors with the same
length as nodelist. Color can be string or rgb (or rgba) tuple of
floats from 0-1. If numeric values are specified they will be
mapped to colors using the cmap and vmin,vmax parameters. See
matplotlib.scatter for more details.
node_shape : string (default='o')
The shape of the node. Specification is as matplotlib.scatter
marker, one of 'so^>v<dph8'.
alpha : float or array of floats (default=None)
The node transparency. This can be a single alpha value,
in which case it will be applied to all the nodes of color. Otherwise,
if it is an array, the elements of alpha will be applied to the colors
in order (cycling through alpha multiple times if necessary).
cmap : Matplotlib colormap (default=None)
Colormap for mapping intensities of nodes
vmin,vmax : floats or None (default=None)
Minimum and maximum for node colormap scaling
linewidths : [None | scalar | sequence] (default=1.0)
Line width of symbol border
edgecolors : [None | scalar | sequence] (default = node_color)
Colors of node borders. Can be a single color or a sequence of colors with the
same length as nodelist. Color can be string or rgb (or rgba) tuple of floats
from 0-1. If numeric values are specified they will be mapped to colors
using the cmap and vmin,vmax parameters. See `~matplotlib.pyplot.scatter` for more details.
label : [None | string]
Label for legend
margins : float or 2-tuple, optional
Sets the padding for axis autoscaling. Increase margin to prevent
clipping for nodes that are near the edges of an image. Values should
be in the range ``[0, 1]``. See :meth:`matplotlib.axes.Axes.margins`
for details. The default is `None`, which uses the Matplotlib default.
hide_ticks : bool, optional
Hide ticks of axes. When `True` (the default), ticks and ticklabels
are removed from the axes. To set ticks and tick labels to the pyplot default,
use ``hide_ticks=False``.
Returns
-------
matplotlib.collections.PathCollection
`PathCollection` of the nodes.
Examples
--------
>>> G = nx.dodecahedral_graph()
>>> nodes = nx.draw_networkx_nodes(G, pos=nx.spring_layout(G))
Also see the NetworkX drawing examples at
https://networkx.org/documentation/latest/auto_examples/index.html
See Also
--------
draw
draw_networkx
draw_networkx_edges
draw_networkx_labels
draw_networkx_edge_labels
| def draw_networkx_nodes(
G,
pos,
nodelist=None,
node_size=300,
node_color="#1f78b4",
node_shape="o",
alpha=None,
cmap=None,
vmin=None,
vmax=None,
ax=None,
linewidths=None,
edgecolors=None,
label=None,
margins=None,
hide_ticks=True,
):
"""Draw the nodes of the graph G.
This draws only the nodes of the graph G.
Parameters
----------
G : graph
A networkx graph
pos : dictionary
A dictionary with nodes as keys and positions as values.
Positions should be sequences of length 2.
ax : Matplotlib Axes object, optional
Draw the graph in the specified Matplotlib axes.
nodelist : list (default list(G))
Draw only specified nodes
node_size : scalar or array (default=300)
Size of nodes. If an array it must be the same length as nodelist.
node_color : color or array of colors (default='#1f78b4')
Node color. Can be a single color or a sequence of colors with the same
length as nodelist. Color can be string or rgb (or rgba) tuple of
floats from 0-1. If numeric values are specified they will be
mapped to colors using the cmap and vmin,vmax parameters. See
matplotlib.scatter for more details.
node_shape : string (default='o')
The shape of the node. Specification is as matplotlib.scatter
marker, one of 'so^>v<dph8'.
alpha : float or array of floats (default=None)
The node transparency. This can be a single alpha value,
in which case it will be applied to all the nodes of color. Otherwise,
if it is an array, the elements of alpha will be applied to the colors
in order (cycling through alpha multiple times if necessary).
cmap : Matplotlib colormap (default=None)
Colormap for mapping intensities of nodes
vmin,vmax : floats or None (default=None)
Minimum and maximum for node colormap scaling
linewidths : [None | scalar | sequence] (default=1.0)
Line width of symbol border
edgecolors : [None | scalar | sequence] (default = node_color)
Colors of node borders. Can be a single color or a sequence of colors with the
same length as nodelist. Color can be string or rgb (or rgba) tuple of floats
from 0-1. If numeric values are specified they will be mapped to colors
using the cmap and vmin,vmax parameters. See `~matplotlib.pyplot.scatter` for more details.
label : [None | string]
Label for legend
margins : float or 2-tuple, optional
Sets the padding for axis autoscaling. Increase margin to prevent
clipping for nodes that are near the edges of an image. Values should
be in the range ``[0, 1]``. See :meth:`matplotlib.axes.Axes.margins`
for details. The default is `None`, which uses the Matplotlib default.
hide_ticks : bool, optional
Hide ticks of axes. When `True` (the default), ticks and ticklabels
are removed from the axes. To set ticks and tick labels to the pyplot default,
use ``hide_ticks=False``.
Returns
-------
matplotlib.collections.PathCollection
`PathCollection` of the nodes.
Examples
--------
>>> G = nx.dodecahedral_graph()
>>> nodes = nx.draw_networkx_nodes(G, pos=nx.spring_layout(G))
Also see the NetworkX drawing examples at
https://networkx.org/documentation/latest/auto_examples/index.html
See Also
--------
draw
draw_networkx
draw_networkx_edges
draw_networkx_labels
draw_networkx_edge_labels
"""
from collections.abc import Iterable
import matplotlib as mpl
import matplotlib.collections # call as mpl.collections
import matplotlib.pyplot as plt
import numpy as np
if ax is None:
ax = plt.gca()
if nodelist is None:
nodelist = list(G)
if len(nodelist) == 0: # empty nodelist, no drawing
return mpl.collections.PathCollection(None)
try:
xy = np.asarray([pos[v] for v in nodelist])
except KeyError as err:
raise nx.NetworkXError(f"Node {err} has no position.") from err
if isinstance(alpha, Iterable):
node_color = apply_alpha(node_color, alpha, nodelist, cmap, vmin, vmax)
alpha = None
node_collection = ax.scatter(
xy[:, 0],
xy[:, 1],
s=node_size,
c=node_color,
marker=node_shape,
cmap=cmap,
vmin=vmin,
vmax=vmax,
alpha=alpha,
linewidths=linewidths,
edgecolors=edgecolors,
label=label,
)
if hide_ticks:
ax.tick_params(
axis="both",
which="both",
bottom=False,
left=False,
labelbottom=False,
labelleft=False,
)
if margins is not None:
if isinstance(margins, Iterable):
ax.margins(*margins)
else:
ax.margins(margins)
node_collection.set_zorder(2)
return node_collection
| (G, pos, nodelist=None, node_size=300, node_color='#1f78b4', node_shape='o', alpha=None, cmap=None, vmin=None, vmax=None, ax=None, linewidths=None, edgecolors=None, label=None, margins=None, hide_ticks=True) | [
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|
30,597 | networkx.drawing.nx_pylab | draw_planar | Draw a planar networkx graph `G` with planar layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.planar_layout(G), **kwargs)
Parameters
----------
G : graph
A planar networkx graph
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Raises
------
NetworkXException
When `G` is not planar
Notes
-----
The layout is computed each time this function is called.
For repeated drawing it is much more efficient to call
`~networkx.drawing.layout.planar_layout` directly and reuse the result::
>>> G = nx.path_graph(5)
>>> pos = nx.planar_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.path_graph(4)
>>> nx.draw_planar(G)
See Also
--------
:func:`~networkx.drawing.layout.planar_layout`
| def draw_planar(G, **kwargs):
"""Draw a planar networkx graph `G` with planar layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.planar_layout(G), **kwargs)
Parameters
----------
G : graph
A planar networkx graph
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Raises
------
NetworkXException
When `G` is not planar
Notes
-----
The layout is computed each time this function is called.
For repeated drawing it is much more efficient to call
`~networkx.drawing.layout.planar_layout` directly and reuse the result::
>>> G = nx.path_graph(5)
>>> pos = nx.planar_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.path_graph(4)
>>> nx.draw_planar(G)
See Also
--------
:func:`~networkx.drawing.layout.planar_layout`
"""
draw(G, planar_layout(G), **kwargs)
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|
30,598 | networkx.drawing.nx_pylab | draw_random | Draw the graph `G` with a random layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.random_layout(G), **kwargs)
Parameters
----------
G : graph
A networkx graph
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Notes
-----
The layout is computed each time this function is called.
For repeated drawing it is much more efficient to call
`~networkx.drawing.layout.random_layout` directly and reuse the result::
>>> G = nx.complete_graph(5)
>>> pos = nx.random_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.lollipop_graph(4, 3)
>>> nx.draw_random(G)
See Also
--------
:func:`~networkx.drawing.layout.random_layout`
| def draw_random(G, **kwargs):
"""Draw the graph `G` with a random layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.random_layout(G), **kwargs)
Parameters
----------
G : graph
A networkx graph
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Notes
-----
The layout is computed each time this function is called.
For repeated drawing it is much more efficient to call
`~networkx.drawing.layout.random_layout` directly and reuse the result::
>>> G = nx.complete_graph(5)
>>> pos = nx.random_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.lollipop_graph(4, 3)
>>> nx.draw_random(G)
See Also
--------
:func:`~networkx.drawing.layout.random_layout`
"""
draw(G, random_layout(G), **kwargs)
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|
30,599 | networkx.drawing.nx_pylab | draw_shell | Draw networkx graph `G` with shell layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.shell_layout(G, nlist=nlist), **kwargs)
Parameters
----------
G : graph
A networkx graph
nlist : list of list of nodes, optional
A list containing lists of nodes representing the shells.
Default is `None`, meaning all nodes are in a single shell.
See `~networkx.drawing.layout.shell_layout` for details.
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Notes
-----
The layout is computed each time this function is called.
For repeated drawing it is much more efficient to call
`~networkx.drawing.layout.shell_layout` directly and reuse the result::
>>> G = nx.complete_graph(5)
>>> pos = nx.shell_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.path_graph(4)
>>> shells = [[0], [1, 2, 3]]
>>> nx.draw_shell(G, nlist=shells)
See Also
--------
:func:`~networkx.drawing.layout.shell_layout`
| def draw_shell(G, nlist=None, **kwargs):
"""Draw networkx graph `G` with shell layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.shell_layout(G, nlist=nlist), **kwargs)
Parameters
----------
G : graph
A networkx graph
nlist : list of list of nodes, optional
A list containing lists of nodes representing the shells.
Default is `None`, meaning all nodes are in a single shell.
See `~networkx.drawing.layout.shell_layout` for details.
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Notes
-----
The layout is computed each time this function is called.
For repeated drawing it is much more efficient to call
`~networkx.drawing.layout.shell_layout` directly and reuse the result::
>>> G = nx.complete_graph(5)
>>> pos = nx.shell_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.path_graph(4)
>>> shells = [[0], [1, 2, 3]]
>>> nx.draw_shell(G, nlist=shells)
See Also
--------
:func:`~networkx.drawing.layout.shell_layout`
"""
draw(G, shell_layout(G, nlist=nlist), **kwargs)
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|
30,600 | networkx.drawing.nx_pylab | draw_spectral | Draw the graph `G` with a spectral 2D layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.spectral_layout(G), **kwargs)
For more information about how node positions are determined, see
`~networkx.drawing.layout.spectral_layout`.
Parameters
----------
G : graph
A networkx graph
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Notes
-----
The layout is computed each time this function is called.
For repeated drawing it is much more efficient to call
`~networkx.drawing.layout.spectral_layout` directly and reuse the result::
>>> G = nx.complete_graph(5)
>>> pos = nx.spectral_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.path_graph(5)
>>> nx.draw_spectral(G)
See Also
--------
:func:`~networkx.drawing.layout.spectral_layout`
| def draw_spectral(G, **kwargs):
"""Draw the graph `G` with a spectral 2D layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.spectral_layout(G), **kwargs)
For more information about how node positions are determined, see
`~networkx.drawing.layout.spectral_layout`.
Parameters
----------
G : graph
A networkx graph
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Notes
-----
The layout is computed each time this function is called.
For repeated drawing it is much more efficient to call
`~networkx.drawing.layout.spectral_layout` directly and reuse the result::
>>> G = nx.complete_graph(5)
>>> pos = nx.spectral_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.path_graph(5)
>>> nx.draw_spectral(G)
See Also
--------
:func:`~networkx.drawing.layout.spectral_layout`
"""
draw(G, spectral_layout(G), **kwargs)
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|
30,601 | networkx.drawing.nx_pylab | draw_spring | Draw the graph `G` with a spring layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.spring_layout(G), **kwargs)
Parameters
----------
G : graph
A networkx graph
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Notes
-----
`~networkx.drawing.layout.spring_layout` is also the default layout for
`draw`, so this function is equivalent to `draw`.
The layout is computed each time this function is called.
For repeated drawing it is much more efficient to call
`~networkx.drawing.layout.spring_layout` directly and reuse the result::
>>> G = nx.complete_graph(5)
>>> pos = nx.spring_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.path_graph(20)
>>> nx.draw_spring(G)
See Also
--------
draw
:func:`~networkx.drawing.layout.spring_layout`
| def draw_spring(G, **kwargs):
"""Draw the graph `G` with a spring layout.
This is a convenience function equivalent to::
nx.draw(G, pos=nx.spring_layout(G), **kwargs)
Parameters
----------
G : graph
A networkx graph
kwargs : optional keywords
See `draw_networkx` for a description of optional keywords.
Notes
-----
`~networkx.drawing.layout.spring_layout` is also the default layout for
`draw`, so this function is equivalent to `draw`.
The layout is computed each time this function is called.
For repeated drawing it is much more efficient to call
`~networkx.drawing.layout.spring_layout` directly and reuse the result::
>>> G = nx.complete_graph(5)
>>> pos = nx.spring_layout(G)
>>> nx.draw(G, pos=pos) # Draw the original graph
>>> # Draw a subgraph, reusing the same node positions
>>> nx.draw(G.subgraph([0, 1, 2]), pos=pos, node_color="red")
Examples
--------
>>> G = nx.path_graph(20)
>>> nx.draw_spring(G)
See Also
--------
draw
:func:`~networkx.drawing.layout.spring_layout`
"""
draw(G, spring_layout(G), **kwargs)
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|
30,603 | networkx.generators.random_graphs | dual_barabasi_albert_graph | Returns a random graph using dual Barabási–Albert preferential attachment
A graph of $n$ nodes is grown by attaching new nodes each with either $m_1$
edges (with probability $p$) or $m_2$ edges (with probability $1-p$) that
are preferentially attached to existing nodes with high degree.
Parameters
----------
n : int
Number of nodes
m1 : int
Number of edges to link each new node to existing nodes with probability $p$
m2 : int
Number of edges to link each new node to existing nodes with probability $1-p$
p : float
The probability of attaching $m_1$ edges (as opposed to $m_2$ edges)
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
initial_graph : Graph or None (default)
Initial network for Barabási–Albert algorithm.
A copy of `initial_graph` is used.
It should be connected for most use cases.
If None, starts from an star graph on max(m1, m2) + 1 nodes.
Returns
-------
G : Graph
Raises
------
NetworkXError
If `m1` and `m2` do not satisfy ``1 <= m1,m2 < n``, or
`p` does not satisfy ``0 <= p <= 1``, or
the initial graph number of nodes m0 does not satisfy m1, m2 <= m0 <= n.
References
----------
.. [1] N. Moshiri "The dual-Barabasi-Albert model", arXiv:1810.10538.
| def dual_barabasi_albert_graph(n, m1, m2, p, seed=None, initial_graph=None):
"""Returns a random graph using dual Barabási–Albert preferential attachment
A graph of $n$ nodes is grown by attaching new nodes each with either $m_1$
edges (with probability $p$) or $m_2$ edges (with probability $1-p$) that
are preferentially attached to existing nodes with high degree.
Parameters
----------
n : int
Number of nodes
m1 : int
Number of edges to link each new node to existing nodes with probability $p$
m2 : int
Number of edges to link each new node to existing nodes with probability $1-p$
p : float
The probability of attaching $m_1$ edges (as opposed to $m_2$ edges)
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
initial_graph : Graph or None (default)
Initial network for Barabási–Albert algorithm.
A copy of `initial_graph` is used.
It should be connected for most use cases.
If None, starts from an star graph on max(m1, m2) + 1 nodes.
Returns
-------
G : Graph
Raises
------
NetworkXError
If `m1` and `m2` do not satisfy ``1 <= m1,m2 < n``, or
`p` does not satisfy ``0 <= p <= 1``, or
the initial graph number of nodes m0 does not satisfy m1, m2 <= m0 <= n.
References
----------
.. [1] N. Moshiri "The dual-Barabasi-Albert model", arXiv:1810.10538.
"""
if m1 < 1 or m1 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m1 >= 1 and m1 < n, m1 = {m1}, n = {n}"
)
if m2 < 1 or m2 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m2 >= 1 and m2 < n, m2 = {m2}, n = {n}"
)
if p < 0 or p > 1:
raise nx.NetworkXError(
f"Dual Barabási–Albert network must have 0 <= p <= 1, p = {p}"
)
# For simplicity, if p == 0 or 1, just return BA
if p == 1:
return barabasi_albert_graph(n, m1, seed)
elif p == 0:
return barabasi_albert_graph(n, m2, seed)
if initial_graph is None:
# Default initial graph : empty graph on max(m1, m2) nodes
G = star_graph(max(m1, m2))
else:
if len(initial_graph) < max(m1, m2) or len(initial_graph) > n:
raise nx.NetworkXError(
f"Barabási–Albert initial graph must have between "
f"max(m1, m2) = {max(m1, m2)} and n = {n} nodes"
)
G = initial_graph.copy()
# Target nodes for new edges
targets = list(G)
# List of existing nodes, with nodes repeated once for each adjacent edge
repeated_nodes = [n for n, d in G.degree() for _ in range(d)]
# Start adding the remaining nodes.
source = len(G)
while source < n:
# Pick which m to use (m1 or m2)
if seed.random() < p:
m = m1
else:
m = m2
# Now choose m unique nodes from the existing nodes
# Pick uniformly from repeated_nodes (preferential attachment)
targets = _random_subset(repeated_nodes, m, seed)
# Add edges to m nodes from the source.
G.add_edges_from(zip([source] * m, targets))
# Add one node to the list for each new edge just created.
repeated_nodes.extend(targets)
# And the new node "source" has m edges to add to the list.
repeated_nodes.extend([source] * m)
source += 1
return G
| (n, m1, m2, p, seed=None, initial_graph=None, *, backend=None, **backend_kwargs) | [
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|
30,606 | networkx.algorithms.distance_measures | eccentricity | Returns the eccentricity of nodes in G.
The eccentricity of a node v is the maximum distance from v to
all other nodes in G.
Parameters
----------
G : NetworkX graph
A graph
v : node, optional
Return value of specified node
sp : dict of dicts, optional
All pairs shortest path lengths as a dictionary of dictionaries
weight : string, function, or None (default=None)
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number.
If this is None, every edge has weight/distance/cost 1.
Weights stored as floating point values can lead to small round-off
errors in distances. Use integer weights to avoid this.
Weights should be positive, since they are distances.
Returns
-------
ecc : dictionary
A dictionary of eccentricity values keyed by node.
Examples
--------
>>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
>>> dict(nx.eccentricity(G))
{1: 2, 2: 3, 3: 2, 4: 2, 5: 3}
>>> dict(nx.eccentricity(G, v=[1, 5])) # This returns the eccentricity of node 1 & 5
{1: 2, 5: 3}
| def effective_graph_resistance(G, weight=None, invert_weight=True):
"""Returns the Effective graph resistance of G.
Also known as the Kirchhoff index.
The effective graph resistance is defined as the sum
of the resistance distance of every node pair in G [1]_.
If weight is not provided, then a weight of 1 is used for all edges.
The effective graph resistance of a disconnected graph is infinite.
Parameters
----------
G : NetworkX graph
A graph
weight : string or None, optional (default=None)
The edge data key used to compute the effective graph resistance.
If None, then each edge has weight 1.
invert_weight : boolean (default=True)
Proper calculation of resistance distance requires building the
Laplacian matrix with the reciprocal of the weight. Not required
if the weight is already inverted. Weight cannot be zero.
Returns
-------
RG : float
The effective graph resistance of `G`.
Raises
------
NetworkXNotImplemented
If `G` is a directed graph.
NetworkXError
If `G` does not contain any nodes.
Examples
--------
>>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
>>> round(nx.effective_graph_resistance(G), 10)
10.25
Notes
-----
The implementation is based on Theorem 2.2 in [2]_. Self-loops are ignored.
Multi-edges are contracted in one edge with weight equal to the harmonic sum of the weights.
References
----------
.. [1] Wolfram
"Kirchhoff Index."
https://mathworld.wolfram.com/KirchhoffIndex.html
.. [2] W. Ellens, F. M. Spieksma, P. Van Mieghem, A. Jamakovic, R. E. Kooij.
Effective graph resistance.
Lin. Alg. Appl. 435:2491-2506, 2011.
"""
import numpy as np
if len(G) == 0:
raise nx.NetworkXError("Graph G must contain at least one node.")
# Disconnected graphs have infinite Effective graph resistance
if not nx.is_connected(G):
return float("inf")
# Invert weights
G = G.copy()
if invert_weight and weight is not None:
if G.is_multigraph():
for u, v, k, d in G.edges(keys=True, data=True):
d[weight] = 1 / d[weight]
else:
for u, v, d in G.edges(data=True):
d[weight] = 1 / d[weight]
# Get Laplacian eigenvalues
mu = np.sort(nx.laplacian_spectrum(G, weight=weight))
# Compute Effective graph resistance based on spectrum of the Laplacian
# Self-loops are ignored
return float(np.sum(1 / mu[1:]) * G.number_of_nodes())
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]
|
30,611 | networkx.algorithms.connectivity.connectivity | edge_connectivity | Returns the edge connectivity of the graph or digraph G.
The edge connectivity is equal to the minimum number of edges that
must be removed to disconnect G or render it trivial. If source
and target nodes are provided, this function returns the local edge
connectivity: the minimum number of edges that must be removed to
break all paths from source to target in G.
Parameters
----------
G : NetworkX graph
Undirected or directed graph
s : node
Source node. Optional. Default value: None.
t : node
Target node. Optional. Default value: None.
flow_func : function
A function for computing the maximum flow among a pair of nodes.
The function has to accept at least three parameters: a Digraph,
a source node, and a target node. And return a residual network
that follows NetworkX conventions (see :meth:`maximum_flow` for
details). If flow_func is None, the default maximum flow function
(:meth:`edmonds_karp`) is used. See below for details. The
choice of the default function may change from version
to version and should not be relied on. Default value: None.
cutoff : integer, float, or None (default: None)
If specified, the maximum flow algorithm will terminate when the
flow value reaches or exceeds the cutoff. This only works for flows
that support the cutoff parameter (most do) and is ignored otherwise.
Returns
-------
K : integer
Edge connectivity for G, or local edge connectivity if source
and target were provided
Examples
--------
>>> # Platonic icosahedral graph is 5-edge-connected
>>> G = nx.icosahedral_graph()
>>> nx.edge_connectivity(G)
5
You can use alternative flow algorithms for the underlying
maximum flow computation. In dense networks the algorithm
:meth:`shortest_augmenting_path` will usually perform better
than the default :meth:`edmonds_karp`, which is faster for
sparse networks with highly skewed degree distributions.
Alternative flow functions have to be explicitly imported
from the flow package.
>>> from networkx.algorithms.flow import shortest_augmenting_path
>>> nx.edge_connectivity(G, flow_func=shortest_augmenting_path)
5
If you specify a pair of nodes (source and target) as parameters,
this function returns the value of local edge connectivity.
>>> nx.edge_connectivity(G, 3, 7)
5
If you need to perform several local computations among different
pairs of nodes on the same graph, it is recommended that you reuse
the data structures used in the maximum flow computations. See
:meth:`local_edge_connectivity` for details.
Notes
-----
This is a flow based implementation of global edge connectivity.
For undirected graphs the algorithm works by finding a 'small'
dominating set of nodes of G (see algorithm 7 in [1]_ ) and
computing local maximum flow (see :meth:`local_edge_connectivity`)
between an arbitrary node in the dominating set and the rest of
nodes in it. This is an implementation of algorithm 6 in [1]_ .
For directed graphs, the algorithm does n calls to the maximum
flow function. This is an implementation of algorithm 8 in [1]_ .
See also
--------
:meth:`local_edge_connectivity`
:meth:`local_node_connectivity`
:meth:`node_connectivity`
:meth:`maximum_flow`
:meth:`edmonds_karp`
:meth:`preflow_push`
:meth:`shortest_augmenting_path`
:meth:`k_edge_components`
:meth:`k_edge_subgraphs`
References
----------
.. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
| @nx._dispatchable
def edge_connectivity(G, s=None, t=None, flow_func=None, cutoff=None):
r"""Returns the edge connectivity of the graph or digraph G.
The edge connectivity is equal to the minimum number of edges that
must be removed to disconnect G or render it trivial. If source
and target nodes are provided, this function returns the local edge
connectivity: the minimum number of edges that must be removed to
break all paths from source to target in G.
Parameters
----------
G : NetworkX graph
Undirected or directed graph
s : node
Source node. Optional. Default value: None.
t : node
Target node. Optional. Default value: None.
flow_func : function
A function for computing the maximum flow among a pair of nodes.
The function has to accept at least three parameters: a Digraph,
a source node, and a target node. And return a residual network
that follows NetworkX conventions (see :meth:`maximum_flow` for
details). If flow_func is None, the default maximum flow function
(:meth:`edmonds_karp`) is used. See below for details. The
choice of the default function may change from version
to version and should not be relied on. Default value: None.
cutoff : integer, float, or None (default: None)
If specified, the maximum flow algorithm will terminate when the
flow value reaches or exceeds the cutoff. This only works for flows
that support the cutoff parameter (most do) and is ignored otherwise.
Returns
-------
K : integer
Edge connectivity for G, or local edge connectivity if source
and target were provided
Examples
--------
>>> # Platonic icosahedral graph is 5-edge-connected
>>> G = nx.icosahedral_graph()
>>> nx.edge_connectivity(G)
5
You can use alternative flow algorithms for the underlying
maximum flow computation. In dense networks the algorithm
:meth:`shortest_augmenting_path` will usually perform better
than the default :meth:`edmonds_karp`, which is faster for
sparse networks with highly skewed degree distributions.
Alternative flow functions have to be explicitly imported
from the flow package.
>>> from networkx.algorithms.flow import shortest_augmenting_path
>>> nx.edge_connectivity(G, flow_func=shortest_augmenting_path)
5
If you specify a pair of nodes (source and target) as parameters,
this function returns the value of local edge connectivity.
>>> nx.edge_connectivity(G, 3, 7)
5
If you need to perform several local computations among different
pairs of nodes on the same graph, it is recommended that you reuse
the data structures used in the maximum flow computations. See
:meth:`local_edge_connectivity` for details.
Notes
-----
This is a flow based implementation of global edge connectivity.
For undirected graphs the algorithm works by finding a 'small'
dominating set of nodes of G (see algorithm 7 in [1]_ ) and
computing local maximum flow (see :meth:`local_edge_connectivity`)
between an arbitrary node in the dominating set and the rest of
nodes in it. This is an implementation of algorithm 6 in [1]_ .
For directed graphs, the algorithm does n calls to the maximum
flow function. This is an implementation of algorithm 8 in [1]_ .
See also
--------
:meth:`local_edge_connectivity`
:meth:`local_node_connectivity`
:meth:`node_connectivity`
:meth:`maximum_flow`
:meth:`edmonds_karp`
:meth:`preflow_push`
:meth:`shortest_augmenting_path`
:meth:`k_edge_components`
:meth:`k_edge_subgraphs`
References
----------
.. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
"""
if (s is not None and t is None) or (s is None and t is not None):
raise nx.NetworkXError("Both source and target must be specified.")
# Local edge connectivity
if s is not None and t is not None:
if s not in G:
raise nx.NetworkXError(f"node {s} not in graph")
if t not in G:
raise nx.NetworkXError(f"node {t} not in graph")
return local_edge_connectivity(G, s, t, flow_func=flow_func, cutoff=cutoff)
# Global edge connectivity
# reuse auxiliary digraph and residual network
H = build_auxiliary_edge_connectivity(G)
R = build_residual_network(H, "capacity")
kwargs = {"flow_func": flow_func, "auxiliary": H, "residual": R}
if G.is_directed():
# Algorithm 8 in [1]
if not nx.is_weakly_connected(G):
return 0
# initial value for \lambda is minimum degree
L = min(d for n, d in G.degree())
nodes = list(G)
n = len(nodes)
if cutoff is not None:
L = min(cutoff, L)
for i in range(n):
kwargs["cutoff"] = L
try:
L = min(L, local_edge_connectivity(G, nodes[i], nodes[i + 1], **kwargs))
except IndexError: # last node!
L = min(L, local_edge_connectivity(G, nodes[i], nodes[0], **kwargs))
return L
else: # undirected
# Algorithm 6 in [1]
if not nx.is_connected(G):
return 0
# initial value for \lambda is minimum degree
L = min(d for n, d in G.degree())
if cutoff is not None:
L = min(cutoff, L)
# A dominating set is \lambda-covering
# We need a dominating set with at least two nodes
for node in G:
D = nx.dominating_set(G, start_with=node)
v = D.pop()
if D:
break
else:
# in complete graphs the dominating sets will always be of one node
# thus we return min degree
return L
for w in D:
kwargs["cutoff"] = L
L = min(L, local_edge_connectivity(G, v, w, **kwargs))
return L
| (G, s=None, t=None, flow_func=None, cutoff=None, *, backend=None, **backend_kwargs) | [
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|
30,618 | networkx.classes.function | edge_subgraph | Returns a view of the subgraph induced by the specified edges.
The induced subgraph contains each edge in `edges` and each
node incident to any of those edges.
Parameters
----------
G : NetworkX Graph
edges : iterable
An iterable of edges. Edges not present in `G` are ignored.
Returns
-------
subgraph : SubGraph View
A read-only edge-induced subgraph of `G`.
Changes to `G` are reflected in the view.
Notes
-----
To create a mutable subgraph with its own copies of nodes
edges and attributes use `subgraph.copy()` or `Graph(subgraph)`
If you create a subgraph of a subgraph recursively you can end up
with a chain of subgraphs that becomes very slow with about 15
nested subgraph views. Luckily the edge_subgraph filter nests
nicely so you can use the original graph as G in this function
to avoid chains. We do not rule out chains programmatically so
that odd cases like an `edge_subgraph` of a `restricted_view`
can be created.
Examples
--------
>>> G = nx.path_graph(5)
>>> H = G.edge_subgraph([(0, 1), (3, 4)])
>>> list(H.nodes)
[0, 1, 3, 4]
>>> list(H.edges)
[(0, 1), (3, 4)]
| def edge_subgraph(G, edges):
"""Returns a view of the subgraph induced by the specified edges.
The induced subgraph contains each edge in `edges` and each
node incident to any of those edges.
Parameters
----------
G : NetworkX Graph
edges : iterable
An iterable of edges. Edges not present in `G` are ignored.
Returns
-------
subgraph : SubGraph View
A read-only edge-induced subgraph of `G`.
Changes to `G` are reflected in the view.
Notes
-----
To create a mutable subgraph with its own copies of nodes
edges and attributes use `subgraph.copy()` or `Graph(subgraph)`
If you create a subgraph of a subgraph recursively you can end up
with a chain of subgraphs that becomes very slow with about 15
nested subgraph views. Luckily the edge_subgraph filter nests
nicely so you can use the original graph as G in this function
to avoid chains. We do not rule out chains programmatically so
that odd cases like an `edge_subgraph` of a `restricted_view`
can be created.
Examples
--------
>>> G = nx.path_graph(5)
>>> H = G.edge_subgraph([(0, 1), (3, 4)])
>>> list(H.nodes)
[0, 1, 3, 4]
>>> list(H.edges)
[(0, 1), (3, 4)]
"""
nxf = nx.filters
edges = set(edges)
nodes = set()
for e in edges:
nodes.update(e[:2])
induced_nodes = nxf.show_nodes(nodes)
if G.is_multigraph():
if G.is_directed():
induced_edges = nxf.show_multidiedges(edges)
else:
induced_edges = nxf.show_multiedges(edges)
else:
if G.is_directed():
induced_edges = nxf.show_diedges(edges)
else:
induced_edges = nxf.show_edges(edges)
return nx.subgraph_view(G, filter_node=induced_nodes, filter_edge=induced_edges)
| (G, edges) | [
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|
30,622 | networkx.classes.function | edges | Returns an edge view of edges incident to nodes in nbunch.
Return all edges if nbunch is unspecified or nbunch=None.
For digraphs, edges=out_edges
This function wraps the :func:`G.edges <networkx.Graph.edges>` property.
| def edges(G, nbunch=None):
"""Returns an edge view of edges incident to nodes in nbunch.
Return all edges if nbunch is unspecified or nbunch=None.
For digraphs, edges=out_edges
This function wraps the :func:`G.edges <networkx.Graph.edges>` property.
"""
return G.edges(nbunch)
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|
30,623 | networkx.algorithms.distance_measures | effective_graph_resistance | Returns the Effective graph resistance of G.
Also known as the Kirchhoff index.
The effective graph resistance is defined as the sum
of the resistance distance of every node pair in G [1]_.
If weight is not provided, then a weight of 1 is used for all edges.
The effective graph resistance of a disconnected graph is infinite.
Parameters
----------
G : NetworkX graph
A graph
weight : string or None, optional (default=None)
The edge data key used to compute the effective graph resistance.
If None, then each edge has weight 1.
invert_weight : boolean (default=True)
Proper calculation of resistance distance requires building the
Laplacian matrix with the reciprocal of the weight. Not required
if the weight is already inverted. Weight cannot be zero.
Returns
-------
RG : float
The effective graph resistance of `G`.
Raises
------
NetworkXNotImplemented
If `G` is a directed graph.
NetworkXError
If `G` does not contain any nodes.
Examples
--------
>>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
>>> round(nx.effective_graph_resistance(G), 10)
10.25
Notes
-----
The implementation is based on Theorem 2.2 in [2]_. Self-loops are ignored.
Multi-edges are contracted in one edge with weight equal to the harmonic sum of the weights.
References
----------
.. [1] Wolfram
"Kirchhoff Index."
https://mathworld.wolfram.com/KirchhoffIndex.html
.. [2] W. Ellens, F. M. Spieksma, P. Van Mieghem, A. Jamakovic, R. E. Kooij.
Effective graph resistance.
Lin. Alg. Appl. 435:2491-2506, 2011.
| def effective_graph_resistance(G, weight=None, invert_weight=True):
"""Returns the Effective graph resistance of G.
Also known as the Kirchhoff index.
The effective graph resistance is defined as the sum
of the resistance distance of every node pair in G [1]_.
If weight is not provided, then a weight of 1 is used for all edges.
The effective graph resistance of a disconnected graph is infinite.
Parameters
----------
G : NetworkX graph
A graph
weight : string or None, optional (default=None)
The edge data key used to compute the effective graph resistance.
If None, then each edge has weight 1.
invert_weight : boolean (default=True)
Proper calculation of resistance distance requires building the
Laplacian matrix with the reciprocal of the weight. Not required
if the weight is already inverted. Weight cannot be zero.
Returns
-------
RG : float
The effective graph resistance of `G`.
Raises
------
NetworkXNotImplemented
If `G` is a directed graph.
NetworkXError
If `G` does not contain any nodes.
Examples
--------
>>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)])
>>> round(nx.effective_graph_resistance(G), 10)
10.25
Notes
-----
The implementation is based on Theorem 2.2 in [2]_. Self-loops are ignored.
Multi-edges are contracted in one edge with weight equal to the harmonic sum of the weights.
References
----------
.. [1] Wolfram
"Kirchhoff Index."
https://mathworld.wolfram.com/KirchhoffIndex.html
.. [2] W. Ellens, F. M. Spieksma, P. Van Mieghem, A. Jamakovic, R. E. Kooij.
Effective graph resistance.
Lin. Alg. Appl. 435:2491-2506, 2011.
"""
import numpy as np
if len(G) == 0:
raise nx.NetworkXError("Graph G must contain at least one node.")
# Disconnected graphs have infinite Effective graph resistance
if not nx.is_connected(G):
return float("inf")
# Invert weights
G = G.copy()
if invert_weight and weight is not None:
if G.is_multigraph():
for u, v, k, d in G.edges(keys=True, data=True):
d[weight] = 1 / d[weight]
else:
for u, v, d in G.edges(data=True):
d[weight] = 1 / d[weight]
# Get Laplacian eigenvalues
mu = np.sort(nx.laplacian_spectrum(G, weight=weight))
# Compute Effective graph resistance based on spectrum of the Laplacian
# Self-loops are ignored
return float(np.sum(1 / mu[1:]) * G.number_of_nodes())
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|
30,632 | networkx.generators.classic | empty_graph | Returns the empty graph with n nodes and zero edges.
.. plot::
>>> nx.draw(nx.empty_graph(5))
Parameters
----------
n : int or iterable container of nodes (default = 0)
If n is an integer, nodes are from `range(n)`.
If n is a container of nodes, those nodes appear in the graph.
create_using : Graph Instance, Constructor or None
Indicator of type of graph to return.
If a Graph-type instance, then clear and use it.
If None, use the `default` constructor.
If a constructor, call it to create an empty graph.
default : Graph constructor (optional, default = nx.Graph)
The constructor to use if create_using is None.
If None, then nx.Graph is used.
This is used when passing an unknown `create_using` value
through your home-grown function to `empty_graph` and
you want a default constructor other than nx.Graph.
Examples
--------
>>> G = nx.empty_graph(10)
>>> G.number_of_nodes()
10
>>> G.number_of_edges()
0
>>> G = nx.empty_graph("ABC")
>>> G.number_of_nodes()
3
>>> sorted(G)
['A', 'B', 'C']
Notes
-----
The variable create_using should be a Graph Constructor or a
"graph"-like object. Constructors, e.g. `nx.Graph` or `nx.MultiGraph`
will be used to create the returned graph. "graph"-like objects
will be cleared (nodes and edges will be removed) and refitted as
an empty "graph" with nodes specified in n. This capability
is useful for specifying the class-nature of the resulting empty
"graph" (i.e. Graph, DiGraph, MyWeirdGraphClass, etc.).
The variable create_using has three main uses:
Firstly, the variable create_using can be used to create an
empty digraph, multigraph, etc. For example,
>>> n = 10
>>> G = nx.empty_graph(n, create_using=nx.DiGraph)
will create an empty digraph on n nodes.
Secondly, one can pass an existing graph (digraph, multigraph,
etc.) via create_using. For example, if G is an existing graph
(resp. digraph, multigraph, etc.), then empty_graph(n, create_using=G)
will empty G (i.e. delete all nodes and edges using G.clear())
and then add n nodes and zero edges, and return the modified graph.
Thirdly, when constructing your home-grown graph creation function
you can use empty_graph to construct the graph by passing a user
defined create_using to empty_graph. In this case, if you want the
default constructor to be other than nx.Graph, specify `default`.
>>> def mygraph(n, create_using=None):
... G = nx.empty_graph(n, create_using, nx.MultiGraph)
... G.add_edges_from([(0, 1), (0, 1)])
... return G
>>> G = mygraph(3)
>>> G.is_multigraph()
True
>>> G = mygraph(3, nx.Graph)
>>> G.is_multigraph()
False
See also create_empty_copy(G).
| def star_graph(n, create_using=None):
"""Return the star graph
The star graph consists of one center node connected to n outer nodes.
.. plot::
>>> nx.draw(nx.star_graph(6))
Parameters
----------
n : int or iterable
If an integer, node labels are 0 to n with center 0.
If an iterable of nodes, the center is the first.
Warning: n is not checked for duplicates and if present the
resulting graph may not be as desired. Make sure you have no duplicates.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Notes
-----
The graph has n+1 nodes for integer n.
So star_graph(3) is the same as star_graph(range(4)).
"""
n, nodes = n
if isinstance(n, numbers.Integral):
nodes.append(int(n)) # there should be n+1 nodes
G = empty_graph(nodes, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
if len(nodes) > 1:
hub, *spokes = nodes
G.add_edges_from((hub, node) for node in spokes)
return G
| (n=0, create_using=None, default=<class 'networkx.classes.graph.Graph'>, *, backend=None, **backend_kwargs) | [
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|
30,635 | networkx.algorithms.minors.contraction | equivalence_classes | Returns equivalence classes of `relation` when applied to `iterable`.
The equivalence classes, or blocks, consist of objects from `iterable`
which are all equivalent. They are defined to be equivalent if the
`relation` function returns `True` when passed any two objects from that
class, and `False` otherwise. To define an equivalence relation the
function must be reflexive, symmetric and transitive.
Parameters
----------
iterable : list, tuple, or set
An iterable of elements/nodes.
relation : function
A Boolean-valued function that implements an equivalence relation
(reflexive, symmetric, transitive binary relation) on the elements
of `iterable` - it must take two elements and return `True` if
they are related, or `False` if not.
Returns
-------
set of frozensets
A set of frozensets representing the partition induced by the equivalence
relation function `relation` on the elements of `iterable`. Each
member set in the return set represents an equivalence class, or
block, of the partition.
Duplicate elements will be ignored so it makes the most sense for
`iterable` to be a :class:`set`.
Notes
-----
This function does not check that `relation` represents an equivalence
relation. You can check that your equivalence classes provide a partition
using `is_partition`.
Examples
--------
Let `X` be the set of integers from `0` to `9`, and consider an equivalence
relation `R` on `X` of congruence modulo `3`: this means that two integers
`x` and `y` in `X` are equivalent under `R` if they leave the same
remainder when divided by `3`, i.e. `(x - y) mod 3 = 0`.
The equivalence classes of this relation are `{0, 3, 6, 9}`, `{1, 4, 7}`,
`{2, 5, 8}`: `0`, `3`, `6`, `9` are all divisible by `3` and leave zero
remainder; `1`, `4`, `7` leave remainder `1`; while `2`, `5` and `8` leave
remainder `2`. We can see this by calling `equivalence_classes` with
`X` and a function implementation of `R`.
>>> X = set(range(10))
>>> def mod3(x, y):
... return (x - y) % 3 == 0
>>> equivalence_classes(X, mod3) # doctest: +SKIP
{frozenset({1, 4, 7}), frozenset({8, 2, 5}), frozenset({0, 9, 3, 6})}
| def equivalence_classes(iterable, relation):
"""Returns equivalence classes of `relation` when applied to `iterable`.
The equivalence classes, or blocks, consist of objects from `iterable`
which are all equivalent. They are defined to be equivalent if the
`relation` function returns `True` when passed any two objects from that
class, and `False` otherwise. To define an equivalence relation the
function must be reflexive, symmetric and transitive.
Parameters
----------
iterable : list, tuple, or set
An iterable of elements/nodes.
relation : function
A Boolean-valued function that implements an equivalence relation
(reflexive, symmetric, transitive binary relation) on the elements
of `iterable` - it must take two elements and return `True` if
they are related, or `False` if not.
Returns
-------
set of frozensets
A set of frozensets representing the partition induced by the equivalence
relation function `relation` on the elements of `iterable`. Each
member set in the return set represents an equivalence class, or
block, of the partition.
Duplicate elements will be ignored so it makes the most sense for
`iterable` to be a :class:`set`.
Notes
-----
This function does not check that `relation` represents an equivalence
relation. You can check that your equivalence classes provide a partition
using `is_partition`.
Examples
--------
Let `X` be the set of integers from `0` to `9`, and consider an equivalence
relation `R` on `X` of congruence modulo `3`: this means that two integers
`x` and `y` in `X` are equivalent under `R` if they leave the same
remainder when divided by `3`, i.e. `(x - y) mod 3 = 0`.
The equivalence classes of this relation are `{0, 3, 6, 9}`, `{1, 4, 7}`,
`{2, 5, 8}`: `0`, `3`, `6`, `9` are all divisible by `3` and leave zero
remainder; `1`, `4`, `7` leave remainder `1`; while `2`, `5` and `8` leave
remainder `2`. We can see this by calling `equivalence_classes` with
`X` and a function implementation of `R`.
>>> X = set(range(10))
>>> def mod3(x, y):
... return (x - y) % 3 == 0
>>> equivalence_classes(X, mod3) # doctest: +SKIP
{frozenset({1, 4, 7}), frozenset({8, 2, 5}), frozenset({0, 9, 3, 6})}
"""
# For simplicity of implementation, we initialize the return value as a
# list of lists, then convert it to a set of sets at the end of the
# function.
blocks = []
# Determine the equivalence class for each element of the iterable.
for y in iterable:
# Each element y must be in *exactly one* equivalence class.
#
# Each block is guaranteed to be non-empty
for block in blocks:
x = arbitrary_element(block)
if relation(x, y):
block.append(y)
break
else:
# If the element y is not part of any known equivalence class, it
# must be in its own, so we create a new singleton equivalence
# class for it.
blocks.append([y])
return {frozenset(block) for block in blocks}
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|
30,644 | networkx.generators.degree_seq | expected_degree_graph | Returns a random graph with given expected degrees.
Given a sequence of expected degrees $W=(w_0,w_1,\ldots,w_{n-1})$
of length $n$ this algorithm assigns an edge between node $u$ and
node $v$ with probability
.. math::
p_{uv} = \frac{w_u w_v}{\sum_k w_k} .
Parameters
----------
w : list
The list of expected degrees.
selfloops: bool (default=True)
Set to False to remove the possibility of self-loop edges.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
Returns
-------
Graph
Examples
--------
>>> z = [10 for i in range(100)]
>>> G = nx.expected_degree_graph(z)
Notes
-----
The nodes have integer labels corresponding to index of expected degrees
input sequence.
The complexity of this algorithm is $\mathcal{O}(n+m)$ where $n$ is the
number of nodes and $m$ is the expected number of edges.
The model in [1]_ includes the possibility of self-loop edges.
Set selfloops=False to produce a graph without self loops.
For finite graphs this model doesn't produce exactly the given
expected degree sequence. Instead the expected degrees are as
follows.
For the case without self loops (selfloops=False),
.. math::
E[deg(u)] = \sum_{v \ne u} p_{uv}
= w_u \left( 1 - \frac{w_u}{\sum_k w_k} \right) .
NetworkX uses the standard convention that a self-loop edge counts 2
in the degree of a node, so with self loops (selfloops=True),
.. math::
E[deg(u)] = \sum_{v \ne u} p_{uv} + 2 p_{uu}
= w_u \left( 1 + \frac{w_u}{\sum_k w_k} \right) .
References
----------
.. [1] Fan Chung and L. Lu, Connected components in random graphs with
given expected degree sequences, Ann. Combinatorics, 6,
pp. 125-145, 2002.
.. [2] Joel Miller and Aric Hagberg,
Efficient generation of networks with given expected degrees,
in Algorithms and Models for the Web-Graph (WAW 2011),
Alan Frieze, Paul Horn, and Paweł Prałat (Eds), LNCS 6732,
pp. 115-126, 2011.
| def generate(self):
# remaining_degree is mapping from int->remaining degree
self.remaining_degree = dict(enumerate(self.degree))
# add all nodes to make sure we get isolated nodes
self.graph = nx.Graph()
self.graph.add_nodes_from(self.remaining_degree)
# remove zero degree nodes
for n, d in list(self.remaining_degree.items()):
if d == 0:
del self.remaining_degree[n]
if len(self.remaining_degree) > 0:
# build graph in three phases according to how many unmatched edges
self.phase1()
self.phase2()
self.phase3()
return self.graph
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|
30,645 | networkx.generators.random_graphs | extended_barabasi_albert_graph | Returns an extended Barabási–Albert model graph.
An extended Barabási–Albert model graph is a random graph constructed
using preferential attachment. The extended model allows new edges,
rewired edges or new nodes. Based on the probabilities $p$ and $q$
with $p + q < 1$, the growing behavior of the graph is determined as:
1) With $p$ probability, $m$ new edges are added to the graph,
starting from randomly chosen existing nodes and attached preferentially at the other end.
2) With $q$ probability, $m$ existing edges are rewired
by randomly choosing an edge and rewiring one end to a preferentially chosen node.
3) With $(1 - p - q)$ probability, $m$ new nodes are added to the graph
with edges attached preferentially.
When $p = q = 0$, the model behaves just like the Barabási–Alber model.
Parameters
----------
n : int
Number of nodes
m : int
Number of edges with which a new node attaches to existing nodes
p : float
Probability value for adding an edge between existing nodes. p + q < 1
q : float
Probability value of rewiring of existing edges. p + q < 1
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
Returns
-------
G : Graph
Raises
------
NetworkXError
If `m` does not satisfy ``1 <= m < n`` or ``1 >= p + q``
References
----------
.. [1] Albert, R., & Barabási, A. L. (2000)
Topology of evolving networks: local events and universality
Physical review letters, 85(24), 5234.
| def dual_barabasi_albert_graph(n, m1, m2, p, seed=None, initial_graph=None):
"""Returns a random graph using dual Barabási–Albert preferential attachment
A graph of $n$ nodes is grown by attaching new nodes each with either $m_1$
edges (with probability $p$) or $m_2$ edges (with probability $1-p$) that
are preferentially attached to existing nodes with high degree.
Parameters
----------
n : int
Number of nodes
m1 : int
Number of edges to link each new node to existing nodes with probability $p$
m2 : int
Number of edges to link each new node to existing nodes with probability $1-p$
p : float
The probability of attaching $m_1$ edges (as opposed to $m_2$ edges)
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
initial_graph : Graph or None (default)
Initial network for Barabási–Albert algorithm.
A copy of `initial_graph` is used.
It should be connected for most use cases.
If None, starts from an star graph on max(m1, m2) + 1 nodes.
Returns
-------
G : Graph
Raises
------
NetworkXError
If `m1` and `m2` do not satisfy ``1 <= m1,m2 < n``, or
`p` does not satisfy ``0 <= p <= 1``, or
the initial graph number of nodes m0 does not satisfy m1, m2 <= m0 <= n.
References
----------
.. [1] N. Moshiri "The dual-Barabasi-Albert model", arXiv:1810.10538.
"""
if m1 < 1 or m1 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m1 >= 1 and m1 < n, m1 = {m1}, n = {n}"
)
if m2 < 1 or m2 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m2 >= 1 and m2 < n, m2 = {m2}, n = {n}"
)
if p < 0 or p > 1:
raise nx.NetworkXError(
f"Dual Barabási–Albert network must have 0 <= p <= 1, p = {p}"
)
# For simplicity, if p == 0 or 1, just return BA
if p == 1:
return barabasi_albert_graph(n, m1, seed)
elif p == 0:
return barabasi_albert_graph(n, m2, seed)
if initial_graph is None:
# Default initial graph : empty graph on max(m1, m2) nodes
G = star_graph(max(m1, m2))
else:
if len(initial_graph) < max(m1, m2) or len(initial_graph) > n:
raise nx.NetworkXError(
f"Barabási–Albert initial graph must have between "
f"max(m1, m2) = {max(m1, m2)} and n = {n} nodes"
)
G = initial_graph.copy()
# Target nodes for new edges
targets = list(G)
# List of existing nodes, with nodes repeated once for each adjacent edge
repeated_nodes = [n for n, d in G.degree() for _ in range(d)]
# Start adding the remaining nodes.
source = len(G)
while source < n:
# Pick which m to use (m1 or m2)
if seed.random() < p:
m = m1
else:
m = m2
# Now choose m unique nodes from the existing nodes
# Pick uniformly from repeated_nodes (preferential attachment)
targets = _random_subset(repeated_nodes, m, seed)
# Add edges to m nodes from the source.
G.add_edges_from(zip([source] * m, targets))
# Add one node to the list for each new edge just created.
repeated_nodes.extend(targets)
# And the new node "source" has m edges to add to the list.
repeated_nodes.extend([source] * m)
source += 1
return G
| (n, m, p, q, seed=None, *, backend=None, **backend_kwargs) | [
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|
30,647 | networkx.generators.random_graphs | fast_gnp_random_graph | Returns a $G_{n,p}$ random graph, also known as an Erdős-Rényi graph or
a binomial graph.
Parameters
----------
n : int
The number of nodes.
p : float
Probability for edge creation.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
directed : bool, optional (default=False)
If True, this function returns a directed graph.
Notes
-----
The $G_{n,p}$ graph algorithm chooses each of the $[n (n - 1)] / 2$
(undirected) or $n (n - 1)$ (directed) possible edges with probability $p$.
This algorithm [1]_ runs in $O(n + m)$ time, where `m` is the expected number of
edges, which equals $p n (n - 1) / 2$. This should be faster than
:func:`gnp_random_graph` when $p$ is small and the expected number of edges
is small (that is, the graph is sparse).
See Also
--------
gnp_random_graph
References
----------
.. [1] Vladimir Batagelj and Ulrik Brandes,
"Efficient generation of large random networks",
Phys. Rev. E, 71, 036113, 2005.
| def dual_barabasi_albert_graph(n, m1, m2, p, seed=None, initial_graph=None):
"""Returns a random graph using dual Barabási–Albert preferential attachment
A graph of $n$ nodes is grown by attaching new nodes each with either $m_1$
edges (with probability $p$) or $m_2$ edges (with probability $1-p$) that
are preferentially attached to existing nodes with high degree.
Parameters
----------
n : int
Number of nodes
m1 : int
Number of edges to link each new node to existing nodes with probability $p$
m2 : int
Number of edges to link each new node to existing nodes with probability $1-p$
p : float
The probability of attaching $m_1$ edges (as opposed to $m_2$ edges)
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
initial_graph : Graph or None (default)
Initial network for Barabási–Albert algorithm.
A copy of `initial_graph` is used.
It should be connected for most use cases.
If None, starts from an star graph on max(m1, m2) + 1 nodes.
Returns
-------
G : Graph
Raises
------
NetworkXError
If `m1` and `m2` do not satisfy ``1 <= m1,m2 < n``, or
`p` does not satisfy ``0 <= p <= 1``, or
the initial graph number of nodes m0 does not satisfy m1, m2 <= m0 <= n.
References
----------
.. [1] N. Moshiri "The dual-Barabasi-Albert model", arXiv:1810.10538.
"""
if m1 < 1 or m1 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m1 >= 1 and m1 < n, m1 = {m1}, n = {n}"
)
if m2 < 1 or m2 >= n:
raise nx.NetworkXError(
f"Dual Barabási–Albert must have m2 >= 1 and m2 < n, m2 = {m2}, n = {n}"
)
if p < 0 or p > 1:
raise nx.NetworkXError(
f"Dual Barabási–Albert network must have 0 <= p <= 1, p = {p}"
)
# For simplicity, if p == 0 or 1, just return BA
if p == 1:
return barabasi_albert_graph(n, m1, seed)
elif p == 0:
return barabasi_albert_graph(n, m2, seed)
if initial_graph is None:
# Default initial graph : empty graph on max(m1, m2) nodes
G = star_graph(max(m1, m2))
else:
if len(initial_graph) < max(m1, m2) or len(initial_graph) > n:
raise nx.NetworkXError(
f"Barabási–Albert initial graph must have between "
f"max(m1, m2) = {max(m1, m2)} and n = {n} nodes"
)
G = initial_graph.copy()
# Target nodes for new edges
targets = list(G)
# List of existing nodes, with nodes repeated once for each adjacent edge
repeated_nodes = [n for n, d in G.degree() for _ in range(d)]
# Start adding the remaining nodes.
source = len(G)
while source < n:
# Pick which m to use (m1 or m2)
if seed.random() < p:
m = m1
else:
m = m2
# Now choose m unique nodes from the existing nodes
# Pick uniformly from repeated_nodes (preferential attachment)
targets = _random_subset(repeated_nodes, m, seed)
# Add edges to m nodes from the source.
G.add_edges_from(zip([source] * m, targets))
# Add one node to the list for each new edge just created.
repeated_nodes.extend(targets)
# And the new node "source" has m edges to add to the list.
repeated_nodes.extend([source] * m)
source += 1
return G
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|
30,654 | networkx.algorithms.cycles | find_cycle | Returns a cycle found via depth-first traversal.
The cycle is a list of edges indicating the cyclic path.
Orientation of directed edges is controlled by `orientation`.
Parameters
----------
G : graph
A directed/undirected graph/multigraph.
source : node, list of nodes
The node from which the traversal begins. If None, then a source
is chosen arbitrarily and repeatedly until all edges from each node in
the graph are searched.
orientation : None | 'original' | 'reverse' | 'ignore' (default: None)
For directed graphs and directed multigraphs, edge traversals need not
respect the original orientation of the edges.
When set to 'reverse' every edge is traversed in the reverse direction.
When set to 'ignore', every edge is treated as undirected.
When set to 'original', every edge is treated as directed.
In all three cases, the yielded edge tuples add a last entry to
indicate the direction in which that edge was traversed.
If orientation is None, the yielded edge has no direction indicated.
The direction is respected, but not reported.
Returns
-------
edges : directed edges
A list of directed edges indicating the path taken for the loop.
If no cycle is found, then an exception is raised.
For graphs, an edge is of the form `(u, v)` where `u` and `v`
are the tail and head of the edge as determined by the traversal.
For multigraphs, an edge is of the form `(u, v, key)`, where `key` is
the key of the edge. When the graph is directed, then `u` and `v`
are always in the order of the actual directed edge.
If orientation is not None then the edge tuple is extended to include
the direction of traversal ('forward' or 'reverse') on that edge.
Raises
------
NetworkXNoCycle
If no cycle was found.
Examples
--------
In this example, we construct a DAG and find, in the first call, that there
are no directed cycles, and so an exception is raised. In the second call,
we ignore edge orientations and find that there is an undirected cycle.
Note that the second call finds a directed cycle while effectively
traversing an undirected graph, and so, we found an "undirected cycle".
This means that this DAG structure does not form a directed tree (which
is also known as a polytree).
>>> G = nx.DiGraph([(0, 1), (0, 2), (1, 2)])
>>> nx.find_cycle(G, orientation="original")
Traceback (most recent call last):
...
networkx.exception.NetworkXNoCycle: No cycle found.
>>> list(nx.find_cycle(G, orientation="ignore"))
[(0, 1, 'forward'), (1, 2, 'forward'), (0, 2, 'reverse')]
See Also
--------
simple_cycles
| def recursive_simple_cycles(G):
"""Find simple cycles (elementary circuits) of a directed graph.
A `simple cycle`, or `elementary circuit`, is a closed path where
no node appears twice. Two elementary circuits are distinct if they
are not cyclic permutations of each other.
This version uses a recursive algorithm to build a list of cycles.
You should probably use the iterator version called simple_cycles().
Warning: This recursive version uses lots of RAM!
It appears in NetworkX for pedagogical value.
Parameters
----------
G : NetworkX DiGraph
A directed graph
Returns
-------
A list of cycles, where each cycle is represented by a list of nodes
along the cycle.
Example:
>>> edges = [(0, 0), (0, 1), (0, 2), (1, 2), (2, 0), (2, 1), (2, 2)]
>>> G = nx.DiGraph(edges)
>>> nx.recursive_simple_cycles(G)
[[0], [2], [0, 1, 2], [0, 2], [1, 2]]
Notes
-----
The implementation follows pp. 79-80 in [1]_.
The time complexity is $O((n+e)(c+1))$ for $n$ nodes, $e$ edges and $c$
elementary circuits.
References
----------
.. [1] Finding all the elementary circuits of a directed graph.
D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975.
https://doi.org/10.1137/0204007
See Also
--------
simple_cycles, cycle_basis
"""
# Jon Olav Vik, 2010-08-09
def _unblock(thisnode):
"""Recursively unblock and remove nodes from B[thisnode]."""
if blocked[thisnode]:
blocked[thisnode] = False
while B[thisnode]:
_unblock(B[thisnode].pop())
def circuit(thisnode, startnode, component):
closed = False # set to True if elementary path is closed
path.append(thisnode)
blocked[thisnode] = True
for nextnode in component[thisnode]: # direct successors of thisnode
if nextnode == startnode:
result.append(path[:])
closed = True
elif not blocked[nextnode]:
if circuit(nextnode, startnode, component):
closed = True
if closed:
_unblock(thisnode)
else:
for nextnode in component[thisnode]:
if thisnode not in B[nextnode]: # TODO: use set for speedup?
B[nextnode].append(thisnode)
path.pop() # remove thisnode from path
return closed
path = [] # stack of nodes in current path
blocked = defaultdict(bool) # vertex: blocked from search?
B = defaultdict(list) # graph portions that yield no elementary circuit
result = [] # list to accumulate the circuits found
# Johnson's algorithm exclude self cycle edges like (v, v)
# To be backward compatible, we record those cycles in advance
# and then remove from subG
for v in G:
if G.has_edge(v, v):
result.append([v])
G.remove_edge(v, v)
# Johnson's algorithm requires some ordering of the nodes.
# They might not be sortable so we assign an arbitrary ordering.
ordering = dict(zip(G, range(len(G))))
for s in ordering:
# Build the subgraph induced by s and following nodes in the ordering
subgraph = G.subgraph(node for node in G if ordering[node] >= ordering[s])
# Find the strongly connected component in the subgraph
# that contains the least node according to the ordering
strongcomp = nx.strongly_connected_components(subgraph)
mincomp = min(strongcomp, key=lambda ns: min(ordering[n] for n in ns))
component = G.subgraph(mincomp)
if len(component) > 1:
# smallest node in the component according to the ordering
startnode = min(component, key=ordering.__getitem__)
for node in component:
blocked[node] = False
B[node][:] = []
dummy = circuit(startnode, startnode, component)
return result
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|
30,657 | networkx.algorithms.shortest_paths.weighted | find_negative_cycle | Returns a cycle with negative total weight if it exists.
Bellman-Ford is used to find shortest_paths. That algorithm
stops if there exists a negative cycle. This algorithm
picks up from there and returns the found negative cycle.
The cycle consists of a list of nodes in the cycle order. The last
node equals the first to make it a cycle.
You can look up the edge weights in the original graph. In the case
of multigraphs the relevant edge is the minimal weight edge between
the nodes in the 2-tuple.
If the graph has no negative cycle, a NetworkXError is raised.
Parameters
----------
G : NetworkX graph
source: node label
The search for the negative cycle will start from this node.
weight : string or function
If this is a string, then edge weights will be accessed via the
edge attribute with this key (that is, the weight of the edge
joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
such edge attribute exists, the weight of the edge is assumed to
be one.
If this is a function, the weight of an edge is the value
returned by the function. The function must accept exactly three
positional arguments: the two endpoints of an edge and the
dictionary of edge attributes for that edge. The function must
return a number.
Examples
--------
>>> G = nx.DiGraph()
>>> G.add_weighted_edges_from([(0, 1, 2), (1, 2, 2), (2, 0, 1), (1, 4, 2), (4, 0, -5)])
>>> nx.find_negative_cycle(G, 0)
[4, 0, 1, 4]
Returns
-------
cycle : list
A list of nodes in the order of the cycle found. The last node
equals the first to indicate a cycle.
Raises
------
NetworkXError
If no negative cycle is found.
| def _dijkstra_multisource(
G, sources, weight, pred=None, paths=None, cutoff=None, target=None
):
"""Uses Dijkstra's algorithm to find shortest weighted paths
Parameters
----------
G : NetworkX graph
sources : non-empty iterable of nodes
Starting nodes for paths. If this is just an iterable containing
a single node, then all paths computed by this function will
start from that node. If there are two or more nodes in this
iterable, the computed paths may begin from any one of the start
nodes.
weight: function
Function with (u, v, data) input that returns that edge's weight
or None to indicate a hidden edge
pred: dict of lists, optional(default=None)
dict to store a list of predecessors keyed by that node
If None, predecessors are not stored.
paths: dict, optional (default=None)
dict to store the path list from source to each node, keyed by node.
If None, paths are not stored.
target : node label, optional
Ending node for path. Search is halted when target is found.
cutoff : integer or float, optional
Length (sum of edge weights) at which the search is stopped.
If cutoff is provided, only return paths with summed weight <= cutoff.
Returns
-------
distance : dictionary
A mapping from node to shortest distance to that node from one
of the source nodes.
Raises
------
NodeNotFound
If any of `sources` is not in `G`.
Notes
-----
The optional predecessor and path dictionaries can be accessed by
the caller through the original pred and paths objects passed
as arguments. No need to explicitly return pred or paths.
"""
G_succ = G._adj # For speed-up (and works for both directed and undirected graphs)
push = heappush
pop = heappop
dist = {} # dictionary of final distances
seen = {}
# fringe is heapq with 3-tuples (distance,c,node)
# use the count c to avoid comparing nodes (may not be able to)
c = count()
fringe = []
for source in sources:
seen[source] = 0
push(fringe, (0, next(c), source))
while fringe:
(d, _, v) = pop(fringe)
if v in dist:
continue # already searched this node.
dist[v] = d
if v == target:
break
for u, e in G_succ[v].items():
cost = weight(v, u, e)
if cost is None:
continue
vu_dist = dist[v] + cost
if cutoff is not None:
if vu_dist > cutoff:
continue
if u in dist:
u_dist = dist[u]
if vu_dist < u_dist:
raise ValueError("Contradictory paths found:", "negative weights?")
elif pred is not None and vu_dist == u_dist:
pred[u].append(v)
elif u not in seen or vu_dist < seen[u]:
seen[u] = vu_dist
push(fringe, (vu_dist, next(c), u))
if paths is not None:
paths[u] = paths[v] + [u]
if pred is not None:
pred[u] = [v]
elif vu_dist == seen[u]:
if pred is not None:
pred[u].append(v)
# The optional predecessor and path dictionaries can be accessed
# by the caller via the pred and paths objects passed as arguments.
return dist
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|
30,665 | networkx.readwrite.text | forest_str | Creates a nice utf8 representation of a forest
This function has been superseded by
:func:`nx.readwrite.text.generate_network_text`, which should be used
instead.
Parameters
----------
graph : nx.DiGraph | nx.Graph
Graph to represent (must be a tree, forest, or the empty graph)
with_labels : bool
If True will use the "label" attribute of a node to display if it
exists otherwise it will use the node value itself. Defaults to True.
sources : List
Mainly relevant for undirected forests, specifies which nodes to list
first. If unspecified the root nodes of each tree will be used for
directed forests; for undirected forests this defaults to the nodes
with the smallest degree.
write : callable
Function to use to write to, if None new lines are appended to
a list and returned. If set to the `print` function, lines will
be written to stdout as they are generated. If specified,
this function will return None. Defaults to None.
ascii_only : Boolean
If True only ASCII characters are used to construct the visualization
Returns
-------
str | None :
utf8 representation of the tree / forest
Examples
--------
>>> graph = nx.balanced_tree(r=2, h=3, create_using=nx.DiGraph)
>>> print(nx.forest_str(graph))
╙── 0
├─╼ 1
│ ├─╼ 3
│ │ ├─╼ 7
│ │ └─╼ 8
│ └─╼ 4
│ ├─╼ 9
│ └─╼ 10
└─╼ 2
├─╼ 5
│ ├─╼ 11
│ └─╼ 12
└─╼ 6
├─╼ 13
└─╼ 14
>>> graph = nx.balanced_tree(r=1, h=2, create_using=nx.Graph)
>>> print(nx.forest_str(graph))
╙── 0
└── 1
└── 2
>>> print(nx.forest_str(graph, ascii_only=True))
+-- 0
L-- 1
L-- 2
| def forest_str(graph, with_labels=True, sources=None, write=None, ascii_only=False):
"""Creates a nice utf8 representation of a forest
This function has been superseded by
:func:`nx.readwrite.text.generate_network_text`, which should be used
instead.
Parameters
----------
graph : nx.DiGraph | nx.Graph
Graph to represent (must be a tree, forest, or the empty graph)
with_labels : bool
If True will use the "label" attribute of a node to display if it
exists otherwise it will use the node value itself. Defaults to True.
sources : List
Mainly relevant for undirected forests, specifies which nodes to list
first. If unspecified the root nodes of each tree will be used for
directed forests; for undirected forests this defaults to the nodes
with the smallest degree.
write : callable
Function to use to write to, if None new lines are appended to
a list and returned. If set to the `print` function, lines will
be written to stdout as they are generated. If specified,
this function will return None. Defaults to None.
ascii_only : Boolean
If True only ASCII characters are used to construct the visualization
Returns
-------
str | None :
utf8 representation of the tree / forest
Examples
--------
>>> graph = nx.balanced_tree(r=2, h=3, create_using=nx.DiGraph)
>>> print(nx.forest_str(graph))
╙── 0
├─╼ 1
│ ├─╼ 3
│ │ ├─╼ 7
│ │ └─╼ 8
│ └─╼ 4
│ ├─╼ 9
│ └─╼ 10
└─╼ 2
├─╼ 5
│ ├─╼ 11
│ └─╼ 12
└─╼ 6
├─╼ 13
└─╼ 14
>>> graph = nx.balanced_tree(r=1, h=2, create_using=nx.Graph)
>>> print(nx.forest_str(graph))
╙── 0
└── 1
└── 2
>>> print(nx.forest_str(graph, ascii_only=True))
+-- 0
L-- 1
L-- 2
"""
msg = (
"\nforest_str is deprecated as of version 3.1 and will be removed "
"in version 3.3. Use generate_network_text or write_network_text "
"instead.\n"
)
warnings.warn(msg, DeprecationWarning)
if len(graph.nodes) > 0:
if not nx.is_forest(graph):
raise nx.NetworkXNotImplemented("input must be a forest or the empty graph")
printbuf = []
if write is None:
_write = printbuf.append
else:
_write = write
write_network_text(
graph,
_write,
with_labels=with_labels,
sources=sources,
ascii_only=ascii_only,
end="",
)
if write is None:
# Only return a string if the custom write function was not specified
return "\n".join(printbuf)
| (graph, with_labels=True, sources=None, write=None, ascii_only=False) | [
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|
30,666 | networkx.classes.function | freeze | Modify graph to prevent further change by adding or removing
nodes or edges.
Node and edge data can still be modified.
Parameters
----------
G : graph
A NetworkX graph
Examples
--------
>>> G = nx.path_graph(4)
>>> G = nx.freeze(G)
>>> try:
... G.add_edge(4, 5)
... except nx.NetworkXError as err:
... print(str(err))
Frozen graph can't be modified
Notes
-----
To "unfreeze" a graph you must make a copy by creating a new graph object:
>>> graph = nx.path_graph(4)
>>> frozen_graph = nx.freeze(graph)
>>> unfrozen_graph = nx.Graph(frozen_graph)
>>> nx.is_frozen(unfrozen_graph)
False
See Also
--------
is_frozen
| def freeze(G):
"""Modify graph to prevent further change by adding or removing
nodes or edges.
Node and edge data can still be modified.
Parameters
----------
G : graph
A NetworkX graph
Examples
--------
>>> G = nx.path_graph(4)
>>> G = nx.freeze(G)
>>> try:
... G.add_edge(4, 5)
... except nx.NetworkXError as err:
... print(str(err))
Frozen graph can't be modified
Notes
-----
To "unfreeze" a graph you must make a copy by creating a new graph object:
>>> graph = nx.path_graph(4)
>>> frozen_graph = nx.freeze(graph)
>>> unfrozen_graph = nx.Graph(frozen_graph)
>>> nx.is_frozen(unfrozen_graph)
False
See Also
--------
is_frozen
"""
G.add_node = frozen
G.add_nodes_from = frozen
G.remove_node = frozen
G.remove_nodes_from = frozen
G.add_edge = frozen
G.add_edges_from = frozen
G.add_weighted_edges_from = frozen
G.remove_edge = frozen
G.remove_edges_from = frozen
G.clear = frozen
G.clear_edges = frozen
G.frozen = True
return G
| (G) | [
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|
30,672 | networkx.convert_matrix | from_numpy_array | Returns a graph from a 2D NumPy array.
The 2D NumPy array is interpreted as an adjacency matrix for the graph.
Parameters
----------
A : a 2D numpy.ndarray
An adjacency matrix representation of a graph
parallel_edges : Boolean
If this is True, `create_using` is a multigraph, and `A` is an
integer array, then entry *(i, j)* in the array is interpreted as the
number of parallel edges joining vertices *i* and *j* in the graph.
If it is False, then the entries in the array are interpreted as
the weight of a single edge joining the vertices.
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
edge_attr : String, optional (default="weight")
The attribute to which the array values are assigned on each edge. If
it is None, edge attributes will not be assigned.
Notes
-----
For directed graphs, explicitly mention create_using=nx.DiGraph,
and entry i,j of A corresponds to an edge from i to j.
If `create_using` is :class:`networkx.MultiGraph` or
:class:`networkx.MultiDiGraph`, `parallel_edges` is True, and the
entries of `A` are of type :class:`int`, then this function returns a
multigraph (of the same type as `create_using`) with parallel edges.
If `create_using` indicates an undirected multigraph, then only the edges
indicated by the upper triangle of the array `A` will be added to the
graph.
If `edge_attr` is Falsy (False or None), edge attributes will not be
assigned, and the array data will be treated like a binary mask of
edge presence or absence. Otherwise, the attributes will be assigned
as follows:
If the NumPy array has a single data type for each array entry it
will be converted to an appropriate Python data type.
If the NumPy array has a user-specified compound data type the names
of the data fields will be used as attribute keys in the resulting
NetworkX graph.
See Also
--------
to_numpy_array
Examples
--------
Simple integer weights on edges:
>>> import numpy as np
>>> A = np.array([[1, 1], [2, 1]])
>>> G = nx.from_numpy_array(A)
>>> G.edges(data=True)
EdgeDataView([(0, 0, {'weight': 1}), (0, 1, {'weight': 2}), (1, 1, {'weight': 1})])
If `create_using` indicates a multigraph and the array has only integer
entries and `parallel_edges` is False, then the entries will be treated
as weights for edges joining the nodes (without creating parallel edges):
>>> A = np.array([[1, 1], [1, 2]])
>>> G = nx.from_numpy_array(A, create_using=nx.MultiGraph)
>>> G[1][1]
AtlasView({0: {'weight': 2}})
If `create_using` indicates a multigraph and the array has only integer
entries and `parallel_edges` is True, then the entries will be treated
as the number of parallel edges joining those two vertices:
>>> A = np.array([[1, 1], [1, 2]])
>>> temp = nx.MultiGraph()
>>> G = nx.from_numpy_array(A, parallel_edges=True, create_using=temp)
>>> G[1][1]
AtlasView({0: {'weight': 1}, 1: {'weight': 1}})
User defined compound data type on edges:
>>> dt = [("weight", float), ("cost", int)]
>>> A = np.array([[(1.0, 2)]], dtype=dt)
>>> G = nx.from_numpy_array(A)
>>> G.edges()
EdgeView([(0, 0)])
>>> G[0][0]["cost"]
2
>>> G[0][0]["weight"]
1.0
| def to_numpy_array(
G,
nodelist=None,
dtype=None,
order=None,
multigraph_weight=sum,
weight="weight",
nonedge=0.0,
):
"""Returns the graph adjacency matrix as a NumPy array.
Parameters
----------
G : graph
The NetworkX graph used to construct the NumPy array.
nodelist : list, optional
The rows and columns are ordered according to the nodes in `nodelist`.
If `nodelist` is ``None``, then the ordering is produced by ``G.nodes()``.
dtype : NumPy data type, optional
A NumPy data type used to initialize the array. If None, then the NumPy
default is used. The dtype can be structured if `weight=None`, in which
case the dtype field names are used to look up edge attributes. The
result is a structured array where each named field in the dtype
corresponds to the adjacency for that edge attribute. See examples for
details.
order : {'C', 'F'}, optional
Whether to store multidimensional data in C- or Fortran-contiguous
(row- or column-wise) order in memory. If None, then the NumPy default
is used.
multigraph_weight : callable, optional
An function that determines how weights in multigraphs are handled.
The function should accept a sequence of weights and return a single
value. The default is to sum the weights of the multiple edges.
weight : string or None optional (default = 'weight')
The edge attribute that holds the numerical value used for
the edge weight. If an edge does not have that attribute, then the
value 1 is used instead. `weight` must be ``None`` if a structured
dtype is used.
nonedge : array_like (default = 0.0)
The value used to represent non-edges in the adjacency matrix.
The array values corresponding to nonedges are typically set to zero.
However, this could be undesirable if there are array values
corresponding to actual edges that also have the value zero. If so,
one might prefer nonedges to have some other value, such as ``nan``.
Returns
-------
A : NumPy ndarray
Graph adjacency matrix
Raises
------
NetworkXError
If `dtype` is a structured dtype and `G` is a multigraph
ValueError
If `dtype` is a structured dtype and `weight` is not `None`
See Also
--------
from_numpy_array
Notes
-----
For directed graphs, entry ``i, j`` corresponds to an edge from ``i`` to ``j``.
Entries in the adjacency matrix are given by the `weight` edge attribute.
When an edge does not have a weight attribute, the value of the entry is
set to the number 1. For multiple (parallel) edges, the values of the
entries are determined by the `multigraph_weight` parameter. The default is
to sum the weight attributes for each of the parallel edges.
When `nodelist` does not contain every node in `G`, the adjacency matrix is
built from the subgraph of `G` that is induced by the nodes in `nodelist`.
The convention used for self-loop edges in graphs is to assign the
diagonal array entry value to the weight attribute of the edge
(or the number 1 if the edge has no weight attribute). If the
alternate convention of doubling the edge weight is desired the
resulting NumPy array can be modified as follows:
>>> import numpy as np
>>> G = nx.Graph([(1, 1)])
>>> A = nx.to_numpy_array(G)
>>> A
array([[1.]])
>>> A[np.diag_indices_from(A)] *= 2
>>> A
array([[2.]])
Examples
--------
>>> G = nx.MultiDiGraph()
>>> G.add_edge(0, 1, weight=2)
0
>>> G.add_edge(1, 0)
0
>>> G.add_edge(2, 2, weight=3)
0
>>> G.add_edge(2, 2)
1
>>> nx.to_numpy_array(G, nodelist=[0, 1, 2])
array([[0., 2., 0.],
[1., 0., 0.],
[0., 0., 4.]])
When `nodelist` argument is used, nodes of `G` which do not appear in the `nodelist`
and their edges are not included in the adjacency matrix. Here is an example:
>>> G = nx.Graph()
>>> G.add_edge(3, 1)
>>> G.add_edge(2, 0)
>>> G.add_edge(2, 1)
>>> G.add_edge(3, 0)
>>> nx.to_numpy_array(G, nodelist=[1, 2, 3])
array([[0., 1., 1.],
[1., 0., 0.],
[1., 0., 0.]])
This function can also be used to create adjacency matrices for multiple
edge attributes with structured dtypes:
>>> G = nx.Graph()
>>> G.add_edge(0, 1, weight=10)
>>> G.add_edge(1, 2, cost=5)
>>> G.add_edge(2, 3, weight=3, cost=-4.0)
>>> dtype = np.dtype([("weight", int), ("cost", float)])
>>> A = nx.to_numpy_array(G, dtype=dtype, weight=None)
>>> A["weight"]
array([[ 0, 10, 0, 0],
[10, 0, 1, 0],
[ 0, 1, 0, 3],
[ 0, 0, 3, 0]])
>>> A["cost"]
array([[ 0., 1., 0., 0.],
[ 1., 0., 5., 0.],
[ 0., 5., 0., -4.],
[ 0., 0., -4., 0.]])
As stated above, the argument "nonedge" is useful especially when there are
actually edges with weight 0 in the graph. Setting a nonedge value different than 0,
makes it much clearer to differentiate such 0-weighted edges and actual nonedge values.
>>> G = nx.Graph()
>>> G.add_edge(3, 1, weight=2)
>>> G.add_edge(2, 0, weight=0)
>>> G.add_edge(2, 1, weight=0)
>>> G.add_edge(3, 0, weight=1)
>>> nx.to_numpy_array(G, nonedge=-1.0)
array([[-1., 2., -1., 1.],
[ 2., -1., 0., -1.],
[-1., 0., -1., 0.],
[ 1., -1., 0., -1.]])
"""
import numpy as np
if nodelist is None:
nodelist = list(G)
nlen = len(nodelist)
# Input validation
nodeset = set(nodelist)
if nodeset - set(G):
raise nx.NetworkXError(f"Nodes {nodeset - set(G)} in nodelist is not in G")
if len(nodeset) < nlen:
raise nx.NetworkXError("nodelist contains duplicates.")
A = np.full((nlen, nlen), fill_value=nonedge, dtype=dtype, order=order)
# Corner cases: empty nodelist or graph without any edges
if nlen == 0 or G.number_of_edges() == 0:
return A
# If dtype is structured and weight is None, use dtype field names as
# edge attributes
edge_attrs = None # Only single edge attribute by default
if A.dtype.names:
if weight is None:
edge_attrs = dtype.names
else:
raise ValueError(
"Specifying `weight` not supported for structured dtypes\n."
"To create adjacency matrices from structured dtypes, use `weight=None`."
)
# Map nodes to row/col in matrix
idx = dict(zip(nodelist, range(nlen)))
if len(nodelist) < len(G):
G = G.subgraph(nodelist).copy()
# Collect all edge weights and reduce with `multigraph_weights`
if G.is_multigraph():
if edge_attrs:
raise nx.NetworkXError(
"Structured arrays are not supported for MultiGraphs"
)
d = defaultdict(list)
for u, v, wt in G.edges(data=weight, default=1.0):
d[(idx[u], idx[v])].append(wt)
i, j = np.array(list(d.keys())).T # indices
wts = [multigraph_weight(ws) for ws in d.values()] # reduced weights
else:
i, j, wts = [], [], []
# Special branch: multi-attr adjacency from structured dtypes
if edge_attrs:
# Extract edges with all data
for u, v, data in G.edges(data=True):
i.append(idx[u])
j.append(idx[v])
wts.append(data)
# Map each attribute to the appropriate named field in the
# structured dtype
for attr in edge_attrs:
attr_data = [wt.get(attr, 1.0) for wt in wts]
A[attr][i, j] = attr_data
if not G.is_directed():
A[attr][j, i] = attr_data
return A
for u, v, wt in G.edges(data=weight, default=1.0):
i.append(idx[u])
j.append(idx[v])
wts.append(wt)
# Set array values with advanced indexing
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|
30,673 | networkx.convert_matrix | from_pandas_adjacency | Returns a graph from Pandas DataFrame.
The Pandas DataFrame is interpreted as an adjacency matrix for the graph.
Parameters
----------
df : Pandas DataFrame
An adjacency matrix representation of a graph
create_using : NetworkX graph constructor, optional (default=nx.Graph)
Graph type to create. If graph instance, then cleared before populated.
Notes
-----
For directed graphs, explicitly mention create_using=nx.DiGraph,
and entry i,j of df corresponds to an edge from i to j.
If `df` has a single data type for each entry it will be converted to an
appropriate Python data type.
If you have node attributes stored in a separate dataframe `df_nodes`,
you can load those attributes to the graph `G` using the following code:
```
df_nodes = pd.DataFrame({"node_id": [1, 2, 3], "attribute1": ["A", "B", "C"]})
G.add_nodes_from((n, dict(d)) for n, d in df_nodes.iterrows())
```
If `df` has a user-specified compound data type the names
of the data fields will be used as attribute keys in the resulting
NetworkX graph.
See Also
--------
to_pandas_adjacency
Examples
--------
Simple integer weights on edges:
>>> import pandas as pd
>>> pd.options.display.max_columns = 20
>>> df = pd.DataFrame([[1, 1], [2, 1]])
>>> df
0 1
0 1 1
1 2 1
>>> G = nx.from_pandas_adjacency(df)
>>> G.name = "Graph from pandas adjacency matrix"
>>> print(G)
Graph named 'Graph from pandas adjacency matrix' with 2 nodes and 3 edges
| def to_numpy_array(
G,
nodelist=None,
dtype=None,
order=None,
multigraph_weight=sum,
weight="weight",
nonedge=0.0,
):
"""Returns the graph adjacency matrix as a NumPy array.
Parameters
----------
G : graph
The NetworkX graph used to construct the NumPy array.
nodelist : list, optional
The rows and columns are ordered according to the nodes in `nodelist`.
If `nodelist` is ``None``, then the ordering is produced by ``G.nodes()``.
dtype : NumPy data type, optional
A NumPy data type used to initialize the array. If None, then the NumPy
default is used. The dtype can be structured if `weight=None`, in which
case the dtype field names are used to look up edge attributes. The
result is a structured array where each named field in the dtype
corresponds to the adjacency for that edge attribute. See examples for
details.
order : {'C', 'F'}, optional
Whether to store multidimensional data in C- or Fortran-contiguous
(row- or column-wise) order in memory. If None, then the NumPy default
is used.
multigraph_weight : callable, optional
An function that determines how weights in multigraphs are handled.
The function should accept a sequence of weights and return a single
value. The default is to sum the weights of the multiple edges.
weight : string or None optional (default = 'weight')
The edge attribute that holds the numerical value used for
the edge weight. If an edge does not have that attribute, then the
value 1 is used instead. `weight` must be ``None`` if a structured
dtype is used.
nonedge : array_like (default = 0.0)
The value used to represent non-edges in the adjacency matrix.
The array values corresponding to nonedges are typically set to zero.
However, this could be undesirable if there are array values
corresponding to actual edges that also have the value zero. If so,
one might prefer nonedges to have some other value, such as ``nan``.
Returns
-------
A : NumPy ndarray
Graph adjacency matrix
Raises
------
NetworkXError
If `dtype` is a structured dtype and `G` is a multigraph
ValueError
If `dtype` is a structured dtype and `weight` is not `None`
See Also
--------
from_numpy_array
Notes
-----
For directed graphs, entry ``i, j`` corresponds to an edge from ``i`` to ``j``.
Entries in the adjacency matrix are given by the `weight` edge attribute.
When an edge does not have a weight attribute, the value of the entry is
set to the number 1. For multiple (parallel) edges, the values of the
entries are determined by the `multigraph_weight` parameter. The default is
to sum the weight attributes for each of the parallel edges.
When `nodelist` does not contain every node in `G`, the adjacency matrix is
built from the subgraph of `G` that is induced by the nodes in `nodelist`.
The convention used for self-loop edges in graphs is to assign the
diagonal array entry value to the weight attribute of the edge
(or the number 1 if the edge has no weight attribute). If the
alternate convention of doubling the edge weight is desired the
resulting NumPy array can be modified as follows:
>>> import numpy as np
>>> G = nx.Graph([(1, 1)])
>>> A = nx.to_numpy_array(G)
>>> A
array([[1.]])
>>> A[np.diag_indices_from(A)] *= 2
>>> A
array([[2.]])
Examples
--------
>>> G = nx.MultiDiGraph()
>>> G.add_edge(0, 1, weight=2)
0
>>> G.add_edge(1, 0)
0
>>> G.add_edge(2, 2, weight=3)
0
>>> G.add_edge(2, 2)
1
>>> nx.to_numpy_array(G, nodelist=[0, 1, 2])
array([[0., 2., 0.],
[1., 0., 0.],
[0., 0., 4.]])
When `nodelist` argument is used, nodes of `G` which do not appear in the `nodelist`
and their edges are not included in the adjacency matrix. Here is an example:
>>> G = nx.Graph()
>>> G.add_edge(3, 1)
>>> G.add_edge(2, 0)
>>> G.add_edge(2, 1)
>>> G.add_edge(3, 0)
>>> nx.to_numpy_array(G, nodelist=[1, 2, 3])
array([[0., 1., 1.],
[1., 0., 0.],
[1., 0., 0.]])
This function can also be used to create adjacency matrices for multiple
edge attributes with structured dtypes:
>>> G = nx.Graph()
>>> G.add_edge(0, 1, weight=10)
>>> G.add_edge(1, 2, cost=5)
>>> G.add_edge(2, 3, weight=3, cost=-4.0)
>>> dtype = np.dtype([("weight", int), ("cost", float)])
>>> A = nx.to_numpy_array(G, dtype=dtype, weight=None)
>>> A["weight"]
array([[ 0, 10, 0, 0],
[10, 0, 1, 0],
[ 0, 1, 0, 3],
[ 0, 0, 3, 0]])
>>> A["cost"]
array([[ 0., 1., 0., 0.],
[ 1., 0., 5., 0.],
[ 0., 5., 0., -4.],
[ 0., 0., -4., 0.]])
As stated above, the argument "nonedge" is useful especially when there are
actually edges with weight 0 in the graph. Setting a nonedge value different than 0,
makes it much clearer to differentiate such 0-weighted edges and actual nonedge values.
>>> G = nx.Graph()
>>> G.add_edge(3, 1, weight=2)
>>> G.add_edge(2, 0, weight=0)
>>> G.add_edge(2, 1, weight=0)
>>> G.add_edge(3, 0, weight=1)
>>> nx.to_numpy_array(G, nonedge=-1.0)
array([[-1., 2., -1., 1.],
[ 2., -1., 0., -1.],
[-1., 0., -1., 0.],
[ 1., -1., 0., -1.]])
"""
import numpy as np
if nodelist is None:
nodelist = list(G)
nlen = len(nodelist)
# Input validation
nodeset = set(nodelist)
if nodeset - set(G):
raise nx.NetworkXError(f"Nodes {nodeset - set(G)} in nodelist is not in G")
if len(nodeset) < nlen:
raise nx.NetworkXError("nodelist contains duplicates.")
A = np.full((nlen, nlen), fill_value=nonedge, dtype=dtype, order=order)
# Corner cases: empty nodelist or graph without any edges
if nlen == 0 or G.number_of_edges() == 0:
return A
# If dtype is structured and weight is None, use dtype field names as
# edge attributes
edge_attrs = None # Only single edge attribute by default
if A.dtype.names:
if weight is None:
edge_attrs = dtype.names
else:
raise ValueError(
"Specifying `weight` not supported for structured dtypes\n."
"To create adjacency matrices from structured dtypes, use `weight=None`."
)
# Map nodes to row/col in matrix
idx = dict(zip(nodelist, range(nlen)))
if len(nodelist) < len(G):
G = G.subgraph(nodelist).copy()
# Collect all edge weights and reduce with `multigraph_weights`
if G.is_multigraph():
if edge_attrs:
raise nx.NetworkXError(
"Structured arrays are not supported for MultiGraphs"
)
d = defaultdict(list)
for u, v, wt in G.edges(data=weight, default=1.0):
d[(idx[u], idx[v])].append(wt)
i, j = np.array(list(d.keys())).T # indices
wts = [multigraph_weight(ws) for ws in d.values()] # reduced weights
else:
i, j, wts = [], [], []
# Special branch: multi-attr adjacency from structured dtypes
if edge_attrs:
# Extract edges with all data
for u, v, data in G.edges(data=True):
i.append(idx[u])
j.append(idx[v])
wts.append(data)
# Map each attribute to the appropriate named field in the
# structured dtype
for attr in edge_attrs:
attr_data = [wt.get(attr, 1.0) for wt in wts]
A[attr][i, j] = attr_data
if not G.is_directed():
A[attr][j, i] = attr_data
return A
for u, v, wt in G.edges(data=weight, default=1.0):
i.append(idx[u])
j.append(idx[v])
wts.append(wt)
# Set array values with advanced indexing
A[i, j] | (df, create_using=None, *, backend=None, **backend_kwargs) | [
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]
|
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