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env-llmeval/lib/python3.10/site-packages/networkx/algorithms/community/louvain.py

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+"""Function for detecting communities based on Louvain Community Detection
+Algorithm"""
+
+import itertools
+from collections import defaultdict, deque
+
+import networkx as nx
+from networkx.algorithms.community import modularity
+from networkx.utils import py_random_state
+
+__all__ = ["louvain_communities", "louvain_partitions"]
+
+
+@py_random_state("seed")
+@nx._dispatchable(edge_attrs="weight")
+def louvain_communities(
+    G, weight="weight", resolution=1, threshold=0.0000001, max_level=None, seed=None
+):
+    r"""Find the best partition of a graph using the Louvain Community Detection
+    Algorithm.
+
+    Louvain Community Detection Algorithm is a simple method to extract the community
+    structure of a network. This is a heuristic method based on modularity optimization. [1]_
+
+    The algorithm works in 2 steps. On the first step it assigns every node to be
+    in its own community and then for each node it tries to find the maximum positive
+    modularity gain by moving each node to all of its neighbor communities. If no positive
+    gain is achieved the node remains in its original community.
+
+    The modularity gain obtained by moving an isolated node $i$ into a community $C$ can
+    easily be calculated by the following formula (combining [1]_ [2]_ and some algebra):
+
+    .. math::
+        \Delta Q = \frac{k_{i,in}}{2m} - \gamma\frac{ \Sigma_{tot} \cdot k_i}{2m^2}
+
+    where $m$ is the size of the graph, $k_{i,in}$ is the sum of the weights of the links
+    from $i$ to nodes in $C$, $k_i$ is the sum of the weights of the links incident to node $i$,
+    $\Sigma_{tot}$ is the sum of the weights of the links incident to nodes in $C$ and $\gamma$
+    is the resolution parameter.
+
+    For the directed case the modularity gain can be computed using this formula according to [3]_
+
+    .. math::
+        \Delta Q = \frac{k_{i,in}}{m}
+        - \gamma\frac{k_i^{out} \cdot\Sigma_{tot}^{in} + k_i^{in} \cdot \Sigma_{tot}^{out}}{m^2}
+
+    where $k_i^{out}$, $k_i^{in}$ are the outer and inner weighted degrees of node $i$ and
+    $\Sigma_{tot}^{in}$, $\Sigma_{tot}^{out}$ are the sum of in-going and out-going links incident
+    to nodes in $C$.
+
+    The first phase continues until no individual move can improve the modularity.
+
+    The second phase consists in building a new network whose nodes are now the communities
+    found in the first phase. To do so, the weights of the links between the new nodes are given by
+    the sum of the weight of the links between nodes in the corresponding two communities. Once this
+    phase is complete it is possible to reapply the first phase creating bigger communities with
+    increased modularity.
+
+    The above two phases are executed until no modularity gain is achieved (or is less than
+    the `threshold`, or until `max_levels` is reached).
+
+    Be careful with self-loops in the input graph. These are treated as
+    previously reduced communities -- as if the process had been started
+    in the middle of the algorithm. Large self-loop edge weights thus
+    represent strong communities and in practice may be hard to add
+    other nodes to.  If your input graph edge weights for self-loops
+    do not represent already reduced communities you may want to remove
+    the self-loops before inputting that graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+    weight : string or None, optional (default="weight")
+        The name of an edge attribute that holds the numerical value
+        used as a weight. If None then each edge has weight 1.
+    resolution : float, optional (default=1)
+        If resolution is less than 1, the algorithm favors larger communities.
+        Greater than 1 favors smaller communities
+    threshold : float, optional (default=0.0000001)
+        Modularity gain threshold for each level. If the gain of modularity
+        between 2 levels of the algorithm is less than the given threshold
+        then the algorithm stops and returns the resulting communities.
+    max_level : int or None, optional (default=None)
+        The maximum number of levels (steps of the algorithm) to compute.
+        Must be a positive integer or None. If None, then there is no max
+        level and the threshold parameter determines the stopping condition.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    list
+        A list of sets (partition of `G`). Each set represents one community and contains
+        all the nodes that constitute it.
+
+    Examples
+    --------
+    >>> import networkx as nx
+    >>> G = nx.petersen_graph()
+    >>> nx.community.louvain_communities(G, seed=123)
+    [{0, 4, 5, 7, 9}, {1, 2, 3, 6, 8}]
+
+    Notes
+    -----
+    The order in which the nodes are considered can affect the final output. In the algorithm
+    the ordering happens using a random shuffle.
+
+    References
+    ----------
+    .. [1] Blondel, V.D. et al. Fast unfolding of communities in
+       large networks. J. Stat. Mech 10008, 1-12(2008). https://doi.org/10.1088/1742-5468/2008/10/P10008
+    .. [2] Traag, V.A., Waltman, L. & van Eck, N.J. From Louvain to Leiden: guaranteeing
+       well-connected communities. Sci Rep 9, 5233 (2019). https://doi.org/10.1038/s41598-019-41695-z
+    .. [3] Nicolas Dugué, Anthony Perez. Directed Louvain : maximizing modularity in directed networks.
+        [Research Report] Université d’Orléans. 2015. hal-01231784. https://hal.archives-ouvertes.fr/hal-01231784
+
+    See Also
+    --------
+    louvain_partitions
+    """
+
+    partitions = louvain_partitions(G, weight, resolution, threshold, seed)
+    if max_level is not None:
+        if max_level <= 0:
+            raise ValueError("max_level argument must be a positive integer or None")
+        partitions = itertools.islice(partitions, max_level)
+    final_partition = deque(partitions, maxlen=1)
+    return final_partition.pop()
+
+
+@py_random_state("seed")
+@nx._dispatchable(edge_attrs="weight")
+def louvain_partitions(
+    G, weight="weight", resolution=1, threshold=0.0000001, seed=None
+):
+    """Yields partitions for each level of the Louvain Community Detection Algorithm
+
+    Louvain Community Detection Algorithm is a simple method to extract the community
+    structure of a network. This is a heuristic method based on modularity optimization. [1]_
+
+    The partitions at each level (step of the algorithm) form a dendrogram of communities.
+    A dendrogram is a diagram representing a tree and each level represents
+    a partition of the G graph. The top level contains the smallest communities
+    and as you traverse to the bottom of the tree the communities get bigger
+    and the overall modularity increases making the partition better.
+
+    Each level is generated by executing the two phases of the Louvain Community
+    Detection Algorithm.
+
+    Be careful with self-loops in the input graph. These are treated as
+    previously reduced communities -- as if the process had been started
+    in the middle of the algorithm. Large self-loop edge weights thus
+    represent strong communities and in practice may be hard to add
+    other nodes to.  If your input graph edge weights for self-loops
+    do not represent already reduced communities you may want to remove
+    the self-loops before inputting that graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+    weight : string or None, optional (default="weight")
+     The name of an edge attribute that holds the numerical value
+     used as a weight. If None then each edge has weight 1.
+    resolution : float, optional (default=1)
+        If resolution is less than 1, the algorithm favors larger communities.
+        Greater than 1 favors smaller communities
+    threshold : float, optional (default=0.0000001)
+     Modularity gain threshold for each level. If the gain of modularity
+     between 2 levels of the algorithm is less than the given threshold
+     then the algorithm stops and returns the resulting communities.
+    seed : integer, random_state, or None (default)
+     Indicator of random number generation state.
+     See :ref:`Randomness<randomness>`.
+
+    Yields
+    ------
+    list
+        A list of sets (partition of `G`). Each set represents one community and contains
+        all the nodes that constitute it.
+
+    References
+    ----------
+    .. [1] Blondel, V.D. et al. Fast unfolding of communities in
+       large networks. J. Stat. Mech 10008, 1-12(2008)
+
+    See Also
+    --------
+    louvain_communities
+    """
+
+    partition = [{u} for u in G.nodes()]
+    if nx.is_empty(G):
+        yield partition
+        return
+    mod = modularity(G, partition, resolution=resolution, weight=weight)
+    is_directed = G.is_directed()
+    if G.is_multigraph():
+        graph = _convert_multigraph(G, weight, is_directed)
+    else:
+        graph = G.__class__()
+        graph.add_nodes_from(G)
+        graph.add_weighted_edges_from(G.edges(data=weight, default=1))
+
+    m = graph.size(weight="weight")
+    partition, inner_partition, improvement = _one_level(
+        graph, m, partition, resolution, is_directed, seed
+    )
+    improvement = True
+    while improvement:
+        # gh-5901 protect the sets in the yielded list from further manipulation here
+        yield [s.copy() for s in partition]
+        new_mod = modularity(
+            graph, inner_partition, resolution=resolution, weight="weight"
+        )
+        if new_mod - mod <= threshold:
+            return
+        mod = new_mod
+        graph = _gen_graph(graph, inner_partition)
+        partition, inner_partition, improvement = _one_level(
+            graph, m, partition, resolution, is_directed, seed
+        )
+
+
+def _one_level(G, m, partition, resolution=1, is_directed=False, seed=None):
+    """Calculate one level of the Louvain partitions tree
+
+    Parameters
+    ----------
+    G : NetworkX Graph/DiGraph
+        The graph from which to detect communities
+    m : number
+        The size of the graph `G`.
+    partition : list of sets of nodes
+        A valid partition of the graph `G`
+    resolution : positive number
+        The resolution parameter for computing the modularity of a partition
+    is_directed : bool
+        True if `G` is a directed graph.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    """
+    node2com = {u: i for i, u in enumerate(G.nodes())}
+    inner_partition = [{u} for u in G.nodes()]
+    if is_directed:
+        in_degrees = dict(G.in_degree(weight="weight"))
+        out_degrees = dict(G.out_degree(weight="weight"))
+        Stot_in = list(in_degrees.values())
+        Stot_out = list(out_degrees.values())
+        # Calculate weights for both in and out neighbors without considering self-loops
+        nbrs = {}
+        for u in G:
+            nbrs[u] = defaultdict(float)
+            for _, n, wt in G.out_edges(u, data="weight"):
+                if u != n:
+                    nbrs[u][n] += wt
+            for n, _, wt in G.in_edges(u, data="weight"):
+                if u != n:
+                    nbrs[u][n] += wt
+    else:
+        degrees = dict(G.degree(weight="weight"))
+        Stot = list(degrees.values())
+        nbrs = {u: {v: data["weight"] for v, data in G[u].items() if v != u} for u in G}
+    rand_nodes = list(G.nodes)
+    seed.shuffle(rand_nodes)
+    nb_moves = 1
+    improvement = False
+    while nb_moves > 0:
+        nb_moves = 0
+        for u in rand_nodes:
+            best_mod = 0
+            best_com = node2com[u]
+            weights2com = _neighbor_weights(nbrs[u], node2com)
+            if is_directed:
+                in_degree = in_degrees[u]
+                out_degree = out_degrees[u]
+                Stot_in[best_com] -= in_degree
+                Stot_out[best_com] -= out_degree
+                remove_cost = (
+                    -weights2com[best_com] / m
+                    + resolution
+                    * (out_degree * Stot_in[best_com] + in_degree * Stot_out[best_com])
+                    / m**2
+                )
+            else:
+                degree = degrees[u]
+                Stot[best_com] -= degree
+                remove_cost = -weights2com[best_com] / m + resolution * (
+                    Stot[best_com] * degree
+                ) / (2 * m**2)
+            for nbr_com, wt in weights2com.items():
+                if is_directed:
+                    gain = (
+                        remove_cost
+                        + wt / m
+                        - resolution
+                        * (
+                            out_degree * Stot_in[nbr_com]
+                            + in_degree * Stot_out[nbr_com]
+                        )
+                        / m**2
+                    )
+                else:
+                    gain = (
+                        remove_cost
+                        + wt / m
+                        - resolution * (Stot[nbr_com] * degree) / (2 * m**2)
+                    )
+                if gain > best_mod:
+                    best_mod = gain
+                    best_com = nbr_com
+            if is_directed:
+                Stot_in[best_com] += in_degree
+                Stot_out[best_com] += out_degree
+            else:
+                Stot[best_com] += degree
+            if best_com != node2com[u]:
+                com = G.nodes[u].get("nodes", {u})
+                partition[node2com[u]].difference_update(com)
+                inner_partition[node2com[u]].remove(u)
+                partition[best_com].update(com)
+                inner_partition[best_com].add(u)
+                improvement = True
+                nb_moves += 1
+                node2com[u] = best_com
+    partition = list(filter(len, partition))
+    inner_partition = list(filter(len, inner_partition))
+    return partition, inner_partition, improvement
+
+
+def _neighbor_weights(nbrs, node2com):
+    """Calculate weights between node and its neighbor communities.
+
+    Parameters
+    ----------
+    nbrs : dictionary
+           Dictionary with nodes' neighbors as keys and their edge weight as value.
+    node2com : dictionary
+           Dictionary with all graph's nodes as keys and their community index as value.
+
+    """
+    weights = defaultdict(float)
+    for nbr, wt in nbrs.items():
+        weights[node2com[nbr]] += wt
+    return weights
+
+
+def _gen_graph(G, partition):
+    """Generate a new graph based on the partitions of a given graph"""
+    H = G.__class__()
+    node2com = {}
+    for i, part in enumerate(partition):
+        nodes = set()
+        for node in part:
+            node2com[node] = i
+            nodes.update(G.nodes[node].get("nodes", {node}))
+        H.add_node(i, nodes=nodes)
+
+    for node1, node2, wt in G.edges(data=True):
+        wt = wt["weight"]
+        com1 = node2com[node1]
+        com2 = node2com[node2]
+        temp = H.get_edge_data(com1, com2, {"weight": 0})["weight"]
+        H.add_edge(com1, com2, weight=wt + temp)
+    return H
+
+
+def _convert_multigraph(G, weight, is_directed):
+    """Convert a Multigraph to normal Graph"""
+    if is_directed:
+        H = nx.DiGraph()
+    else:
+        H = nx.Graph()
+    H.add_nodes_from(G)
+    for u, v, wt in G.edges(data=weight, default=1):
+        if H.has_edge(u, v):
+            H[u][v]["weight"] += wt
+        else:
+            H.add_edge(u, v, weight=wt)
+    return H

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/__init__.py

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+from .connected import *
+from .strongly_connected import *
+from .weakly_connected import *
+from .attracting import *
+from .biconnected import *
+from .semiconnected import *

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/attracting.py

@@ -0,0 +1,114 @@
+"""Attracting components."""
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = [
+    "number_attracting_components",
+    "attracting_components",
+    "is_attracting_component",
+]
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def attracting_components(G):
+    """Generates the attracting components in `G`.
+
+    An attracting component in a directed graph `G` is a strongly connected
+    component with the property that a random walker on the graph will never
+    leave the component, once it enters the component.
+
+    The nodes in attracting components can also be thought of as recurrent
+    nodes.  If a random walker enters the attractor containing the node, then
+    the node will be visited infinitely often.
+
+    To obtain induced subgraphs on each component use:
+    ``(G.subgraph(c).copy() for c in attracting_components(G))``
+
+    Parameters
+    ----------
+    G : DiGraph, MultiDiGraph
+        The graph to be analyzed.
+
+    Returns
+    -------
+    attractors : generator of sets
+        A generator of sets of nodes, one for each attracting component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is undirected.
+
+    See Also
+    --------
+    number_attracting_components
+    is_attracting_component
+
+    """
+    scc = list(nx.strongly_connected_components(G))
+    cG = nx.condensation(G, scc)
+    for n in cG:
+        if cG.out_degree(n) == 0:
+            yield scc[n]
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def number_attracting_components(G):
+    """Returns the number of attracting components in `G`.
+
+    Parameters
+    ----------
+    G : DiGraph, MultiDiGraph
+        The graph to be analyzed.
+
+    Returns
+    -------
+    n : int
+        The number of attracting components in G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is undirected.
+
+    See Also
+    --------
+    attracting_components
+    is_attracting_component
+
+    """
+    return sum(1 for ac in attracting_components(G))
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def is_attracting_component(G):
+    """Returns True if `G` consists of a single attracting component.
+
+    Parameters
+    ----------
+    G : DiGraph, MultiDiGraph
+        The graph to be analyzed.
+
+    Returns
+    -------
+    attracting : bool
+        True if `G` has a single attracting component. Otherwise, False.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is undirected.
+
+    See Also
+    --------
+    attracting_components
+    number_attracting_components
+
+    """
+    ac = list(attracting_components(G))
+    if len(ac) == 1:
+        return len(ac[0]) == len(G)
+    return False

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/biconnected.py

@@ -0,0 +1,393 @@
+"""Biconnected components and articulation points."""
+from itertools import chain
+
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = [
+    "biconnected_components",
+    "biconnected_component_edges",
+    "is_biconnected",
+    "articulation_points",
+]
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def is_biconnected(G):
+    """Returns True if the graph is biconnected, False otherwise.
+
+    A graph is biconnected if, and only if, it cannot be disconnected by
+    removing only one node (and all edges incident on that node).  If
+    removing a node increases the number of disconnected components
+    in the graph, that node is called an articulation point, or cut
+    vertex.  A biconnected graph has no articulation points.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        An undirected graph.
+
+    Returns
+    -------
+    biconnected : bool
+        True if the graph is biconnected, False otherwise.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is not undirected.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> print(nx.is_biconnected(G))
+    False
+    >>> G.add_edge(0, 3)
+    >>> print(nx.is_biconnected(G))
+    True
+
+    See Also
+    --------
+    biconnected_components
+    articulation_points
+    biconnected_component_edges
+    is_strongly_connected
+    is_weakly_connected
+    is_connected
+    is_semiconnected
+
+    Notes
+    -----
+    The algorithm to find articulation points and biconnected
+    components is implemented using a non-recursive depth-first-search
+    (DFS) that keeps track of the highest level that back edges reach
+    in the DFS tree.  A node `n` is an articulation point if, and only
+    if, there exists a subtree rooted at `n` such that there is no
+    back edge from any successor of `n` that links to a predecessor of
+    `n` in the DFS tree.  By keeping track of all the edges traversed
+    by the DFS we can obtain the biconnected components because all
+    edges of a bicomponent will be traversed consecutively between
+    articulation points.
+
+    References
+    ----------
+    .. [1] Hopcroft, J.; Tarjan, R. (1973).
+       "Efficient algorithms for graph manipulation".
+       Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
+
+    """
+    bccs = biconnected_components(G)
+    try:
+        bcc = next(bccs)
+    except StopIteration:
+        # No bicomponents (empty graph?)
+        return False
+    try:
+        next(bccs)
+    except StopIteration:
+        # Only one bicomponent
+        return len(bcc) == len(G)
+    else:
+        # Multiple bicomponents
+        return False
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def biconnected_component_edges(G):
+    """Returns a generator of lists of edges, one list for each biconnected
+    component of the input graph.
+
+    Biconnected components are maximal subgraphs such that the removal of a
+    node (and all edges incident on that node) will not disconnect the
+    subgraph.  Note that nodes may be part of more than one biconnected
+    component.  Those nodes are articulation points, or cut vertices.
+    However, each edge belongs to one, and only one, biconnected component.
+
+    Notice that by convention a dyad is considered a biconnected component.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        An undirected graph.
+
+    Returns
+    -------
+    edges : generator of lists
+        Generator of lists of edges, one list for each bicomponent.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is not undirected.
+
+    Examples
+    --------
+    >>> G = nx.barbell_graph(4, 2)
+    >>> print(nx.is_biconnected(G))
+    False
+    >>> bicomponents_edges = list(nx.biconnected_component_edges(G))
+    >>> len(bicomponents_edges)
+    5
+    >>> G.add_edge(2, 8)
+    >>> print(nx.is_biconnected(G))
+    True
+    >>> bicomponents_edges = list(nx.biconnected_component_edges(G))
+    >>> len(bicomponents_edges)
+    1
+
+    See Also
+    --------
+    is_biconnected,
+    biconnected_components,
+    articulation_points,
+
+    Notes
+    -----
+    The algorithm to find articulation points and biconnected
+    components is implemented using a non-recursive depth-first-search
+    (DFS) that keeps track of the highest level that back edges reach
+    in the DFS tree.  A node `n` is an articulation point if, and only
+    if, there exists a subtree rooted at `n` such that there is no
+    back edge from any successor of `n` that links to a predecessor of
+    `n` in the DFS tree.  By keeping track of all the edges traversed
+    by the DFS we can obtain the biconnected components because all
+    edges of a bicomponent will be traversed consecutively between
+    articulation points.
+
+    References
+    ----------
+    .. [1] Hopcroft, J.; Tarjan, R. (1973).
+           "Efficient algorithms for graph manipulation".
+           Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
+
+    """
+    yield from _biconnected_dfs(G, components=True)
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def biconnected_components(G):
+    """Returns a generator of sets of nodes, one set for each biconnected
+    component of the graph
+
+    Biconnected components are maximal subgraphs such that the removal of a
+    node (and all edges incident on that node) will not disconnect the
+    subgraph. Note that nodes may be part of more than one biconnected
+    component.  Those nodes are articulation points, or cut vertices.  The
+    removal of articulation points will increase the number of connected
+    components of the graph.
+
+    Notice that by convention a dyad is considered a biconnected component.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        An undirected graph.
+
+    Returns
+    -------
+    nodes : generator
+        Generator of sets of nodes, one set for each biconnected component.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is not undirected.
+
+    Examples
+    --------
+    >>> G = nx.lollipop_graph(5, 1)
+    >>> print(nx.is_biconnected(G))
+    False
+    >>> bicomponents = list(nx.biconnected_components(G))
+    >>> len(bicomponents)
+    2
+    >>> G.add_edge(0, 5)
+    >>> print(nx.is_biconnected(G))
+    True
+    >>> bicomponents = list(nx.biconnected_components(G))
+    >>> len(bicomponents)
+    1
+
+    You can generate a sorted list of biconnected components, largest
+    first, using sort.
+
+    >>> G.remove_edge(0, 5)
+    >>> [len(c) for c in sorted(nx.biconnected_components(G), key=len, reverse=True)]
+    [5, 2]
+
+    If you only want the largest connected component, it's more
+    efficient to use max instead of sort.
+
+    >>> Gc = max(nx.biconnected_components(G), key=len)
+
+    To create the components as subgraphs use:
+    ``(G.subgraph(c).copy() for c in biconnected_components(G))``
+
+    See Also
+    --------
+    is_biconnected
+    articulation_points
+    biconnected_component_edges
+    k_components : this function is a special case where k=2
+    bridge_components : similar to this function, but is defined using
+        2-edge-connectivity instead of 2-node-connectivity.
+
+    Notes
+    -----
+    The algorithm to find articulation points and biconnected
+    components is implemented using a non-recursive depth-first-search
+    (DFS) that keeps track of the highest level that back edges reach
+    in the DFS tree.  A node `n` is an articulation point if, and only
+    if, there exists a subtree rooted at `n` such that there is no
+    back edge from any successor of `n` that links to a predecessor of
+    `n` in the DFS tree.  By keeping track of all the edges traversed
+    by the DFS we can obtain the biconnected components because all
+    edges of a bicomponent will be traversed consecutively between
+    articulation points.
+
+    References
+    ----------
+    .. [1] Hopcroft, J.; Tarjan, R. (1973).
+           "Efficient algorithms for graph manipulation".
+           Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
+
+    """
+    for comp in _biconnected_dfs(G, components=True):
+        yield set(chain.from_iterable(comp))
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def articulation_points(G):
+    """Yield the articulation points, or cut vertices, of a graph.
+
+    An articulation point or cut vertex is any node whose removal (along with
+    all its incident edges) increases the number of connected components of
+    a graph.  An undirected connected graph without articulation points is
+    biconnected. Articulation points belong to more than one biconnected
+    component of a graph.
+
+    Notice that by convention a dyad is considered a biconnected component.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        An undirected graph.
+
+    Yields
+    ------
+    node
+        An articulation point in the graph.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is not undirected.
+
+    Examples
+    --------
+
+    >>> G = nx.barbell_graph(4, 2)
+    >>> print(nx.is_biconnected(G))
+    False
+    >>> len(list(nx.articulation_points(G)))
+    4
+    >>> G.add_edge(2, 8)
+    >>> print(nx.is_biconnected(G))
+    True
+    >>> len(list(nx.articulation_points(G)))
+    0
+
+    See Also
+    --------
+    is_biconnected
+    biconnected_components
+    biconnected_component_edges
+
+    Notes
+    -----
+    The algorithm to find articulation points and biconnected
+    components is implemented using a non-recursive depth-first-search
+    (DFS) that keeps track of the highest level that back edges reach
+    in the DFS tree.  A node `n` is an articulation point if, and only
+    if, there exists a subtree rooted at `n` such that there is no
+    back edge from any successor of `n` that links to a predecessor of
+    `n` in the DFS tree.  By keeping track of all the edges traversed
+    by the DFS we can obtain the biconnected components because all
+    edges of a bicomponent will be traversed consecutively between
+    articulation points.
+
+    References
+    ----------
+    .. [1] Hopcroft, J.; Tarjan, R. (1973).
+           "Efficient algorithms for graph manipulation".
+           Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
+
+    """
+    seen = set()
+    for articulation in _biconnected_dfs(G, components=False):
+        if articulation not in seen:
+            seen.add(articulation)
+            yield articulation
+
+
+@not_implemented_for("directed")
+def _biconnected_dfs(G, components=True):
+    # depth-first search algorithm to generate articulation points
+    # and biconnected components
+    visited = set()
+    for start in G:
+        if start in visited:
+            continue
+        discovery = {start: 0}  # time of first discovery of node during search
+        low = {start: 0}
+        root_children = 0
+        visited.add(start)
+        edge_stack = []
+        stack = [(start, start, iter(G[start]))]
+        edge_index = {}
+        while stack:
+            grandparent, parent, children = stack[-1]
+            try:
+                child = next(children)
+                if grandparent == child:
+                    continue
+                if child in visited:
+                    if discovery[child] <= discovery[parent]:  # back edge
+                        low[parent] = min(low[parent], discovery[child])
+                        if components:
+                            edge_index[parent, child] = len(edge_stack)
+                            edge_stack.append((parent, child))
+                else:
+                    low[child] = discovery[child] = len(discovery)
+                    visited.add(child)
+                    stack.append((parent, child, iter(G[child])))
+                    if components:
+                        edge_index[parent, child] = len(edge_stack)
+                        edge_stack.append((parent, child))
+
+            except StopIteration:
+                stack.pop()
+                if len(stack) > 1:
+                    if low[parent] >= discovery[grandparent]:
+                        if components:
+                            ind = edge_index[grandparent, parent]
+                            yield edge_stack[ind:]
+                            del edge_stack[ind:]
+
+                        else:
+                            yield grandparent
+                    low[grandparent] = min(low[parent], low[grandparent])
+                elif stack:  # length 1 so grandparent is root
+                    root_children += 1
+                    if components:
+                        ind = edge_index[grandparent, parent]
+                        yield edge_stack[ind:]
+                        del edge_stack[ind:]
+        if not components:
+            # root node is articulation point if it has more than 1 child
+            if root_children > 1:
+                yield start

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/connected.py

@@ -0,0 +1,214 @@
+"""Connected components."""
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+from ...utils import arbitrary_element
+
+__all__ = [
+    "number_connected_components",
+    "connected_components",
+    "is_connected",
+    "node_connected_component",
+]
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def connected_components(G):
+    """Generate connected components.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph
+
+    Returns
+    -------
+    comp : generator of sets
+       A generator of sets of nodes, one for each component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    Examples
+    --------
+    Generate a sorted list of connected components, largest first.
+
+    >>> G = nx.path_graph(4)
+    >>> nx.add_path(G, [10, 11, 12])
+    >>> [len(c) for c in sorted(nx.connected_components(G), key=len, reverse=True)]
+    [4, 3]
+
+    If you only want the largest connected component, it's more
+    efficient to use max instead of sort.
+
+    >>> largest_cc = max(nx.connected_components(G), key=len)
+
+    To create the induced subgraph of each component use:
+
+    >>> S = [G.subgraph(c).copy() for c in nx.connected_components(G)]
+
+    See Also
+    --------
+    strongly_connected_components
+    weakly_connected_components
+
+    Notes
+    -----
+    For undirected graphs only.
+
+    """
+    seen = set()
+    for v in G:
+        if v not in seen:
+            c = _plain_bfs(G, v)
+            seen.update(c)
+            yield c
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def number_connected_components(G):
+    """Returns the number of connected components.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    Returns
+    -------
+    n : integer
+       Number of connected components
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (1, 2), (5, 6), (3, 4)])
+    >>> nx.number_connected_components(G)
+    3
+
+    See Also
+    --------
+    connected_components
+    number_weakly_connected_components
+    number_strongly_connected_components
+
+    Notes
+    -----
+    For undirected graphs only.
+
+    """
+    return sum(1 for cc in connected_components(G))
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def is_connected(G):
+    """Returns True if the graph is connected, False otherwise.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+       An undirected graph.
+
+    Returns
+    -------
+    connected : bool
+      True if the graph is connected, false otherwise.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> print(nx.is_connected(G))
+    True
+
+    See Also
+    --------
+    is_strongly_connected
+    is_weakly_connected
+    is_semiconnected
+    is_biconnected
+    connected_components
+
+    Notes
+    -----
+    For undirected graphs only.
+
+    """
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept(
+            "Connectivity is undefined for the null graph."
+        )
+    return sum(1 for node in _plain_bfs(G, arbitrary_element(G))) == len(G)
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def node_connected_component(G, n):
+    """Returns the set of nodes in the component of graph containing node n.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+       An undirected graph.
+
+    n : node label
+       A node in G
+
+    Returns
+    -------
+    comp : set
+       A set of nodes in the component of G containing node n.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (1, 2), (5, 6), (3, 4)])
+    >>> nx.node_connected_component(G, 0)  # nodes of component that contains node 0
+    {0, 1, 2}
+
+    See Also
+    --------
+    connected_components
+
+    Notes
+    -----
+    For undirected graphs only.
+
+    """
+    return _plain_bfs(G, n)
+
+
+def _plain_bfs(G, source):
+    """A fast BFS node generator"""
+    adj = G._adj
+    n = len(adj)
+    seen = {source}
+    nextlevel = [source]
+    while nextlevel:
+        thislevel = nextlevel
+        nextlevel = []
+        for v in thislevel:
+            for w in adj[v]:
+                if w not in seen:
+                    seen.add(w)
+                    nextlevel.append(w)
+            if len(seen) == n:
+                return seen
+    return seen

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/semiconnected.py

@@ -0,0 +1,70 @@
+"""Semiconnectedness."""
+import networkx as nx
+from networkx.utils import not_implemented_for, pairwise
+
+__all__ = ["is_semiconnected"]
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def is_semiconnected(G):
+    r"""Returns True if the graph is semiconnected, False otherwise.
+
+    A graph is semiconnected if and only if for any pair of nodes, either one
+    is reachable from the other, or they are mutually reachable.
+
+    This function uses a theorem that states that a DAG is semiconnected
+    if for any topological sort, for node $v_n$ in that sort, there is an
+    edge $(v_i, v_{i+1})$. That allows us to check if a non-DAG `G` is
+    semiconnected by condensing the graph: i.e. constructing a new graph `H`
+    with nodes being the strongly connected components of `G`, and edges
+    (scc_1, scc_2) if there is a edge $(v_1, v_2)$ in `G` for some
+    $v_1 \in scc_1$ and $v_2 \in scc_2$. That results in a DAG, so we compute
+    the topological sort of `H` and check if for every $n$ there is an edge
+    $(scc_n, scc_{n+1})$.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A directed graph.
+
+    Returns
+    -------
+    semiconnected : bool
+        True if the graph is semiconnected, False otherwise.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is undirected.
+
+    NetworkXPointlessConcept
+        If the graph is empty.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4, create_using=nx.DiGraph())
+    >>> print(nx.is_semiconnected(G))
+    True
+    >>> G = nx.DiGraph([(1, 2), (3, 2)])
+    >>> print(nx.is_semiconnected(G))
+    False
+
+    See Also
+    --------
+    is_strongly_connected
+    is_weakly_connected
+    is_connected
+    is_biconnected
+    """
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept(
+            "Connectivity is undefined for the null graph."
+        )
+
+    if not nx.is_weakly_connected(G):
+        return False
+
+    H = nx.condensation(G)
+
+    return all(H.has_edge(u, v) for u, v in pairwise(nx.topological_sort(H)))

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/strongly_connected.py

@@ -0,0 +1,430 @@
+"""Strongly connected components."""
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = [
+    "number_strongly_connected_components",
+    "strongly_connected_components",
+    "is_strongly_connected",
+    "strongly_connected_components_recursive",
+    "kosaraju_strongly_connected_components",
+    "condensation",
+]
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def strongly_connected_components(G):
+    """Generate nodes in strongly connected components of graph.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        A directed graph.
+
+    Returns
+    -------
+    comp : generator of sets
+        A generator of sets of nodes, one for each strongly connected
+        component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    Generate a sorted list of strongly connected components, largest first.
+
+    >>> G = nx.cycle_graph(4, create_using=nx.DiGraph())
+    >>> nx.add_cycle(G, [10, 11, 12])
+    >>> [len(c) for c in sorted(nx.strongly_connected_components(G), key=len, reverse=True)]
+    [4, 3]
+
+    If you only want the largest component, it's more efficient to
+    use max instead of sort.
+
+    >>> largest = max(nx.strongly_connected_components(G), key=len)
+
+    See Also
+    --------
+    connected_components
+    weakly_connected_components
+    kosaraju_strongly_connected_components
+
+    Notes
+    -----
+    Uses Tarjan's algorithm[1]_ with Nuutila's modifications[2]_.
+    Nonrecursive version of algorithm.
+
+    References
+    ----------
+    .. [1] Depth-first search and linear graph algorithms, R. Tarjan
+       SIAM Journal of Computing 1(2):146-160, (1972).
+
+    .. [2] On finding the strongly connected components in a directed graph.
+       E. Nuutila and E. Soisalon-Soinen
+       Information Processing Letters 49(1): 9-14, (1994)..
+
+    """
+    preorder = {}
+    lowlink = {}
+    scc_found = set()
+    scc_queue = []
+    i = 0  # Preorder counter
+    neighbors = {v: iter(G[v]) for v in G}
+    for source in G:
+        if source not in scc_found:
+            queue = [source]
+            while queue:
+                v = queue[-1]
+                if v not in preorder:
+                    i = i + 1
+                    preorder[v] = i
+                done = True
+                for w in neighbors[v]:
+                    if w not in preorder:
+                        queue.append(w)
+                        done = False
+                        break
+                if done:
+                    lowlink[v] = preorder[v]
+                    for w in G[v]:
+                        if w not in scc_found:
+                            if preorder[w] > preorder[v]:
+                                lowlink[v] = min([lowlink[v], lowlink[w]])
+                            else:
+                                lowlink[v] = min([lowlink[v], preorder[w]])
+                    queue.pop()
+                    if lowlink[v] == preorder[v]:
+                        scc = {v}
+                        while scc_queue and preorder[scc_queue[-1]] > preorder[v]:
+                            k = scc_queue.pop()
+                            scc.add(k)
+                        scc_found.update(scc)
+                        yield scc
+                    else:
+                        scc_queue.append(v)
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def kosaraju_strongly_connected_components(G, source=None):
+    """Generate nodes in strongly connected components of graph.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        A directed graph.
+
+    Returns
+    -------
+    comp : generator of sets
+        A generator of sets of nodes, one for each strongly connected
+        component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    Generate a sorted list of strongly connected components, largest first.
+
+    >>> G = nx.cycle_graph(4, create_using=nx.DiGraph())
+    >>> nx.add_cycle(G, [10, 11, 12])
+    >>> [
+    ...     len(c)
+    ...     for c in sorted(
+    ...         nx.kosaraju_strongly_connected_components(G), key=len, reverse=True
+    ...     )
+    ... ]
+    [4, 3]
+
+    If you only want the largest component, it's more efficient to
+    use max instead of sort.
+
+    >>> largest = max(nx.kosaraju_strongly_connected_components(G), key=len)
+
+    See Also
+    --------
+    strongly_connected_components
+
+    Notes
+    -----
+    Uses Kosaraju's algorithm.
+
+    """
+    post = list(nx.dfs_postorder_nodes(G.reverse(copy=False), source=source))
+
+    seen = set()
+    while post:
+        r = post.pop()
+        if r in seen:
+            continue
+        c = nx.dfs_preorder_nodes(G, r)
+        new = {v for v in c if v not in seen}
+        seen.update(new)
+        yield new
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def strongly_connected_components_recursive(G):
+    """Generate nodes in strongly connected components of graph.
+
+    .. deprecated:: 3.2
+
+       This function is deprecated and will be removed in a future version of
+       NetworkX. Use `strongly_connected_components` instead.
+
+    Recursive version of algorithm.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        A directed graph.
+
+    Returns
+    -------
+    comp : generator of sets
+        A generator of sets of nodes, one for each strongly connected
+        component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    Generate a sorted list of strongly connected components, largest first.
+
+    >>> G = nx.cycle_graph(4, create_using=nx.DiGraph())
+    >>> nx.add_cycle(G, [10, 11, 12])
+    >>> [
+    ...     len(c)
+    ...     for c in sorted(
+    ...         nx.strongly_connected_components_recursive(G), key=len, reverse=True
+    ...     )
+    ... ]
+    [4, 3]
+
+    If you only want the largest component, it's more efficient to
+    use max instead of sort.
+
+    >>> largest = max(nx.strongly_connected_components_recursive(G), key=len)
+
+    To create the induced subgraph of the components use:
+    >>> S = [G.subgraph(c).copy() for c in nx.weakly_connected_components(G)]
+
+    See Also
+    --------
+    connected_components
+
+    Notes
+    -----
+    Uses Tarjan's algorithm[1]_ with Nuutila's modifications[2]_.
+
+    References
+    ----------
+    .. [1] Depth-first search and linear graph algorithms, R. Tarjan
+       SIAM Journal of Computing 1(2):146-160, (1972).
+
+    .. [2] On finding the strongly connected components in a directed graph.
+       E. Nuutila and E. Soisalon-Soinen
+       Information Processing Letters 49(1): 9-14, (1994)..
+
+    """
+    import warnings
+
+    warnings.warn(
+        (
+            "\n\nstrongly_connected_components_recursive is deprecated and will be\n"
+            "removed in the future. Use strongly_connected_components instead."
+        ),
+        category=DeprecationWarning,
+        stacklevel=2,
+    )
+
+    yield from strongly_connected_components(G)
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def number_strongly_connected_components(G):
+    """Returns number of strongly connected components in graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       A directed graph.
+
+    Returns
+    -------
+    n : integer
+       Number of strongly connected components
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph(
+    ...     [(0, 1), (1, 2), (2, 0), (2, 3), (4, 5), (3, 4), (5, 6), (6, 3), (6, 7)]
+    ... )
+    >>> nx.number_strongly_connected_components(G)
+    3
+
+    See Also
+    --------
+    strongly_connected_components
+    number_connected_components
+    number_weakly_connected_components
+
+    Notes
+    -----
+    For directed graphs only.
+    """
+    return sum(1 for scc in strongly_connected_components(G))
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def is_strongly_connected(G):
+    """Test directed graph for strong connectivity.
+
+    A directed graph is strongly connected if and only if every vertex in
+    the graph is reachable from every other vertex.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+       A directed graph.
+
+    Returns
+    -------
+    connected : bool
+      True if the graph is strongly connected, False otherwise.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(0, 1), (1, 2), (2, 3), (3, 0), (2, 4), (4, 2)])
+    >>> nx.is_strongly_connected(G)
+    True
+    >>> G.remove_edge(2, 3)
+    >>> nx.is_strongly_connected(G)
+    False
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    See Also
+    --------
+    is_weakly_connected
+    is_semiconnected
+    is_connected
+    is_biconnected
+    strongly_connected_components
+
+    Notes
+    -----
+    For directed graphs only.
+    """
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept(
+            """Connectivity is undefined for the null graph."""
+        )
+
+    return len(next(strongly_connected_components(G))) == len(G)
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable(returns_graph=True)
+def condensation(G, scc=None):
+    """Returns the condensation of G.
+
+    The condensation of G is the graph with each of the strongly connected
+    components contracted into a single node.
+
+    Parameters
+    ----------
+    G : NetworkX DiGraph
+       A directed graph.
+
+    scc:  list or generator (optional, default=None)
+       Strongly connected components. If provided, the elements in
+       `scc` must partition the nodes in `G`. If not provided, it will be
+       calculated as scc=nx.strongly_connected_components(G).
+
+    Returns
+    -------
+    C : NetworkX DiGraph
+       The condensation graph C of G.  The node labels are integers
+       corresponding to the index of the component in the list of
+       strongly connected components of G.  C has a graph attribute named
+       'mapping' with a dictionary mapping the original nodes to the
+       nodes in C to which they belong.  Each node in C also has a node
+       attribute 'members' with the set of original nodes in G that
+       form the SCC that the node in C represents.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    Contracting two sets of strongly connected nodes into two distinct SCC
+    using the barbell graph.
+
+    >>> G = nx.barbell_graph(4, 0)
+    >>> G.remove_edge(3, 4)
+    >>> G = nx.DiGraph(G)
+    >>> H = nx.condensation(G)
+    >>> H.nodes.data()
+    NodeDataView({0: {'members': {0, 1, 2, 3}}, 1: {'members': {4, 5, 6, 7}}})
+    >>> H.graph["mapping"]
+    {0: 0, 1: 0, 2: 0, 3: 0, 4: 1, 5: 1, 6: 1, 7: 1}
+
+    Contracting a complete graph into one single SCC.
+
+    >>> G = nx.complete_graph(7, create_using=nx.DiGraph)
+    >>> H = nx.condensation(G)
+    >>> H.nodes
+    NodeView((0,))
+    >>> H.nodes.data()
+    NodeDataView({0: {'members': {0, 1, 2, 3, 4, 5, 6}}})
+
+    Notes
+    -----
+    After contracting all strongly connected components to a single node,
+    the resulting graph is a directed acyclic graph.
+
+    """
+    if scc is None:
+        scc = nx.strongly_connected_components(G)
+    mapping = {}
+    members = {}
+    C = nx.DiGraph()
+    # Add mapping dict as graph attribute
+    C.graph["mapping"] = mapping
+    if len(G) == 0:
+        return C
+    for i, component in enumerate(scc):
+        members[i] = component
+        mapping.update((n, i) for n in component)
+    number_of_components = i + 1
+    C.add_nodes_from(range(number_of_components))
+    C.add_edges_from(
+        (mapping[u], mapping[v]) for u, v in G.edges() if mapping[u] != mapping[v]
+    )
+    # Add a list of members (ie original nodes) to each node (ie scc) in C.
+    nx.set_node_attributes(C, members, "members")
+    return C

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_attracting.py

@@ -0,0 +1,70 @@
+import pytest
+
+import networkx as nx
+from networkx import NetworkXNotImplemented
+
+
+class TestAttractingComponents:
+    @classmethod
+    def setup_class(cls):
+        cls.G1 = nx.DiGraph()
+        cls.G1.add_edges_from(
+            [
+                (5, 11),
+                (11, 2),
+                (11, 9),
+                (11, 10),
+                (7, 11),
+                (7, 8),
+                (8, 9),
+                (3, 8),
+                (3, 10),
+            ]
+        )
+        cls.G2 = nx.DiGraph()
+        cls.G2.add_edges_from([(0, 1), (0, 2), (1, 1), (1, 2), (2, 1)])
+
+        cls.G3 = nx.DiGraph()
+        cls.G3.add_edges_from([(0, 1), (1, 2), (2, 1), (0, 3), (3, 4), (4, 3)])
+
+        cls.G4 = nx.DiGraph()
+
+    def test_attracting_components(self):
+        ac = list(nx.attracting_components(self.G1))
+        assert {2} in ac
+        assert {9} in ac
+        assert {10} in ac
+
+        ac = list(nx.attracting_components(self.G2))
+        ac = [tuple(sorted(x)) for x in ac]
+        assert ac == [(1, 2)]
+
+        ac = list(nx.attracting_components(self.G3))
+        ac = [tuple(sorted(x)) for x in ac]
+        assert (1, 2) in ac
+        assert (3, 4) in ac
+        assert len(ac) == 2
+
+        ac = list(nx.attracting_components(self.G4))
+        assert ac == []
+
+    def test_number_attacting_components(self):
+        assert nx.number_attracting_components(self.G1) == 3
+        assert nx.number_attracting_components(self.G2) == 1
+        assert nx.number_attracting_components(self.G3) == 2
+        assert nx.number_attracting_components(self.G4) == 0
+
+    def test_is_attracting_component(self):
+        assert not nx.is_attracting_component(self.G1)
+        assert not nx.is_attracting_component(self.G2)
+        assert not nx.is_attracting_component(self.G3)
+        g2 = self.G3.subgraph([1, 2])
+        assert nx.is_attracting_component(g2)
+        assert not nx.is_attracting_component(self.G4)
+
+    def test_connected_raise(self):
+        G = nx.Graph()
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.attracting_components(G))
+        pytest.raises(NetworkXNotImplemented, nx.number_attracting_components, G)
+        pytest.raises(NetworkXNotImplemented, nx.is_attracting_component, G)

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_biconnected.py

@@ -0,0 +1,248 @@
+import pytest
+
+import networkx as nx
+from networkx import NetworkXNotImplemented
+
+
+def assert_components_edges_equal(x, y):
+    sx = {frozenset(frozenset(e) for e in c) for c in x}
+    sy = {frozenset(frozenset(e) for e in c) for c in y}
+    assert sx == sy
+
+
+def assert_components_equal(x, y):
+    sx = {frozenset(c) for c in x}
+    sy = {frozenset(c) for c in y}
+    assert sx == sy
+
+
+def test_barbell():
+    G = nx.barbell_graph(8, 4)
+    nx.add_path(G, [7, 20, 21, 22])
+    nx.add_cycle(G, [22, 23, 24, 25])
+    pts = set(nx.articulation_points(G))
+    assert pts == {7, 8, 9, 10, 11, 12, 20, 21, 22}
+
+    answer = [
+        {12, 13, 14, 15, 16, 17, 18, 19},
+        {0, 1, 2, 3, 4, 5, 6, 7},
+        {22, 23, 24, 25},
+        {11, 12},
+        {10, 11},
+        {9, 10},
+        {8, 9},
+        {7, 8},
+        {21, 22},
+        {20, 21},
+        {7, 20},
+    ]
+    assert_components_equal(list(nx.biconnected_components(G)), answer)
+
+    G.add_edge(2, 17)
+    pts = set(nx.articulation_points(G))
+    assert pts == {7, 20, 21, 22}
+
+
+def test_articulation_points_repetitions():
+    G = nx.Graph()
+    G.add_edges_from([(0, 1), (1, 2), (1, 3)])
+    assert list(nx.articulation_points(G)) == [1]
+
+
+def test_articulation_points_cycle():
+    G = nx.cycle_graph(3)
+    nx.add_cycle(G, [1, 3, 4])
+    pts = set(nx.articulation_points(G))
+    assert pts == {1}
+
+
+def test_is_biconnected():
+    G = nx.cycle_graph(3)
+    assert nx.is_biconnected(G)
+    nx.add_cycle(G, [1, 3, 4])
+    assert not nx.is_biconnected(G)
+
+
+def test_empty_is_biconnected():
+    G = nx.empty_graph(5)
+    assert not nx.is_biconnected(G)
+    G.add_edge(0, 1)
+    assert not nx.is_biconnected(G)
+
+
+def test_biconnected_components_cycle():
+    G = nx.cycle_graph(3)
+    nx.add_cycle(G, [1, 3, 4])
+    answer = [{0, 1, 2}, {1, 3, 4}]
+    assert_components_equal(list(nx.biconnected_components(G)), answer)
+
+
+def test_biconnected_components1():
+    # graph example from
+    # https://web.archive.org/web/20121229123447/http://www.ibluemojo.com/school/articul_algorithm.html
+    edges = [
+        (0, 1),
+        (0, 5),
+        (0, 6),
+        (0, 14),
+        (1, 5),
+        (1, 6),
+        (1, 14),
+        (2, 4),
+        (2, 10),
+        (3, 4),
+        (3, 15),
+        (4, 6),
+        (4, 7),
+        (4, 10),
+        (5, 14),
+        (6, 14),
+        (7, 9),
+        (8, 9),
+        (8, 12),
+        (8, 13),
+        (10, 15),
+        (11, 12),
+        (11, 13),
+        (12, 13),
+    ]
+    G = nx.Graph(edges)
+    pts = set(nx.articulation_points(G))
+    assert pts == {4, 6, 7, 8, 9}
+    comps = list(nx.biconnected_component_edges(G))
+    answer = [
+        [(3, 4), (15, 3), (10, 15), (10, 4), (2, 10), (4, 2)],
+        [(13, 12), (13, 8), (11, 13), (12, 11), (8, 12)],
+        [(9, 8)],
+        [(7, 9)],
+        [(4, 7)],
+        [(6, 4)],
+        [(14, 0), (5, 1), (5, 0), (14, 5), (14, 1), (6, 14), (6, 0), (1, 6), (0, 1)],
+    ]
+    assert_components_edges_equal(comps, answer)
+
+
+def test_biconnected_components2():
+    G = nx.Graph()
+    nx.add_cycle(G, "ABC")
+    nx.add_cycle(G, "CDE")
+    nx.add_cycle(G, "FIJHG")
+    nx.add_cycle(G, "GIJ")
+    G.add_edge("E", "G")
+    comps = list(nx.biconnected_component_edges(G))
+    answer = [
+        [
+            tuple("GF"),
+            tuple("FI"),
+            tuple("IG"),
+            tuple("IJ"),
+            tuple("JG"),
+            tuple("JH"),
+            tuple("HG"),
+        ],
+        [tuple("EG")],
+        [tuple("CD"), tuple("DE"), tuple("CE")],
+        [tuple("AB"), tuple("BC"), tuple("AC")],
+    ]
+    assert_components_edges_equal(comps, answer)
+
+
+def test_biconnected_davis():
+    D = nx.davis_southern_women_graph()
+    bcc = list(nx.biconnected_components(D))[0]
+    assert set(D) == bcc  # All nodes in a giant bicomponent
+    # So no articulation points
+    assert len(list(nx.articulation_points(D))) == 0
+
+
+def test_biconnected_karate():
+    K = nx.karate_club_graph()
+    answer = [
+        {
+            0,
+            1,
+            2,
+            3,
+            7,
+            8,
+            9,
+            12,
+            13,
+            14,
+            15,
+            17,
+            18,
+            19,
+            20,
+            21,
+            22,
+            23,
+            24,
+            25,
+            26,
+            27,
+            28,
+            29,
+            30,
+            31,
+            32,
+            33,
+        },
+        {0, 4, 5, 6, 10, 16},
+        {0, 11},
+    ]
+    bcc = list(nx.biconnected_components(K))
+    assert_components_equal(bcc, answer)
+    assert set(nx.articulation_points(K)) == {0}
+
+
+def test_biconnected_eppstein():
+    # tests from http://www.ics.uci.edu/~eppstein/PADS/Biconnectivity.py
+    G1 = nx.Graph(
+        {
+            0: [1, 2, 5],
+            1: [0, 5],
+            2: [0, 3, 4],
+            3: [2, 4, 5, 6],
+            4: [2, 3, 5, 6],
+            5: [0, 1, 3, 4],
+            6: [3, 4],
+        }
+    )
+    G2 = nx.Graph(
+        {
+            0: [2, 5],
+            1: [3, 8],
+            2: [0, 3, 5],
+            3: [1, 2, 6, 8],
+            4: [7],
+            5: [0, 2],
+            6: [3, 8],
+            7: [4],
+            8: [1, 3, 6],
+        }
+    )
+    assert nx.is_biconnected(G1)
+    assert not nx.is_biconnected(G2)
+    answer_G2 = [{1, 3, 6, 8}, {0, 2, 5}, {2, 3}, {4, 7}]
+    bcc = list(nx.biconnected_components(G2))
+    assert_components_equal(bcc, answer_G2)
+
+
+def test_null_graph():
+    G = nx.Graph()
+    assert not nx.is_biconnected(G)
+    assert list(nx.biconnected_components(G)) == []
+    assert list(nx.biconnected_component_edges(G)) == []
+    assert list(nx.articulation_points(G)) == []
+
+
+def test_connected_raise():
+    DG = nx.DiGraph()
+    with pytest.raises(NetworkXNotImplemented):
+        next(nx.biconnected_components(DG))
+    with pytest.raises(NetworkXNotImplemented):
+        next(nx.biconnected_component_edges(DG))
+    with pytest.raises(NetworkXNotImplemented):
+        next(nx.articulation_points(DG))
+    pytest.raises(NetworkXNotImplemented, nx.is_biconnected, DG)

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_connected.py

@@ -0,0 +1,117 @@
+import pytest
+
+import networkx as nx
+from networkx import NetworkXNotImplemented
+from networkx import convert_node_labels_to_integers as cnlti
+from networkx.classes.tests import dispatch_interface
+
+
+class TestConnected:
+    @classmethod
+    def setup_class(cls):
+        G1 = cnlti(nx.grid_2d_graph(2, 2), first_label=0, ordering="sorted")
+        G2 = cnlti(nx.lollipop_graph(3, 3), first_label=4, ordering="sorted")
+        G3 = cnlti(nx.house_graph(), first_label=10, ordering="sorted")
+        cls.G = nx.union(G1, G2)
+        cls.G = nx.union(cls.G, G3)
+        cls.DG = nx.DiGraph([(1, 2), (1, 3), (2, 3)])
+        cls.grid = cnlti(nx.grid_2d_graph(4, 4), first_label=1)
+
+        cls.gc = []
+        G = nx.DiGraph()
+        G.add_edges_from(
+            [
+                (1, 2),
+                (2, 3),
+                (2, 8),
+                (3, 4),
+                (3, 7),
+                (4, 5),
+                (5, 3),
+                (5, 6),
+                (7, 4),
+                (7, 6),
+                (8, 1),
+                (8, 7),
+            ]
+        )
+        C = [[3, 4, 5, 7], [1, 2, 8], [6]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (1, 3), (1, 4), (4, 2), (3, 4), (2, 3)])
+        C = [[2, 3, 4], [1]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (2, 3), (3, 2), (2, 1)])
+        C = [[1, 2, 3]]
+        cls.gc.append((G, C))
+
+        # Eppstein's tests
+        G = nx.DiGraph({0: [1], 1: [2, 3], 2: [4, 5], 3: [4, 5], 4: [6], 5: [], 6: []})
+        C = [[0], [1], [2], [3], [4], [5], [6]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph({0: [1], 1: [2, 3, 4], 2: [0, 3], 3: [4], 4: [3]})
+        C = [[0, 1, 2], [3, 4]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        C = []
+        cls.gc.append((G, C))
+
+    # This additionally tests the @nx._dispatchable mechanism, treating
+    # nx.connected_components as if it were a re-implementation from another package
+    @pytest.mark.parametrize("wrapper", [lambda x: x, dispatch_interface.convert])
+    def test_connected_components(self, wrapper):
+        cc = nx.connected_components
+        G = wrapper(self.G)
+        C = {
+            frozenset([0, 1, 2, 3]),
+            frozenset([4, 5, 6, 7, 8, 9]),
+            frozenset([10, 11, 12, 13, 14]),
+        }
+        assert {frozenset(g) for g in cc(G)} == C
+
+    def test_number_connected_components(self):
+        ncc = nx.number_connected_components
+        assert ncc(self.G) == 3
+
+    def test_number_connected_components2(self):
+        ncc = nx.number_connected_components
+        assert ncc(self.grid) == 1
+
+    def test_connected_components2(self):
+        cc = nx.connected_components
+        G = self.grid
+        C = {frozenset([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16])}
+        assert {frozenset(g) for g in cc(G)} == C
+
+    def test_node_connected_components(self):
+        ncc = nx.node_connected_component
+        G = self.grid
+        C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
+        assert ncc(G, 1) == C
+
+    def test_is_connected(self):
+        assert nx.is_connected(self.grid)
+        G = nx.Graph()
+        G.add_nodes_from([1, 2])
+        assert not nx.is_connected(G)
+
+    def test_connected_raise(self):
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.connected_components(self.DG))
+        pytest.raises(NetworkXNotImplemented, nx.number_connected_components, self.DG)
+        pytest.raises(NetworkXNotImplemented, nx.node_connected_component, self.DG, 1)
+        pytest.raises(NetworkXNotImplemented, nx.is_connected, self.DG)
+        pytest.raises(nx.NetworkXPointlessConcept, nx.is_connected, nx.Graph())
+
+    def test_connected_mutability(self):
+        G = self.grid
+        seen = set()
+        for component in nx.connected_components(G):
+            assert len(seen & component) == 0
+            seen.update(component)
+            component.clear()

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_semiconnected.py

@@ -0,0 +1,55 @@
+from itertools import chain
+
+import pytest
+
+import networkx as nx
+
+
+class TestIsSemiconnected:
+    def test_undirected(self):
+        pytest.raises(nx.NetworkXNotImplemented, nx.is_semiconnected, nx.Graph())
+        pytest.raises(nx.NetworkXNotImplemented, nx.is_semiconnected, nx.MultiGraph())
+
+    def test_empty(self):
+        pytest.raises(nx.NetworkXPointlessConcept, nx.is_semiconnected, nx.DiGraph())
+        pytest.raises(
+            nx.NetworkXPointlessConcept, nx.is_semiconnected, nx.MultiDiGraph()
+        )
+
+    def test_single_node_graph(self):
+        G = nx.DiGraph()
+        G.add_node(0)
+        assert nx.is_semiconnected(G)
+
+    def test_path(self):
+        G = nx.path_graph(100, create_using=nx.DiGraph())
+        assert nx.is_semiconnected(G)
+        G.add_edge(100, 99)
+        assert not nx.is_semiconnected(G)
+
+    def test_cycle(self):
+        G = nx.cycle_graph(100, create_using=nx.DiGraph())
+        assert nx.is_semiconnected(G)
+        G = nx.path_graph(100, create_using=nx.DiGraph())
+        G.add_edge(0, 99)
+        assert nx.is_semiconnected(G)
+
+    def test_tree(self):
+        G = nx.DiGraph()
+        G.add_edges_from(
+            chain.from_iterable([(i, 2 * i + 1), (i, 2 * i + 2)] for i in range(100))
+        )
+        assert not nx.is_semiconnected(G)
+
+    def test_dumbbell(self):
+        G = nx.cycle_graph(100, create_using=nx.DiGraph())
+        G.add_edges_from((i + 100, (i + 1) % 100 + 100) for i in range(100))
+        assert not nx.is_semiconnected(G)  # G is disconnected.
+        G.add_edge(100, 99)
+        assert nx.is_semiconnected(G)
+
+    def test_alternating_path(self):
+        G = nx.DiGraph(
+            chain.from_iterable([(i, i - 1), (i, i + 1)] for i in range(0, 100, 2))
+        )
+        assert not nx.is_semiconnected(G)

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_strongly_connected.py

@@ -0,0 +1,203 @@
+import pytest
+
+import networkx as nx
+from networkx import NetworkXNotImplemented
+
+
+class TestStronglyConnected:
+    @classmethod
+    def setup_class(cls):
+        cls.gc = []
+        G = nx.DiGraph()
+        G.add_edges_from(
+            [
+                (1, 2),
+                (2, 3),
+                (2, 8),
+                (3, 4),
+                (3, 7),
+                (4, 5),
+                (5, 3),
+                (5, 6),
+                (7, 4),
+                (7, 6),
+                (8, 1),
+                (8, 7),
+            ]
+        )
+        C = {frozenset([3, 4, 5, 7]), frozenset([1, 2, 8]), frozenset([6])}
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (1, 3), (1, 4), (4, 2), (3, 4), (2, 3)])
+        C = {frozenset([2, 3, 4]), frozenset([1])}
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (2, 3), (3, 2), (2, 1)])
+        C = {frozenset([1, 2, 3])}
+        cls.gc.append((G, C))
+
+        # Eppstein's tests
+        G = nx.DiGraph({0: [1], 1: [2, 3], 2: [4, 5], 3: [4, 5], 4: [6], 5: [], 6: []})
+        C = {
+            frozenset([0]),
+            frozenset([1]),
+            frozenset([2]),
+            frozenset([3]),
+            frozenset([4]),
+            frozenset([5]),
+            frozenset([6]),
+        }
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph({0: [1], 1: [2, 3, 4], 2: [0, 3], 3: [4], 4: [3]})
+        C = {frozenset([0, 1, 2]), frozenset([3, 4])}
+        cls.gc.append((G, C))
+
+    def test_tarjan(self):
+        scc = nx.strongly_connected_components
+        for G, C in self.gc:
+            assert {frozenset(g) for g in scc(G)} == C
+
+    def test_tarjan_recursive(self):
+        scc = nx.strongly_connected_components_recursive
+        for G, C in self.gc:
+            with pytest.deprecated_call():
+                assert {frozenset(g) for g in scc(G)} == C
+
+    def test_kosaraju(self):
+        scc = nx.kosaraju_strongly_connected_components
+        for G, C in self.gc:
+            assert {frozenset(g) for g in scc(G)} == C
+
+    def test_number_strongly_connected_components(self):
+        ncc = nx.number_strongly_connected_components
+        for G, C in self.gc:
+            assert ncc(G) == len(C)
+
+    def test_is_strongly_connected(self):
+        for G, C in self.gc:
+            if len(C) == 1:
+                assert nx.is_strongly_connected(G)
+            else:
+                assert not nx.is_strongly_connected(G)
+
+    def test_contract_scc1(self):
+        G = nx.DiGraph()
+        G.add_edges_from(
+            [
+                (1, 2),
+                (2, 3),
+                (2, 11),
+                (2, 12),
+                (3, 4),
+                (4, 3),
+                (4, 5),
+                (5, 6),
+                (6, 5),
+                (6, 7),
+                (7, 8),
+                (7, 9),
+                (7, 10),
+                (8, 9),
+                (9, 7),
+                (10, 6),
+                (11, 2),
+                (11, 4),
+                (11, 6),
+                (12, 6),
+                (12, 11),
+            ]
+        )
+        scc = list(nx.strongly_connected_components(G))
+        cG = nx.condensation(G, scc)
+        # DAG
+        assert nx.is_directed_acyclic_graph(cG)
+        # nodes
+        assert sorted(cG.nodes()) == [0, 1, 2, 3]
+        # edges
+        mapping = {}
+        for i, component in enumerate(scc):
+            for n in component:
+                mapping[n] = i
+        edge = (mapping[2], mapping[3])
+        assert cG.has_edge(*edge)
+        edge = (mapping[2], mapping[5])
+        assert cG.has_edge(*edge)
+        edge = (mapping[3], mapping[5])
+        assert cG.has_edge(*edge)
+
+    def test_contract_scc_isolate(self):
+        # Bug found and fixed in [1687].
+        G = nx.DiGraph()
+        G.add_edge(1, 2)
+        G.add_edge(2, 1)
+        scc = list(nx.strongly_connected_components(G))
+        cG = nx.condensation(G, scc)
+        assert list(cG.nodes()) == [0]
+        assert list(cG.edges()) == []
+
+    def test_contract_scc_edge(self):
+        G = nx.DiGraph()
+        G.add_edge(1, 2)
+        G.add_edge(2, 1)
+        G.add_edge(2, 3)
+        G.add_edge(3, 4)
+        G.add_edge(4, 3)
+        scc = list(nx.strongly_connected_components(G))
+        cG = nx.condensation(G, scc)
+        assert sorted(cG.nodes()) == [0, 1]
+        if 1 in scc[0]:
+            edge = (0, 1)
+        else:
+            edge = (1, 0)
+        assert list(cG.edges()) == [edge]
+
+    def test_condensation_mapping_and_members(self):
+        G, C = self.gc[1]
+        C = sorted(C, key=len, reverse=True)
+        cG = nx.condensation(G)
+        mapping = cG.graph["mapping"]
+        assert all(n in G for n in mapping)
+        assert all(0 == cN for n, cN in mapping.items() if n in C[0])
+        assert all(1 == cN for n, cN in mapping.items() if n in C[1])
+        for n, d in cG.nodes(data=True):
+            assert set(C[n]) == cG.nodes[n]["members"]
+
+    def test_null_graph(self):
+        G = nx.DiGraph()
+        assert list(nx.strongly_connected_components(G)) == []
+        assert list(nx.kosaraju_strongly_connected_components(G)) == []
+        with pytest.deprecated_call():
+            assert list(nx.strongly_connected_components_recursive(G)) == []
+        assert len(nx.condensation(G)) == 0
+        pytest.raises(
+            nx.NetworkXPointlessConcept, nx.is_strongly_connected, nx.DiGraph()
+        )
+
+    def test_connected_raise(self):
+        G = nx.Graph()
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.strongly_connected_components(G))
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.kosaraju_strongly_connected_components(G))
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.strongly_connected_components_recursive(G))
+        pytest.raises(NetworkXNotImplemented, nx.is_strongly_connected, G)
+        pytest.raises(NetworkXNotImplemented, nx.condensation, G)
+
+    strong_cc_methods = (
+        nx.strongly_connected_components,
+        nx.kosaraju_strongly_connected_components,
+    )
+
+    @pytest.mark.parametrize("get_components", strong_cc_methods)
+    def test_connected_mutability(self, get_components):
+        DG = nx.path_graph(5, create_using=nx.DiGraph)
+        G = nx.disjoint_union(DG, DG)
+        seen = set()
+        for component in get_components(G):
+            assert len(seen & component) == 0
+            seen.update(component)
+            component.clear()

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_weakly_connected.py

@@ -0,0 +1,96 @@
+import pytest
+
+import networkx as nx
+from networkx import NetworkXNotImplemented
+
+
+class TestWeaklyConnected:
+    @classmethod
+    def setup_class(cls):
+        cls.gc = []
+        G = nx.DiGraph()
+        G.add_edges_from(
+            [
+                (1, 2),
+                (2, 3),
+                (2, 8),
+                (3, 4),
+                (3, 7),
+                (4, 5),
+                (5, 3),
+                (5, 6),
+                (7, 4),
+                (7, 6),
+                (8, 1),
+                (8, 7),
+            ]
+        )
+        C = [[3, 4, 5, 7], [1, 2, 8], [6]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (1, 3), (1, 4), (4, 2), (3, 4), (2, 3)])
+        C = [[2, 3, 4], [1]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (2, 3), (3, 2), (2, 1)])
+        C = [[1, 2, 3]]
+        cls.gc.append((G, C))
+
+        # Eppstein's tests
+        G = nx.DiGraph({0: [1], 1: [2, 3], 2: [4, 5], 3: [4, 5], 4: [6], 5: [], 6: []})
+        C = [[0], [1], [2], [3], [4], [5], [6]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph({0: [1], 1: [2, 3, 4], 2: [0, 3], 3: [4], 4: [3]})
+        C = [[0, 1, 2], [3, 4]]
+        cls.gc.append((G, C))
+
+    def test_weakly_connected_components(self):
+        for G, C in self.gc:
+            U = G.to_undirected()
+            w = {frozenset(g) for g in nx.weakly_connected_components(G)}
+            c = {frozenset(g) for g in nx.connected_components(U)}
+            assert w == c
+
+    def test_number_weakly_connected_components(self):
+        for G, C in self.gc:
+            U = G.to_undirected()
+            w = nx.number_weakly_connected_components(G)
+            c = nx.number_connected_components(U)
+            assert w == c
+
+    def test_is_weakly_connected(self):
+        for G, C in self.gc:
+            U = G.to_undirected()
+            assert nx.is_weakly_connected(G) == nx.is_connected(U)
+
+    def test_null_graph(self):
+        G = nx.DiGraph()
+        assert list(nx.weakly_connected_components(G)) == []
+        assert nx.number_weakly_connected_components(G) == 0
+        with pytest.raises(nx.NetworkXPointlessConcept):
+            next(nx.is_weakly_connected(G))
+
+    def test_connected_raise(self):
+        G = nx.Graph()
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.weakly_connected_components(G))
+        pytest.raises(NetworkXNotImplemented, nx.number_weakly_connected_components, G)
+        pytest.raises(NetworkXNotImplemented, nx.is_weakly_connected, G)
+
+    def test_connected_mutability(self):
+        DG = nx.path_graph(5, create_using=nx.DiGraph)
+        G = nx.disjoint_union(DG, DG)
+        seen = set()
+        for component in nx.weakly_connected_components(G):
+            assert len(seen & component) == 0
+            seen.update(component)
+            component.clear()
+
+
+def test_is_weakly_connected_empty_graph_raises():
+    G = nx.DiGraph()
+    with pytest.raises(nx.NetworkXPointlessConcept, match="Connectivity is undefined"):
+        nx.is_weakly_connected(G)

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/components/weakly_connected.py

@@ -0,0 +1,193 @@
+"""Weakly connected components."""
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = [
+    "number_weakly_connected_components",
+    "weakly_connected_components",
+    "is_weakly_connected",
+]
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def weakly_connected_components(G):
+    """Generate weakly connected components of G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A directed graph
+
+    Returns
+    -------
+    comp : generator of sets
+        A generator of sets of nodes, one for each weakly connected
+        component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    Generate a sorted list of weakly connected components, largest first.
+
+    >>> G = nx.path_graph(4, create_using=nx.DiGraph())
+    >>> nx.add_path(G, [10, 11, 12])
+    >>> [len(c) for c in sorted(nx.weakly_connected_components(G), key=len, reverse=True)]
+    [4, 3]
+
+    If you only want the largest component, it's more efficient to
+    use max instead of sort:
+
+    >>> largest_cc = max(nx.weakly_connected_components(G), key=len)
+
+    See Also
+    --------
+    connected_components
+    strongly_connected_components
+
+    Notes
+    -----
+    For directed graphs only.
+
+    """
+    seen = set()
+    for v in G:
+        if v not in seen:
+            c = set(_plain_bfs(G, v))
+            seen.update(c)
+            yield c
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def number_weakly_connected_components(G):
+    """Returns the number of weakly connected components in G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A directed graph.
+
+    Returns
+    -------
+    n : integer
+        Number of weakly connected components
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(0, 1), (2, 1), (3, 4)])
+    >>> nx.number_weakly_connected_components(G)
+    2
+
+    See Also
+    --------
+    weakly_connected_components
+    number_connected_components
+    number_strongly_connected_components
+
+    Notes
+    -----
+    For directed graphs only.
+
+    """
+    return sum(1 for wcc in weakly_connected_components(G))
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def is_weakly_connected(G):
+    """Test directed graph for weak connectivity.
+
+    A directed graph is weakly connected if and only if the graph
+    is connected when the direction of the edge between nodes is ignored.
+
+    Note that if a graph is strongly connected (i.e. the graph is connected
+    even when we account for directionality), it is by definition weakly
+    connected as well.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        A directed graph.
+
+    Returns
+    -------
+    connected : bool
+        True if the graph is weakly connected, False otherwise.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(0, 1), (2, 1)])
+    >>> G.add_node(3)
+    >>> nx.is_weakly_connected(G)  # node 3 is not connected to the graph
+    False
+    >>> G.add_edge(2, 3)
+    >>> nx.is_weakly_connected(G)
+    True
+
+    See Also
+    --------
+    is_strongly_connected
+    is_semiconnected
+    is_connected
+    is_biconnected
+    weakly_connected_components
+
+    Notes
+    -----
+    For directed graphs only.
+
+    """
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept(
+            """Connectivity is undefined for the null graph."""
+        )
+
+    return len(next(weakly_connected_components(G))) == len(G)
+
+
+def _plain_bfs(G, source):
+    """A fast BFS node generator
+
+    The direction of the edge between nodes is ignored.
+
+    For directed graphs only.
+
+    """
+    n = len(G)
+    Gsucc = G._succ
+    Gpred = G._pred
+    seen = {source}
+    nextlevel = [source]
+
+    yield source
+    while nextlevel:
+        thislevel = nextlevel
+        nextlevel = []
+        for v in thislevel:
+            for w in Gsucc[v]:
+                if w not in seen:
+                    seen.add(w)
+                    nextlevel.append(w)
+                    yield w
+            for w in Gpred[v]:
+                if w not in seen:
+                    seen.add(w)
+                    nextlevel.append(w)
+                    yield w
+            if len(seen) == n:
+                return

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/flow/tests/netgen-2.gpickle.bz2

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3b17e66cdeda8edb8d1dec72626c77f1f65dd4675e3f76dc2fc4fd84aa038e30
+size 18972

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__init__.py

@@ -0,0 +1,7 @@
+from networkx.algorithms.isomorphism.isomorph import *
+from networkx.algorithms.isomorphism.vf2userfunc import *
+from networkx.algorithms.isomorphism.matchhelpers import *
+from networkx.algorithms.isomorphism.temporalisomorphvf2 import *
+from networkx.algorithms.isomorphism.ismags import *
+from networkx.algorithms.isomorphism.tree_isomorphism import *
+from networkx.algorithms.isomorphism.vf2pp import *

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/isomorphism/ismags.py

@@ -0,0 +1,1163 @@
+"""
+ISMAGS Algorithm
+================
+
+Provides a Python implementation of the ISMAGS algorithm. [1]_
+
+It is capable of finding (subgraph) isomorphisms between two graphs, taking the
+symmetry of the subgraph into account. In most cases the VF2 algorithm is
+faster (at least on small graphs) than this implementation, but in some cases
+there is an exponential number of isomorphisms that are symmetrically
+equivalent. In that case, the ISMAGS algorithm will provide only one solution
+per symmetry group.
+
+>>> petersen = nx.petersen_graph()
+>>> ismags = nx.isomorphism.ISMAGS(petersen, petersen)
+>>> isomorphisms = list(ismags.isomorphisms_iter(symmetry=False))
+>>> len(isomorphisms)
+120
+>>> isomorphisms = list(ismags.isomorphisms_iter(symmetry=True))
+>>> answer = [{0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9}]
+>>> answer == isomorphisms
+True
+
+In addition, this implementation also provides an interface to find the
+largest common induced subgraph [2]_ between any two graphs, again taking
+symmetry into account. Given `graph` and `subgraph` the algorithm will remove
+nodes from the `subgraph` until `subgraph` is isomorphic to a subgraph of
+`graph`. Since only the symmetry of `subgraph` is taken into account it is
+worth thinking about how you provide your graphs:
+
+>>> graph1 = nx.path_graph(4)
+>>> graph2 = nx.star_graph(3)
+>>> ismags = nx.isomorphism.ISMAGS(graph1, graph2)
+>>> ismags.is_isomorphic()
+False
+>>> largest_common_subgraph = list(ismags.largest_common_subgraph())
+>>> answer = [{1: 0, 0: 1, 2: 2}, {2: 0, 1: 1, 3: 2}]
+>>> answer == largest_common_subgraph
+True
+>>> ismags2 = nx.isomorphism.ISMAGS(graph2, graph1)
+>>> largest_common_subgraph = list(ismags2.largest_common_subgraph())
+>>> answer = [
+...     {1: 0, 0: 1, 2: 2},
+...     {1: 0, 0: 1, 3: 2},
+...     {2: 0, 0: 1, 1: 2},
+...     {2: 0, 0: 1, 3: 2},
+...     {3: 0, 0: 1, 1: 2},
+...     {3: 0, 0: 1, 2: 2},
+... ]
+>>> answer == largest_common_subgraph
+True
+
+However, when not taking symmetry into account, it doesn't matter:
+
+>>> largest_common_subgraph = list(ismags.largest_common_subgraph(symmetry=False))
+>>> answer = [
+...     {1: 0, 0: 1, 2: 2},
+...     {1: 0, 2: 1, 0: 2},
+...     {2: 0, 1: 1, 3: 2},
+...     {2: 0, 3: 1, 1: 2},
+...     {1: 0, 0: 1, 2: 3},
+...     {1: 0, 2: 1, 0: 3},
+...     {2: 0, 1: 1, 3: 3},
+...     {2: 0, 3: 1, 1: 3},
+...     {1: 0, 0: 2, 2: 3},
+...     {1: 0, 2: 2, 0: 3},
+...     {2: 0, 1: 2, 3: 3},
+...     {2: 0, 3: 2, 1: 3},
+... ]
+>>> answer == largest_common_subgraph
+True
+>>> largest_common_subgraph = list(ismags2.largest_common_subgraph(symmetry=False))
+>>> answer = [
+...     {1: 0, 0: 1, 2: 2},
+...     {1: 0, 0: 1, 3: 2},
+...     {2: 0, 0: 1, 1: 2},
+...     {2: 0, 0: 1, 3: 2},
+...     {3: 0, 0: 1, 1: 2},
+...     {3: 0, 0: 1, 2: 2},
+...     {1: 1, 0: 2, 2: 3},
+...     {1: 1, 0: 2, 3: 3},
+...     {2: 1, 0: 2, 1: 3},
+...     {2: 1, 0: 2, 3: 3},
+...     {3: 1, 0: 2, 1: 3},
+...     {3: 1, 0: 2, 2: 3},
+... ]
+>>> answer == largest_common_subgraph
+True
+
+Notes
+-----
+- The current implementation works for undirected graphs only. The algorithm
+  in general should work for directed graphs as well though.
+- Node keys for both provided graphs need to be fully orderable as well as
+  hashable.
+- Node and edge equality is assumed to be transitive: if A is equal to B, and
+  B is equal to C, then A is equal to C.
+
+References
+----------
+.. [1] M. Houbraken, S. Demeyer, T. Michoel, P. Audenaert, D. Colle,
+   M. Pickavet, "The Index-Based Subgraph Matching Algorithm with General
+   Symmetries (ISMAGS): Exploiting Symmetry for Faster Subgraph
+   Enumeration", PLoS One 9(5): e97896, 2014.
+   https://doi.org/10.1371/journal.pone.0097896
+.. [2] https://en.wikipedia.org/wiki/Maximum_common_induced_subgraph
+"""
+
+__all__ = ["ISMAGS"]
+
+import itertools
+from collections import Counter, defaultdict
+from functools import reduce, wraps
+
+
+def are_all_equal(iterable):
+    """
+    Returns ``True`` if and only if all elements in `iterable` are equal; and
+    ``False`` otherwise.
+
+    Parameters
+    ----------
+    iterable: collections.abc.Iterable
+        The container whose elements will be checked.
+
+    Returns
+    -------
+    bool
+        ``True`` iff all elements in `iterable` compare equal, ``False``
+        otherwise.
+    """
+    try:
+        shape = iterable.shape
+    except AttributeError:
+        pass
+    else:
+        if len(shape) > 1:
+            message = "The function does not works on multidimensional arrays."
+            raise NotImplementedError(message) from None
+
+    iterator = iter(iterable)
+    first = next(iterator, None)
+    return all(item == first for item in iterator)
+
+
+def make_partitions(items, test):
+    """
+    Partitions items into sets based on the outcome of ``test(item1, item2)``.
+    Pairs of items for which `test` returns `True` end up in the same set.
+
+    Parameters
+    ----------
+    items : collections.abc.Iterable[collections.abc.Hashable]
+        Items to partition
+    test : collections.abc.Callable[collections.abc.Hashable, collections.abc.Hashable]
+        A function that will be called with 2 arguments, taken from items.
+        Should return `True` if those 2 items need to end up in the same
+        partition, and `False` otherwise.
+
+    Returns
+    -------
+    list[set]
+        A list of sets, with each set containing part of the items in `items`,
+        such that ``all(test(*pair) for pair in  itertools.combinations(set, 2))
+        == True``
+
+    Notes
+    -----
+    The function `test` is assumed to be transitive: if ``test(a, b)`` and
+    ``test(b, c)`` return ``True``, then ``test(a, c)`` must also be ``True``.
+    """
+    partitions = []
+    for item in items:
+        for partition in partitions:
+            p_item = next(iter(partition))
+            if test(item, p_item):
+                partition.add(item)
+                break
+        else:  # No break
+            partitions.append({item})
+    return partitions
+
+
+def partition_to_color(partitions):
+    """
+    Creates a dictionary that maps each item in each partition to the index of
+    the partition to which it belongs.
+
+    Parameters
+    ----------
+    partitions: collections.abc.Sequence[collections.abc.Iterable]
+        As returned by :func:`make_partitions`.
+
+    Returns
+    -------
+    dict
+    """
+    colors = {}
+    for color, keys in enumerate(partitions):
+        for key in keys:
+            colors[key] = color
+    return colors
+
+
+def intersect(collection_of_sets):
+    """
+    Given an collection of sets, returns the intersection of those sets.
+
+    Parameters
+    ----------
+    collection_of_sets: collections.abc.Collection[set]
+        A collection of sets.
+
+    Returns
+    -------
+    set
+        An intersection of all sets in `collection_of_sets`. Will have the same
+        type as the item initially taken from `collection_of_sets`.
+    """
+    collection_of_sets = list(collection_of_sets)
+    first = collection_of_sets.pop()
+    out = reduce(set.intersection, collection_of_sets, set(first))
+    return type(first)(out)
+
+
+class ISMAGS:
+    """
+    Implements the ISMAGS subgraph matching algorithm. [1]_ ISMAGS stands for
+    "Index-based Subgraph Matching Algorithm with General Symmetries". As the
+    name implies, it is symmetry aware and will only generate non-symmetric
+    isomorphisms.
+
+    Notes
+    -----
+    The implementation imposes additional conditions compared to the VF2
+    algorithm on the graphs provided and the comparison functions
+    (:attr:`node_equality` and :attr:`edge_equality`):
+
+     - Node keys in both graphs must be orderable as well as hashable.
+     - Equality must be transitive: if A is equal to B, and B is equal to C,
+       then A must be equal to C.
+
+    Attributes
+    ----------
+    graph: networkx.Graph
+    subgraph: networkx.Graph
+    node_equality: collections.abc.Callable
+        The function called to see if two nodes should be considered equal.
+        It's signature looks like this:
+        ``f(graph1: networkx.Graph, node1, graph2: networkx.Graph, node2) -> bool``.
+        `node1` is a node in `graph1`, and `node2` a node in `graph2`.
+        Constructed from the argument `node_match`.
+    edge_equality: collections.abc.Callable
+        The function called to see if two edges should be considered equal.
+        It's signature looks like this:
+        ``f(graph1: networkx.Graph, edge1, graph2: networkx.Graph, edge2) -> bool``.
+        `edge1` is an edge in `graph1`, and `edge2` an edge in `graph2`.
+        Constructed from the argument `edge_match`.
+
+    References
+    ----------
+    .. [1] M. Houbraken, S. Demeyer, T. Michoel, P. Audenaert, D. Colle,
+       M. Pickavet, "The Index-Based Subgraph Matching Algorithm with General
+       Symmetries (ISMAGS): Exploiting Symmetry for Faster Subgraph
+       Enumeration", PLoS One 9(5): e97896, 2014.
+       https://doi.org/10.1371/journal.pone.0097896
+    """
+
+    def __init__(self, graph, subgraph, node_match=None, edge_match=None, cache=None):
+        """
+        Parameters
+        ----------
+        graph: networkx.Graph
+        subgraph: networkx.Graph
+        node_match: collections.abc.Callable or None
+            Function used to determine whether two nodes are equivalent. Its
+            signature should look like ``f(n1: dict, n2: dict) -> bool``, with
+            `n1` and `n2` node property dicts. See also
+            :func:`~networkx.algorithms.isomorphism.categorical_node_match` and
+            friends.
+            If `None`, all nodes are considered equal.
+        edge_match: collections.abc.Callable or None
+            Function used to determine whether two edges are equivalent. Its
+            signature should look like ``f(e1: dict, e2: dict) -> bool``, with
+            `e1` and `e2` edge property dicts. See also
+            :func:`~networkx.algorithms.isomorphism.categorical_edge_match` and
+            friends.
+            If `None`, all edges are considered equal.
+        cache: collections.abc.Mapping
+            A cache used for caching graph symmetries.
+        """
+        # TODO: graph and subgraph setter methods that invalidate the caches.
+        # TODO: allow for precomputed partitions and colors
+        self.graph = graph
+        self.subgraph = subgraph
+        self._symmetry_cache = cache
+        # Naming conventions are taken from the original paper. For your
+        # sanity:
+        #   sg: subgraph
+        #   g: graph
+        #   e: edge(s)
+        #   n: node(s)
+        # So: sgn means "subgraph nodes".
+        self._sgn_partitions_ = None
+        self._sge_partitions_ = None
+
+        self._sgn_colors_ = None
+        self._sge_colors_ = None
+
+        self._gn_partitions_ = None
+        self._ge_partitions_ = None
+
+        self._gn_colors_ = None
+        self._ge_colors_ = None
+
+        self._node_compat_ = None
+        self._edge_compat_ = None
+
+        if node_match is None:
+            self.node_equality = self._node_match_maker(lambda n1, n2: True)
+            self._sgn_partitions_ = [set(self.subgraph.nodes)]
+            self._gn_partitions_ = [set(self.graph.nodes)]
+            self._node_compat_ = {0: 0}
+        else:
+            self.node_equality = self._node_match_maker(node_match)
+        if edge_match is None:
+            self.edge_equality = self._edge_match_maker(lambda e1, e2: True)
+            self._sge_partitions_ = [set(self.subgraph.edges)]
+            self._ge_partitions_ = [set(self.graph.edges)]
+            self._edge_compat_ = {0: 0}
+        else:
+            self.edge_equality = self._edge_match_maker(edge_match)
+
+    @property
+    def _sgn_partitions(self):
+        if self._sgn_partitions_ is None:
+
+            def nodematch(node1, node2):
+                return self.node_equality(self.subgraph, node1, self.subgraph, node2)
+
+            self._sgn_partitions_ = make_partitions(self.subgraph.nodes, nodematch)
+        return self._sgn_partitions_
+
+    @property
+    def _sge_partitions(self):
+        if self._sge_partitions_ is None:
+
+            def edgematch(edge1, edge2):
+                return self.edge_equality(self.subgraph, edge1, self.subgraph, edge2)
+
+            self._sge_partitions_ = make_partitions(self.subgraph.edges, edgematch)
+        return self._sge_partitions_
+
+    @property
+    def _gn_partitions(self):
+        if self._gn_partitions_ is None:
+
+            def nodematch(node1, node2):
+                return self.node_equality(self.graph, node1, self.graph, node2)
+
+            self._gn_partitions_ = make_partitions(self.graph.nodes, nodematch)
+        return self._gn_partitions_
+
+    @property
+    def _ge_partitions(self):
+        if self._ge_partitions_ is None:
+
+            def edgematch(edge1, edge2):
+                return self.edge_equality(self.graph, edge1, self.graph, edge2)
+
+            self._ge_partitions_ = make_partitions(self.graph.edges, edgematch)
+        return self._ge_partitions_
+
+    @property
+    def _sgn_colors(self):
+        if self._sgn_colors_ is None:
+            self._sgn_colors_ = partition_to_color(self._sgn_partitions)
+        return self._sgn_colors_
+
+    @property
+    def _sge_colors(self):
+        if self._sge_colors_ is None:
+            self._sge_colors_ = partition_to_color(self._sge_partitions)
+        return self._sge_colors_
+
+    @property
+    def _gn_colors(self):
+        if self._gn_colors_ is None:
+            self._gn_colors_ = partition_to_color(self._gn_partitions)
+        return self._gn_colors_
+
+    @property
+    def _ge_colors(self):
+        if self._ge_colors_ is None:
+            self._ge_colors_ = partition_to_color(self._ge_partitions)
+        return self._ge_colors_
+
+    @property
+    def _node_compatibility(self):
+        if self._node_compat_ is not None:
+            return self._node_compat_
+        self._node_compat_ = {}
+        for sgn_part_color, gn_part_color in itertools.product(
+            range(len(self._sgn_partitions)), range(len(self._gn_partitions))
+        ):
+            sgn = next(iter(self._sgn_partitions[sgn_part_color]))
+            gn = next(iter(self._gn_partitions[gn_part_color]))
+            if self.node_equality(self.subgraph, sgn, self.graph, gn):
+                self._node_compat_[sgn_part_color] = gn_part_color
+        return self._node_compat_
+
+    @property
+    def _edge_compatibility(self):
+        if self._edge_compat_ is not None:
+            return self._edge_compat_
+        self._edge_compat_ = {}
+        for sge_part_color, ge_part_color in itertools.product(
+            range(len(self._sge_partitions)), range(len(self._ge_partitions))
+        ):
+            sge = next(iter(self._sge_partitions[sge_part_color]))
+            ge = next(iter(self._ge_partitions[ge_part_color]))
+            if self.edge_equality(self.subgraph, sge, self.graph, ge):
+                self._edge_compat_[sge_part_color] = ge_part_color
+        return self._edge_compat_
+
+    @staticmethod
+    def _node_match_maker(cmp):
+        @wraps(cmp)
+        def comparer(graph1, node1, graph2, node2):
+            return cmp(graph1.nodes[node1], graph2.nodes[node2])
+
+        return comparer
+
+    @staticmethod
+    def _edge_match_maker(cmp):
+        @wraps(cmp)
+        def comparer(graph1, edge1, graph2, edge2):
+            return cmp(graph1.edges[edge1], graph2.edges[edge2])
+
+        return comparer
+
+    def find_isomorphisms(self, symmetry=True):
+        """Find all subgraph isomorphisms between subgraph and graph
+
+        Finds isomorphisms where :attr:`subgraph` <= :attr:`graph`.
+
+        Parameters
+        ----------
+        symmetry: bool
+            Whether symmetry should be taken into account. If False, found
+            isomorphisms may be symmetrically equivalent.
+
+        Yields
+        ------
+        dict
+            The found isomorphism mappings of {graph_node: subgraph_node}.
+        """
+        # The networkx VF2 algorithm is slightly funny in when it yields an
+        # empty dict and when not.
+        if not self.subgraph:
+            yield {}
+            return
+        elif not self.graph:
+            return
+        elif len(self.graph) < len(self.subgraph):
+            return
+
+        if symmetry:
+            _, cosets = self.analyze_symmetry(
+                self.subgraph, self._sgn_partitions, self._sge_colors
+            )
+            constraints = self._make_constraints(cosets)
+        else:
+            constraints = []
+
+        candidates = self._find_nodecolor_candidates()
+        la_candidates = self._get_lookahead_candidates()
+        for sgn in self.subgraph:
+            extra_candidates = la_candidates[sgn]
+            if extra_candidates:
+                candidates[sgn] = candidates[sgn] | {frozenset(extra_candidates)}
+
+        if any(candidates.values()):
+            start_sgn = min(candidates, key=lambda n: min(candidates[n], key=len))
+            candidates[start_sgn] = (intersect(candidates[start_sgn]),)
+            yield from self._map_nodes(start_sgn, candidates, constraints)
+        else:
+            return
+
+    @staticmethod
+    def _find_neighbor_color_count(graph, node, node_color, edge_color):
+        """
+        For `node` in `graph`, count the number of edges of a specific color
+        it has to nodes of a specific color.
+        """
+        counts = Counter()
+        neighbors = graph[node]
+        for neighbor in neighbors:
+            n_color = node_color[neighbor]
+            if (node, neighbor) in edge_color:
+                e_color = edge_color[node, neighbor]
+            else:
+                e_color = edge_color[neighbor, node]
+            counts[e_color, n_color] += 1
+        return counts
+
+    def _get_lookahead_candidates(self):
+        """
+        Returns a mapping of {subgraph node: collection of graph nodes} for
+        which the graph nodes are feasible candidates for the subgraph node, as
+        determined by looking ahead one edge.
+        """
+        g_counts = {}
+        for gn in self.graph:
+            g_counts[gn] = self._find_neighbor_color_count(
+                self.graph, gn, self._gn_colors, self._ge_colors
+            )
+        candidates = defaultdict(set)
+        for sgn in self.subgraph:
+            sg_count = self._find_neighbor_color_count(
+                self.subgraph, sgn, self._sgn_colors, self._sge_colors
+            )
+            new_sg_count = Counter()
+            for (sge_color, sgn_color), count in sg_count.items():
+                try:
+                    ge_color = self._edge_compatibility[sge_color]
+                    gn_color = self._node_compatibility[sgn_color]
+                except KeyError:
+                    pass
+                else:
+                    new_sg_count[ge_color, gn_color] = count
+
+            for gn, g_count in g_counts.items():
+                if all(new_sg_count[x] <= g_count[x] for x in new_sg_count):
+                    # Valid candidate
+                    candidates[sgn].add(gn)
+        return candidates
+
+    def largest_common_subgraph(self, symmetry=True):
+        """
+        Find the largest common induced subgraphs between :attr:`subgraph` and
+        :attr:`graph`.
+
+        Parameters
+        ----------
+        symmetry: bool
+            Whether symmetry should be taken into account. If False, found
+            largest common subgraphs may be symmetrically equivalent.
+
+        Yields
+        ------
+        dict
+            The found isomorphism mappings of {graph_node: subgraph_node}.
+        """
+        # The networkx VF2 algorithm is slightly funny in when it yields an
+        # empty dict and when not.
+        if not self.subgraph:
+            yield {}
+            return
+        elif not self.graph:
+            return
+
+        if symmetry:
+            _, cosets = self.analyze_symmetry(
+                self.subgraph, self._sgn_partitions, self._sge_colors
+            )
+            constraints = self._make_constraints(cosets)
+        else:
+            constraints = []
+
+        candidates = self._find_nodecolor_candidates()
+
+        if any(candidates.values()):
+            yield from self._largest_common_subgraph(candidates, constraints)
+        else:
+            return
+
+    def analyze_symmetry(self, graph, node_partitions, edge_colors):
+        """
+        Find a minimal set of permutations and corresponding co-sets that
+        describe the symmetry of `graph`, given the node and edge equalities
+        given by `node_partitions` and `edge_colors`, respectively.
+
+        Parameters
+        ----------
+        graph : networkx.Graph
+            The graph whose symmetry should be analyzed.
+        node_partitions : list of sets
+            A list of sets containing node keys. Node keys in the same set
+            are considered equivalent. Every node key in `graph` should be in
+            exactly one of the sets. If all nodes are equivalent, this should
+            be ``[set(graph.nodes)]``.
+        edge_colors : dict mapping edges to their colors
+            A dict mapping every edge in `graph` to its corresponding color.
+            Edges with the same color are considered equivalent. If all edges
+            are equivalent, this should be ``{e: 0 for e in graph.edges}``.
+
+
+        Returns
+        -------
+        set[frozenset]
+            The found permutations. This is a set of frozensets of pairs of node
+            keys which can be exchanged without changing :attr:`subgraph`.
+        dict[collections.abc.Hashable, set[collections.abc.Hashable]]
+            The found co-sets. The co-sets is a dictionary of
+            ``{node key: set of node keys}``.
+            Every key-value pair describes which ``values`` can be interchanged
+            without changing nodes less than ``key``.
+        """
+        if self._symmetry_cache is not None:
+            key = hash(
+                (
+                    tuple(graph.nodes),
+                    tuple(graph.edges),
+                    tuple(map(tuple, node_partitions)),
+                    tuple(edge_colors.items()),
+                )
+            )
+            if key in self._symmetry_cache:
+                return self._symmetry_cache[key]
+        node_partitions = list(
+            self._refine_node_partitions(graph, node_partitions, edge_colors)
+        )
+        assert len(node_partitions) == 1
+        node_partitions = node_partitions[0]
+        permutations, cosets = self._process_ordered_pair_partitions(
+            graph, node_partitions, node_partitions, edge_colors
+        )
+        if self._symmetry_cache is not None:
+            self._symmetry_cache[key] = permutations, cosets
+        return permutations, cosets
+
+    def is_isomorphic(self, symmetry=False):
+        """
+        Returns True if :attr:`graph` is isomorphic to :attr:`subgraph` and
+        False otherwise.
+
+        Returns
+        -------
+        bool
+        """
+        return len(self.subgraph) == len(self.graph) and self.subgraph_is_isomorphic(
+            symmetry
+        )
+
+    def subgraph_is_isomorphic(self, symmetry=False):
+        """
+        Returns True if a subgraph of :attr:`graph` is isomorphic to
+        :attr:`subgraph` and False otherwise.
+
+        Returns
+        -------
+        bool
+        """
+        # symmetry=False, since we only need to know whether there is any
+        # example; figuring out all symmetry elements probably costs more time
+        # than it gains.
+        isom = next(self.subgraph_isomorphisms_iter(symmetry=symmetry), None)
+        return isom is not None
+
+    def isomorphisms_iter(self, symmetry=True):
+        """
+        Does the same as :meth:`find_isomorphisms` if :attr:`graph` and
+        :attr:`subgraph` have the same number of nodes.
+        """
+        if len(self.graph) == len(self.subgraph):
+            yield from self.subgraph_isomorphisms_iter(symmetry=symmetry)
+
+    def subgraph_isomorphisms_iter(self, symmetry=True):
+        """Alternative name for :meth:`find_isomorphisms`."""
+        return self.find_isomorphisms(symmetry)
+
+    def _find_nodecolor_candidates(self):
+        """
+        Per node in subgraph find all nodes in graph that have the same color.
+        """
+        candidates = defaultdict(set)
+        for sgn in self.subgraph.nodes:
+            sgn_color = self._sgn_colors[sgn]
+            if sgn_color in self._node_compatibility:
+                gn_color = self._node_compatibility[sgn_color]
+                candidates[sgn].add(frozenset(self._gn_partitions[gn_color]))
+            else:
+                candidates[sgn].add(frozenset())
+        candidates = dict(candidates)
+        for sgn, options in candidates.items():
+            candidates[sgn] = frozenset(options)
+        return candidates
+
+    @staticmethod
+    def _make_constraints(cosets):
+        """
+        Turn cosets into constraints.
+        """
+        constraints = []
+        for node_i, node_ts in cosets.items():
+            for node_t in node_ts:
+                if node_i != node_t:
+                    # Node i must be smaller than node t.
+                    constraints.append((node_i, node_t))
+        return constraints
+
+    @staticmethod
+    def _find_node_edge_color(graph, node_colors, edge_colors):
+        """
+        For every node in graph, come up with a color that combines 1) the
+        color of the node, and 2) the number of edges of a color to each type
+        of node.
+        """
+        counts = defaultdict(lambda: defaultdict(int))
+        for node1, node2 in graph.edges:
+            if (node1, node2) in edge_colors:
+                # FIXME directed graphs
+                ecolor = edge_colors[node1, node2]
+            else:
+                ecolor = edge_colors[node2, node1]
+            # Count per node how many edges it has of what color to nodes of
+            # what color
+            counts[node1][ecolor, node_colors[node2]] += 1
+            counts[node2][ecolor, node_colors[node1]] += 1
+
+        node_edge_colors = {}
+        for node in graph.nodes:
+            node_edge_colors[node] = node_colors[node], set(counts[node].items())
+
+        return node_edge_colors
+
+    @staticmethod
+    def _get_permutations_by_length(items):
+        """
+        Get all permutations of items, but only permute items with the same
+        length.
+
+        >>> found = list(ISMAGS._get_permutations_by_length([[1], [2], [3, 4], [4, 5]]))
+        >>> answer = [
+        ...     (([1], [2]), ([3, 4], [4, 5])),
+        ...     (([1], [2]), ([4, 5], [3, 4])),
+        ...     (([2], [1]), ([3, 4], [4, 5])),
+        ...     (([2], [1]), ([4, 5], [3, 4])),
+        ... ]
+        >>> found == answer
+        True
+        """
+        by_len = defaultdict(list)
+        for item in items:
+            by_len[len(item)].append(item)
+
+        yield from itertools.product(
+            *(itertools.permutations(by_len[l]) for l in sorted(by_len))
+        )
+
+    @classmethod
+    def _refine_node_partitions(cls, graph, node_partitions, edge_colors, branch=False):
+        """
+        Given a partition of nodes in graph, make the partitions smaller such
+        that all nodes in a partition have 1) the same color, and 2) the same
+        number of edges to specific other partitions.
+        """
+
+        def equal_color(node1, node2):
+            return node_edge_colors[node1] == node_edge_colors[node2]
+
+        node_partitions = list(node_partitions)
+        node_colors = partition_to_color(node_partitions)
+        node_edge_colors = cls._find_node_edge_color(graph, node_colors, edge_colors)
+        if all(
+            are_all_equal(node_edge_colors[node] for node in partition)
+            for partition in node_partitions
+        ):
+            yield node_partitions
+            return
+
+        new_partitions = []
+        output = [new_partitions]
+        for partition in node_partitions:
+            if not are_all_equal(node_edge_colors[node] for node in partition):
+                refined = make_partitions(partition, equal_color)
+                if (
+                    branch
+                    and len(refined) != 1
+                    and len({len(r) for r in refined}) != len([len(r) for r in refined])
+                ):
+                    # This is where it breaks. There are multiple new cells
+                    # in refined with the same length, and their order
+                    # matters.
+                    # So option 1) Hit it with a big hammer and simply make all
+                    # orderings.
+                    permutations = cls._get_permutations_by_length(refined)
+                    new_output = []
+                    for n_p in output:
+                        for permutation in permutations:
+                            new_output.append(n_p + list(permutation[0]))
+                    output = new_output
+                else:
+                    for n_p in output:
+                        n_p.extend(sorted(refined, key=len))
+            else:
+                for n_p in output:
+                    n_p.append(partition)
+        for n_p in output:
+            yield from cls._refine_node_partitions(graph, n_p, edge_colors, branch)
+
+    def _edges_of_same_color(self, sgn1, sgn2):
+        """
+        Returns all edges in :attr:`graph` that have the same colour as the
+        edge between sgn1 and sgn2 in :attr:`subgraph`.
+        """
+        if (sgn1, sgn2) in self._sge_colors:
+            # FIXME directed graphs
+            sge_color = self._sge_colors[sgn1, sgn2]
+        else:
+            sge_color = self._sge_colors[sgn2, sgn1]
+        if sge_color in self._edge_compatibility:
+            ge_color = self._edge_compatibility[sge_color]
+            g_edges = self._ge_partitions[ge_color]
+        else:
+            g_edges = []
+        return g_edges
+
+    def _map_nodes(self, sgn, candidates, constraints, mapping=None, to_be_mapped=None):
+        """
+        Find all subgraph isomorphisms honoring constraints.
+        """
+        if mapping is None:
+            mapping = {}
+        else:
+            mapping = mapping.copy()
+        if to_be_mapped is None:
+            to_be_mapped = set(self.subgraph.nodes)
+
+        # Note, we modify candidates here. Doesn't seem to affect results, but
+        # remember this.
+        # candidates = candidates.copy()
+        sgn_candidates = intersect(candidates[sgn])
+        candidates[sgn] = frozenset([sgn_candidates])
+        for gn in sgn_candidates:
+            # We're going to try to map sgn to gn.
+            if gn in mapping.values() or sgn not in to_be_mapped:
+                # gn is already mapped to something
+                continue  # pragma: no cover
+
+            # REDUCTION and COMBINATION
+            mapping[sgn] = gn
+            # BASECASE
+            if to_be_mapped == set(mapping.keys()):
+                yield {v: k for k, v in mapping.items()}
+                continue
+            left_to_map = to_be_mapped - set(mapping.keys())
+
+            new_candidates = candidates.copy()
+            sgn_nbrs = set(self.subgraph[sgn])
+            not_gn_nbrs = set(self.graph.nodes) - set(self.graph[gn])
+            for sgn2 in left_to_map:
+                if sgn2 not in sgn_nbrs:
+                    gn2_options = not_gn_nbrs
+                else:
+                    # Get all edges to gn of the right color:
+                    g_edges = self._edges_of_same_color(sgn, sgn2)
+                    # FIXME directed graphs
+                    # And all nodes involved in those which are connected to gn
+                    gn2_options = {n for e in g_edges for n in e if gn in e}
+                # Node color compatibility should be taken care of by the
+                # initial candidate lists made by find_subgraphs
+
+                # Add gn2_options to the right collection. Since new_candidates
+                # is a dict of frozensets of frozensets of node indices it's
+                # a bit clunky. We can't do .add, and + also doesn't work. We
+                # could do |, but I deem union to be clearer.
+                new_candidates[sgn2] = new_candidates[sgn2].union(
+                    [frozenset(gn2_options)]
+                )
+
+                if (sgn, sgn2) in constraints:
+                    gn2_options = {gn2 for gn2 in self.graph if gn2 > gn}
+                elif (sgn2, sgn) in constraints:
+                    gn2_options = {gn2 for gn2 in self.graph if gn2 < gn}
+                else:
+                    continue  # pragma: no cover
+                new_candidates[sgn2] = new_candidates[sgn2].union(
+                    [frozenset(gn2_options)]
+                )
+
+            # The next node is the one that is unmapped and has fewest
+            # candidates
+            next_sgn = min(left_to_map, key=lambda n: min(new_candidates[n], key=len))
+            yield from self._map_nodes(
+                next_sgn,
+                new_candidates,
+                constraints,
+                mapping=mapping,
+                to_be_mapped=to_be_mapped,
+            )
+            # Unmap sgn-gn. Strictly not necessary since it'd get overwritten
+            # when making a new mapping for sgn.
+            # del mapping[sgn]
+
+    def _largest_common_subgraph(self, candidates, constraints, to_be_mapped=None):
+        """
+        Find all largest common subgraphs honoring constraints.
+        """
+        if to_be_mapped is None:
+            to_be_mapped = {frozenset(self.subgraph.nodes)}
+
+        # The LCS problem is basically a repeated subgraph isomorphism problem
+        # with smaller and smaller subgraphs. We store the nodes that are
+        # "part of" the subgraph in to_be_mapped, and we make it a little
+        # smaller every iteration.
+
+        current_size = len(next(iter(to_be_mapped), []))
+
+        found_iso = False
+        if current_size <= len(self.graph):
+            # There's no point in trying to find isomorphisms of
+            # graph >= subgraph if subgraph has more nodes than graph.
+
+            # Try the isomorphism first with the nodes with lowest ID. So sort
+            # them. Those are more likely to be part of the final
+            # correspondence. This makes finding the first answer(s) faster. In
+            # theory.
+            for nodes in sorted(to_be_mapped, key=sorted):
+                # Find the isomorphism between subgraph[to_be_mapped] <= graph
+                next_sgn = min(nodes, key=lambda n: min(candidates[n], key=len))
+                isomorphs = self._map_nodes(
+                    next_sgn, candidates, constraints, to_be_mapped=nodes
+                )
+
+                # This is effectively `yield from isomorphs`, except that we look
+                # whether an item was yielded.
+                try:
+                    item = next(isomorphs)
+                except StopIteration:
+                    pass
+                else:
+                    yield item
+                    yield from isomorphs
+                    found_iso = True
+
+        # BASECASE
+        if found_iso or current_size == 1:
+            # Shrinking has no point because either 1) we end up with a smaller
+            # common subgraph (and we want the largest), or 2) there'll be no
+            # more subgraph.
+            return
+
+        left_to_be_mapped = set()
+        for nodes in to_be_mapped:
+            for sgn in nodes:
+                # We're going to remove sgn from to_be_mapped, but subject to
+                # symmetry constraints. We know that for every constraint we
+                # have those subgraph nodes are equal. So whenever we would
+                # remove the lower part of a constraint, remove the higher
+                # instead. This is all dealth with by _remove_node. And because
+                # left_to_be_mapped is a set, we don't do double work.
+
+                # And finally, make the subgraph one node smaller.
+                # REDUCTION
+                new_nodes = self._remove_node(sgn, nodes, constraints)
+                left_to_be_mapped.add(new_nodes)
+        # COMBINATION
+        yield from self._largest_common_subgraph(
+            candidates, constraints, to_be_mapped=left_to_be_mapped
+        )
+
+    @staticmethod
+    def _remove_node(node, nodes, constraints):
+        """
+        Returns a new set where node has been removed from nodes, subject to
+        symmetry constraints. We know, that for every constraint we have
+        those subgraph nodes are equal. So whenever we would remove the
+        lower part of a constraint, remove the higher instead.
+        """
+        while True:
+            for low, high in constraints:
+                if low == node and high in nodes:
+                    node = high
+                    break
+            else:  # no break, couldn't find node in constraints
+                break
+        return frozenset(nodes - {node})
+
+    @staticmethod
+    def _find_permutations(top_partitions, bottom_partitions):
+        """
+        Return the pairs of top/bottom partitions where the partitions are
+        different. Ensures that all partitions in both top and bottom
+        partitions have size 1.
+        """
+        # Find permutations
+        permutations = set()
+        for top, bot in zip(top_partitions, bottom_partitions):
+            # top and bot have only one element
+            if len(top) != 1 or len(bot) != 1:
+                raise IndexError(
+                    "Not all nodes are coupled. This is"
+                    f" impossible: {top_partitions}, {bottom_partitions}"
+                )
+            if top != bot:
+                permutations.add(frozenset((next(iter(top)), next(iter(bot)))))
+        return permutations
+
+    @staticmethod
+    def _update_orbits(orbits, permutations):
+        """
+        Update orbits based on permutations. Orbits is modified in place.
+        For every pair of items in permutations their respective orbits are
+        merged.
+        """
+        for permutation in permutations:
+            node, node2 = permutation
+            # Find the orbits that contain node and node2, and replace the
+            # orbit containing node with the union
+            first = second = None
+            for idx, orbit in enumerate(orbits):
+                if first is not None and second is not None:
+                    break
+                if node in orbit:
+                    first = idx
+                if node2 in orbit:
+                    second = idx
+            if first != second:
+                orbits[first].update(orbits[second])
+                del orbits[second]
+
+    def _couple_nodes(
+        self,
+        top_partitions,
+        bottom_partitions,
+        pair_idx,
+        t_node,
+        b_node,
+        graph,
+        edge_colors,
+    ):
+        """
+        Generate new partitions from top and bottom_partitions where t_node is
+        coupled to b_node. pair_idx is the index of the partitions where t_ and
+        b_node can be found.
+        """
+        t_partition = top_partitions[pair_idx]
+        b_partition = bottom_partitions[pair_idx]
+        assert t_node in t_partition and b_node in b_partition
+        # Couple node to node2. This means they get their own partition
+        new_top_partitions = [top.copy() for top in top_partitions]
+        new_bottom_partitions = [bot.copy() for bot in bottom_partitions]
+        new_t_groups = {t_node}, t_partition - {t_node}
+        new_b_groups = {b_node}, b_partition - {b_node}
+        # Replace the old partitions with the coupled ones
+        del new_top_partitions[pair_idx]
+        del new_bottom_partitions[pair_idx]
+        new_top_partitions[pair_idx:pair_idx] = new_t_groups
+        new_bottom_partitions[pair_idx:pair_idx] = new_b_groups
+
+        new_top_partitions = self._refine_node_partitions(
+            graph, new_top_partitions, edge_colors
+        )
+        new_bottom_partitions = self._refine_node_partitions(
+            graph, new_bottom_partitions, edge_colors, branch=True
+        )
+        new_top_partitions = list(new_top_partitions)
+        assert len(new_top_partitions) == 1
+        new_top_partitions = new_top_partitions[0]
+        for bot in new_bottom_partitions:
+            yield list(new_top_partitions), bot
+
+    def _process_ordered_pair_partitions(
+        self,
+        graph,
+        top_partitions,
+        bottom_partitions,
+        edge_colors,
+        orbits=None,
+        cosets=None,
+    ):
+        """
+        Processes ordered pair partitions as per the reference paper. Finds and
+        returns all permutations and cosets that leave the graph unchanged.
+        """
+        if orbits is None:
+            orbits = [{node} for node in graph.nodes]
+        else:
+            # Note that we don't copy orbits when we are given one. This means
+            # we leak information between the recursive branches. This is
+            # intentional!
+            orbits = orbits
+        if cosets is None:
+            cosets = {}
+        else:
+            cosets = cosets.copy()
+
+        assert all(
+            len(t_p) == len(b_p) for t_p, b_p in zip(top_partitions, bottom_partitions)
+        )
+
+        # BASECASE
+        if all(len(top) == 1 for top in top_partitions):
+            # All nodes are mapped
+            permutations = self._find_permutations(top_partitions, bottom_partitions)
+            self._update_orbits(orbits, permutations)
+            if permutations:
+                return [permutations], cosets
+            else:
+                return [], cosets
+
+        permutations = []
+        unmapped_nodes = {
+            (node, idx)
+            for idx, t_partition in enumerate(top_partitions)
+            for node in t_partition
+            if len(t_partition) > 1
+        }
+        node, pair_idx = min(unmapped_nodes)
+        b_partition = bottom_partitions[pair_idx]
+
+        for node2 in sorted(b_partition):
+            if len(b_partition) == 1:
+                # Can never result in symmetry
+                continue
+            if node != node2 and any(
+                node in orbit and node2 in orbit for orbit in orbits
+            ):
+                # Orbit prune branch
+                continue
+            # REDUCTION
+            # Couple node to node2
+            partitions = self._couple_nodes(
+                top_partitions,
+                bottom_partitions,
+                pair_idx,
+                node,
+                node2,
+                graph,
+                edge_colors,
+            )
+            for opp in partitions:
+                new_top_partitions, new_bottom_partitions = opp
+
+                new_perms, new_cosets = self._process_ordered_pair_partitions(
+                    graph,
+                    new_top_partitions,
+                    new_bottom_partitions,
+                    edge_colors,
+                    orbits,
+                    cosets,
+                )
+                # COMBINATION
+                permutations += new_perms
+                cosets.update(new_cosets)
+
+        mapped = {
+            k
+            for top, bottom in zip(top_partitions, bottom_partitions)
+            for k in top
+            if len(top) == 1 and top == bottom
+        }
+        ks = {k for k in graph.nodes if k < node}
+        # Have all nodes with ID < node been mapped?
+        find_coset = ks <= mapped and node not in cosets
+        if find_coset:
+            # Find the orbit that contains node
+            for orbit in orbits:
+                if node in orbit:
+                    cosets[node] = orbit.copy()
+        return permutations, cosets

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/isomorphism/isomorph.py

@@ -0,0 +1,248 @@
+"""
+Graph isomorphism functions.
+"""
+import networkx as nx
+from networkx.exception import NetworkXError
+
+__all__ = [
+    "could_be_isomorphic",
+    "fast_could_be_isomorphic",
+    "faster_could_be_isomorphic",
+    "is_isomorphic",
+]
+
+
+@nx._dispatchable(graphs={"G1": 0, "G2": 1})
+def could_be_isomorphic(G1, G2):
+    """Returns False if graphs are definitely not isomorphic.
+    True does NOT guarantee isomorphism.
+
+    Parameters
+    ----------
+    G1, G2 : graphs
+       The two graphs G1 and G2 must be the same type.
+
+    Notes
+    -----
+    Checks for matching degree, triangle, and number of cliques sequences.
+    The triangle sequence contains the number of triangles each node is part of.
+    The clique sequence contains for each node the number of maximal cliques
+    involving that node.
+
+    """
+
+    # Check global properties
+    if G1.order() != G2.order():
+        return False
+
+    # Check local properties
+    d1 = G1.degree()
+    t1 = nx.triangles(G1)
+    clqs_1 = list(nx.find_cliques(G1))
+    c1 = {n: sum(1 for c in clqs_1 if n in c) for n in G1}  # number of cliques
+    props1 = [[d, t1[v], c1[v]] for v, d in d1]
+    props1.sort()
+
+    d2 = G2.degree()
+    t2 = nx.triangles(G2)
+    clqs_2 = list(nx.find_cliques(G2))
+    c2 = {n: sum(1 for c in clqs_2 if n in c) for n in G2}  # number of cliques
+    props2 = [[d, t2[v], c2[v]] for v, d in d2]
+    props2.sort()
+
+    if props1 != props2:
+        return False
+
+    # OK...
+    return True
+
+
+graph_could_be_isomorphic = could_be_isomorphic
+
+
+@nx._dispatchable(graphs={"G1": 0, "G2": 1})
+def fast_could_be_isomorphic(G1, G2):
+    """Returns False if graphs are definitely not isomorphic.
+
+    True does NOT guarantee isomorphism.
+
+    Parameters
+    ----------
+    G1, G2 : graphs
+       The two graphs G1 and G2 must be the same type.
+
+    Notes
+    -----
+    Checks for matching degree and triangle sequences. The triangle
+    sequence contains the number of triangles each node is part of.
+    """
+    # Check global properties
+    if G1.order() != G2.order():
+        return False
+
+    # Check local properties
+    d1 = G1.degree()
+    t1 = nx.triangles(G1)
+    props1 = [[d, t1[v]] for v, d in d1]
+    props1.sort()
+
+    d2 = G2.degree()
+    t2 = nx.triangles(G2)
+    props2 = [[d, t2[v]] for v, d in d2]
+    props2.sort()
+
+    if props1 != props2:
+        return False
+
+    # OK...
+    return True
+
+
+fast_graph_could_be_isomorphic = fast_could_be_isomorphic
+
+
+@nx._dispatchable(graphs={"G1": 0, "G2": 1})
+def faster_could_be_isomorphic(G1, G2):
+    """Returns False if graphs are definitely not isomorphic.
+
+    True does NOT guarantee isomorphism.
+
+    Parameters
+    ----------
+    G1, G2 : graphs
+       The two graphs G1 and G2 must be the same type.
+
+    Notes
+    -----
+    Checks for matching degree sequences.
+    """
+    # Check global properties
+    if G1.order() != G2.order():
+        return False
+
+    # Check local properties
+    d1 = sorted(d for n, d in G1.degree())
+    d2 = sorted(d for n, d in G2.degree())
+
+    if d1 != d2:
+        return False
+
+    # OK...
+    return True
+
+
+faster_graph_could_be_isomorphic = faster_could_be_isomorphic
+
+
+@nx._dispatchable(
+    graphs={"G1": 0, "G2": 1},
+    preserve_edge_attrs="edge_match",
+    preserve_node_attrs="node_match",
+)
+def is_isomorphic(G1, G2, node_match=None, edge_match=None):
+    """Returns True if the graphs G1 and G2 are isomorphic and False otherwise.
+
+    Parameters
+    ----------
+    G1, G2: graphs
+        The two graphs G1 and G2 must be the same type.
+
+    node_match : callable
+        A function that returns True if node n1 in G1 and n2 in G2 should
+        be considered equal during the isomorphism test.
+        If node_match is not specified then node attributes are not considered.
+
+        The function will be called like
+
+           node_match(G1.nodes[n1], G2.nodes[n2]).
+
+        That is, the function will receive the node attribute dictionaries
+        for n1 and n2 as inputs.
+
+    edge_match : callable
+        A function that returns True if the edge attribute dictionary
+        for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should
+        be considered equal during the isomorphism test.  If edge_match is
+        not specified then edge attributes are not considered.
+
+        The function will be called like
+
+           edge_match(G1[u1][v1], G2[u2][v2]).
+
+        That is, the function will receive the edge attribute dictionaries
+        of the edges under consideration.
+
+    Notes
+    -----
+    Uses the vf2 algorithm [1]_.
+
+    Examples
+    --------
+    >>> import networkx.algorithms.isomorphism as iso
+
+    For digraphs G1 and G2, using 'weight' edge attribute (default: 1)
+
+    >>> G1 = nx.DiGraph()
+    >>> G2 = nx.DiGraph()
+    >>> nx.add_path(G1, [1, 2, 3, 4], weight=1)
+    >>> nx.add_path(G2, [10, 20, 30, 40], weight=2)
+    >>> em = iso.numerical_edge_match("weight", 1)
+    >>> nx.is_isomorphic(G1, G2)  # no weights considered
+    True
+    >>> nx.is_isomorphic(G1, G2, edge_match=em)  # match weights
+    False
+
+    For multidigraphs G1 and G2, using 'fill' node attribute (default: '')
+
+    >>> G1 = nx.MultiDiGraph()
+    >>> G2 = nx.MultiDiGraph()
+    >>> G1.add_nodes_from([1, 2, 3], fill="red")
+    >>> G2.add_nodes_from([10, 20, 30, 40], fill="red")
+    >>> nx.add_path(G1, [1, 2, 3, 4], weight=3, linewidth=2.5)
+    >>> nx.add_path(G2, [10, 20, 30, 40], weight=3)
+    >>> nm = iso.categorical_node_match("fill", "red")
+    >>> nx.is_isomorphic(G1, G2, node_match=nm)
+    True
+
+    For multidigraphs G1 and G2, using 'weight' edge attribute (default: 7)
+
+    >>> G1.add_edge(1, 2, weight=7)
+    1
+    >>> G2.add_edge(10, 20)
+    1
+    >>> em = iso.numerical_multiedge_match("weight", 7, rtol=1e-6)
+    >>> nx.is_isomorphic(G1, G2, edge_match=em)
+    True
+
+    For multigraphs G1 and G2, using 'weight' and 'linewidth' edge attributes
+    with default values 7 and 2.5. Also using 'fill' node attribute with
+    default value 'red'.
+
+    >>> em = iso.numerical_multiedge_match(["weight", "linewidth"], [7, 2.5])
+    >>> nm = iso.categorical_node_match("fill", "red")
+    >>> nx.is_isomorphic(G1, G2, edge_match=em, node_match=nm)
+    True
+
+    See Also
+    --------
+    numerical_node_match, numerical_edge_match, numerical_multiedge_match
+    categorical_node_match, categorical_edge_match, categorical_multiedge_match
+
+    References
+    ----------
+    .. [1]  L. P. Cordella, P. Foggia, C. Sansone, M. Vento,
+       "An Improved Algorithm for Matching Large Graphs",
+       3rd IAPR-TC15 Workshop  on Graph-based Representations in
+       Pattern Recognition, Cuen, pp. 149-159, 2001.
+       https://www.researchgate.net/publication/200034365_An_Improved_Algorithm_for_Matching_Large_Graphs
+    """
+    if G1.is_directed() and G2.is_directed():
+        GM = nx.algorithms.isomorphism.DiGraphMatcher
+    elif (not G1.is_directed()) and (not G2.is_directed()):
+        GM = nx.algorithms.isomorphism.GraphMatcher
+    else:
+        raise NetworkXError("Graphs G1 and G2 are not of the same type.")
+
+    gm = GM(G1, G2, node_match=node_match, edge_match=edge_match)
+
+    return gm.is_isomorphic()

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/isomorphism/isomorphvf2.py

@@ -0,0 +1,1065 @@
+"""
+*************
+VF2 Algorithm
+*************
+
+An implementation of VF2 algorithm for graph isomorphism testing.
+
+The simplest interface to use this module is to call the
+:func:`is_isomorphic <networkx.algorithms.isomorphism.is_isomorphic>`
+function.
+
+Introduction
+------------
+
+The GraphMatcher and DiGraphMatcher are responsible for matching
+graphs or directed graphs in a predetermined manner.  This
+usually means a check for an isomorphism, though other checks
+are also possible.  For example, a subgraph of one graph
+can be checked for isomorphism to a second graph.
+
+Matching is done via syntactic feasibility. It is also possible
+to check for semantic feasibility. Feasibility, then, is defined
+as the logical AND of the two functions.
+
+To include a semantic check, the (Di)GraphMatcher class should be
+subclassed, and the
+:meth:`semantic_feasibility <networkx.algorithms.isomorphism.GraphMatcher.semantic_feasibility>`
+function should be redefined.  By default, the semantic feasibility function always
+returns ``True``.  The effect of this is that semantics are not
+considered in the matching of G1 and G2.
+
+Examples
+--------
+
+Suppose G1 and G2 are isomorphic graphs. Verification is as follows:
+
+>>> from networkx.algorithms import isomorphism
+>>> G1 = nx.path_graph(4)
+>>> G2 = nx.path_graph(4)
+>>> GM = isomorphism.GraphMatcher(G1, G2)
+>>> GM.is_isomorphic()
+True
+
+GM.mapping stores the isomorphism mapping from G1 to G2.
+
+>>> GM.mapping
+{0: 0, 1: 1, 2: 2, 3: 3}
+
+
+Suppose G1 and G2 are isomorphic directed graphs.
+Verification is as follows:
+
+>>> G1 = nx.path_graph(4, create_using=nx.DiGraph())
+>>> G2 = nx.path_graph(4, create_using=nx.DiGraph())
+>>> DiGM = isomorphism.DiGraphMatcher(G1, G2)
+>>> DiGM.is_isomorphic()
+True
+
+DiGM.mapping stores the isomorphism mapping from G1 to G2.
+
+>>> DiGM.mapping
+{0: 0, 1: 1, 2: 2, 3: 3}
+
+
+
+Subgraph Isomorphism
+--------------------
+Graph theory literature can be ambiguous about the meaning of the
+above statement, and we seek to clarify it now.
+
+In the VF2 literature, a mapping `M` is said to be a graph-subgraph
+isomorphism iff `M` is an isomorphism between `G2` and a subgraph of `G1`.
+Thus, to say that `G1` and `G2` are graph-subgraph isomorphic is to say
+that a subgraph of `G1` is isomorphic to `G2`.
+
+Other literature uses the phrase 'subgraph isomorphic' as in '`G1` does
+not have a subgraph isomorphic to `G2`'.  Another use is as an in adverb
+for isomorphic.  Thus, to say that `G1` and `G2` are subgraph isomorphic
+is to say that a subgraph of `G1` is isomorphic to `G2`.
+
+Finally, the term 'subgraph' can have multiple meanings. In this
+context, 'subgraph' always means a 'node-induced subgraph'. Edge-induced
+subgraph isomorphisms are not directly supported, but one should be
+able to perform the check by making use of
+:func:`line_graph <networkx.generators.line.line_graph>`. For
+subgraphs which are not induced, the term 'monomorphism' is preferred
+over 'isomorphism'.
+
+Let ``G = (N, E)`` be a graph with a set of nodes `N` and set of edges `E`.
+
+If ``G' = (N', E')`` is a subgraph, then:
+    `N'` is a subset of `N` and
+    `E'` is a subset of `E`.
+
+If ``G' = (N', E')`` is a node-induced subgraph, then:
+    `N'` is a subset of `N` and
+    `E'` is the subset of edges in `E` relating nodes in `N'`.
+
+If `G' = (N', E')` is an edge-induced subgraph, then:
+    `N'` is the subset of nodes in `N` related by edges in `E'` and
+    `E'` is a subset of `E`.
+
+If `G' = (N', E')` is a monomorphism, then:
+    `N'` is a subset of `N` and
+    `E'` is a subset of the set of edges in `E` relating nodes in `N'`.
+
+Note that if `G'` is a node-induced subgraph of `G`, then it is always a
+subgraph monomorphism of `G`, but the opposite is not always true, as a
+monomorphism can have fewer edges.
+
+References
+----------
+[1]   Luigi P. Cordella, Pasquale Foggia, Carlo Sansone, Mario Vento,
+      "A (Sub)Graph Isomorphism Algorithm for Matching Large Graphs",
+      IEEE Transactions on Pattern Analysis and Machine Intelligence,
+      vol. 26,  no. 10,  pp. 1367-1372,  Oct.,  2004.
+      http://ieeexplore.ieee.org/iel5/34/29305/01323804.pdf
+
+[2]   L. P. Cordella, P. Foggia, C. Sansone, M. Vento, "An Improved
+      Algorithm for Matching Large Graphs", 3rd IAPR-TC15 Workshop
+      on Graph-based Representations in Pattern Recognition, Cuen,
+      pp. 149-159, 2001.
+      https://www.researchgate.net/publication/200034365_An_Improved_Algorithm_for_Matching_Large_Graphs
+
+See Also
+--------
+:meth:`semantic_feasibility <networkx.algorithms.isomorphism.GraphMatcher.semantic_feasibility>`
+:meth:`syntactic_feasibility <networkx.algorithms.isomorphism.GraphMatcher.syntactic_feasibility>`
+
+Notes
+-----
+
+The implementation handles both directed and undirected graphs as well
+as multigraphs.
+
+In general, the subgraph isomorphism problem is NP-complete whereas the
+graph isomorphism problem is most likely not NP-complete (although no
+polynomial-time algorithm is known to exist).
+
+"""
+
+# This work was originally coded by Christopher Ellison
+# as part of the Computational Mechanics Python (CMPy) project.
+# James P. Crutchfield, principal investigator.
+# Complexity Sciences Center and Physics Department, UC Davis.
+
+import sys
+
+__all__ = ["GraphMatcher", "DiGraphMatcher"]
+
+
+class GraphMatcher:
+    """Implementation of VF2 algorithm for matching undirected graphs.
+
+    Suitable for Graph and MultiGraph instances.
+    """
+
+    def __init__(self, G1, G2):
+        """Initialize GraphMatcher.
+
+        Parameters
+        ----------
+        G1,G2: NetworkX Graph or MultiGraph instances.
+           The two graphs to check for isomorphism or monomorphism.
+
+        Examples
+        --------
+        To create a GraphMatcher which checks for syntactic feasibility:
+
+        >>> from networkx.algorithms import isomorphism
+        >>> G1 = nx.path_graph(4)
+        >>> G2 = nx.path_graph(4)
+        >>> GM = isomorphism.GraphMatcher(G1, G2)
+        """
+        self.G1 = G1
+        self.G2 = G2
+        self.G1_nodes = set(G1.nodes())
+        self.G2_nodes = set(G2.nodes())
+        self.G2_node_order = {n: i for i, n in enumerate(G2)}
+
+        # Set recursion limit.
+        self.old_recursion_limit = sys.getrecursionlimit()
+        expected_max_recursion_level = len(self.G2)
+        if self.old_recursion_limit < 1.5 * expected_max_recursion_level:
+            # Give some breathing room.
+            sys.setrecursionlimit(int(1.5 * expected_max_recursion_level))
+
+        # Declare that we will be searching for a graph-graph isomorphism.
+        self.test = "graph"
+
+        # Initialize state
+        self.initialize()
+
+    def reset_recursion_limit(self):
+        """Restores the recursion limit."""
+        # TODO:
+        # Currently, we use recursion and set the recursion level higher.
+        # It would be nice to restore the level, but because the
+        # (Di)GraphMatcher classes make use of cyclic references, garbage
+        # collection will never happen when we define __del__() to
+        # restore the recursion level. The result is a memory leak.
+        # So for now, we do not automatically restore the recursion level,
+        # and instead provide a method to do this manually. Eventually,
+        # we should turn this into a non-recursive implementation.
+        sys.setrecursionlimit(self.old_recursion_limit)
+
+    def candidate_pairs_iter(self):
+        """Iterator over candidate pairs of nodes in G1 and G2."""
+
+        # All computations are done using the current state!
+
+        G1_nodes = self.G1_nodes
+        G2_nodes = self.G2_nodes
+        min_key = self.G2_node_order.__getitem__
+
+        # First we compute the inout-terminal sets.
+        T1_inout = [node for node in self.inout_1 if node not in self.core_1]
+        T2_inout = [node for node in self.inout_2 if node not in self.core_2]
+
+        # If T1_inout and T2_inout are both nonempty.
+        # P(s) = T1_inout x {min T2_inout}
+        if T1_inout and T2_inout:
+            node_2 = min(T2_inout, key=min_key)
+            for node_1 in T1_inout:
+                yield node_1, node_2
+
+        else:
+            # If T1_inout and T2_inout were both empty....
+            # P(s) = (N_1 - M_1) x {min (N_2 - M_2)}
+            # if not (T1_inout or T2_inout):  # as suggested by  [2], incorrect
+            if 1:  # as inferred from [1], correct
+                # First we determine the candidate node for G2
+                other_node = min(G2_nodes - set(self.core_2), key=min_key)
+                for node in self.G1:
+                    if node not in self.core_1:
+                        yield node, other_node
+
+        # For all other cases, we don't have any candidate pairs.
+
+    def initialize(self):
+        """Reinitializes the state of the algorithm.
+
+        This method should be redefined if using something other than GMState.
+        If only subclassing GraphMatcher, a redefinition is not necessary.
+
+        """
+
+        # core_1[n] contains the index of the node paired with n, which is m,
+        #           provided n is in the mapping.
+        # core_2[m] contains the index of the node paired with m, which is n,
+        #           provided m is in the mapping.
+        self.core_1 = {}
+        self.core_2 = {}
+
+        # See the paper for definitions of M_x and T_x^{y}
+
+        # inout_1[n]  is non-zero if n is in M_1 or in T_1^{inout}
+        # inout_2[m]  is non-zero if m is in M_2 or in T_2^{inout}
+        #
+        # The value stored is the depth of the SSR tree when the node became
+        # part of the corresponding set.
+        self.inout_1 = {}
+        self.inout_2 = {}
+        # Practically, these sets simply store the nodes in the subgraph.
+
+        self.state = GMState(self)
+
+        # Provide a convenient way to access the isomorphism mapping.
+        self.mapping = self.core_1.copy()
+
+    def is_isomorphic(self):
+        """Returns True if G1 and G2 are isomorphic graphs."""
+
+        # Let's do two very quick checks!
+        # QUESTION: Should we call faster_graph_could_be_isomorphic(G1,G2)?
+        # For now, I just copy the code.
+
+        # Check global properties
+        if self.G1.order() != self.G2.order():
+            return False
+
+        # Check local properties
+        d1 = sorted(d for n, d in self.G1.degree())
+        d2 = sorted(d for n, d in self.G2.degree())
+        if d1 != d2:
+            return False
+
+        try:
+            x = next(self.isomorphisms_iter())
+            return True
+        except StopIteration:
+            return False
+
+    def isomorphisms_iter(self):
+        """Generator over isomorphisms between G1 and G2."""
+        # Declare that we are looking for a graph-graph isomorphism.
+        self.test = "graph"
+        self.initialize()
+        yield from self.match()
+
+    def match(self):
+        """Extends the isomorphism mapping.
+
+        This function is called recursively to determine if a complete
+        isomorphism can be found between G1 and G2.  It cleans up the class
+        variables after each recursive call. If an isomorphism is found,
+        we yield the mapping.
+
+        """
+        if len(self.core_1) == len(self.G2):
+            # Save the final mapping, otherwise garbage collection deletes it.
+            self.mapping = self.core_1.copy()
+            # The mapping is complete.
+            yield self.mapping
+        else:
+            for G1_node, G2_node in self.candidate_pairs_iter():
+                if self.syntactic_feasibility(G1_node, G2_node):
+                    if self.semantic_feasibility(G1_node, G2_node):
+                        # Recursive call, adding the feasible state.
+                        newstate = self.state.__class__(self, G1_node, G2_node)
+                        yield from self.match()
+
+                        # restore data structures
+                        newstate.restore()
+
+    def semantic_feasibility(self, G1_node, G2_node):
+        """Returns True if adding (G1_node, G2_node) is semantically feasible.
+
+        The semantic feasibility function should return True if it is
+        acceptable to add the candidate pair (G1_node, G2_node) to the current
+        partial isomorphism mapping.   The logic should focus on semantic
+        information contained in the edge data or a formalized node class.
+
+        By acceptable, we mean that the subsequent mapping can still become a
+        complete isomorphism mapping.  Thus, if adding the candidate pair
+        definitely makes it so that the subsequent mapping cannot become a
+        complete isomorphism mapping, then this function must return False.
+
+        The default semantic feasibility function always returns True. The
+        effect is that semantics are not considered in the matching of G1
+        and G2.
+
+        The semantic checks might differ based on the what type of test is
+        being performed.  A keyword description of the test is stored in
+        self.test.  Here is a quick description of the currently implemented
+        tests::
+
+          test='graph'
+            Indicates that the graph matcher is looking for a graph-graph
+            isomorphism.
+
+          test='subgraph'
+            Indicates that the graph matcher is looking for a subgraph-graph
+            isomorphism such that a subgraph of G1 is isomorphic to G2.
+
+          test='mono'
+            Indicates that the graph matcher is looking for a subgraph-graph
+            monomorphism such that a subgraph of G1 is monomorphic to G2.
+
+        Any subclass which redefines semantic_feasibility() must maintain
+        the above form to keep the match() method functional. Implementations
+        should consider multigraphs.
+        """
+        return True
+
+    def subgraph_is_isomorphic(self):
+        """Returns True if a subgraph of G1 is isomorphic to G2."""
+        try:
+            x = next(self.subgraph_isomorphisms_iter())
+            return True
+        except StopIteration:
+            return False
+
+    def subgraph_is_monomorphic(self):
+        """Returns True if a subgraph of G1 is monomorphic to G2."""
+        try:
+            x = next(self.subgraph_monomorphisms_iter())
+            return True
+        except StopIteration:
+            return False
+
+    #    subgraph_is_isomorphic.__doc__ += "\n" + subgraph.replace('\n','\n'+indent)
+
+    def subgraph_isomorphisms_iter(self):
+        """Generator over isomorphisms between a subgraph of G1 and G2."""
+        # Declare that we are looking for graph-subgraph isomorphism.
+        self.test = "subgraph"
+        self.initialize()
+        yield from self.match()
+
+    def subgraph_monomorphisms_iter(self):
+        """Generator over monomorphisms between a subgraph of G1 and G2."""
+        # Declare that we are looking for graph-subgraph monomorphism.
+        self.test = "mono"
+        self.initialize()
+        yield from self.match()
+
+    #    subgraph_isomorphisms_iter.__doc__ += "\n" + subgraph.replace('\n','\n'+indent)
+
+    def syntactic_feasibility(self, G1_node, G2_node):
+        """Returns True if adding (G1_node, G2_node) is syntactically feasible.
+
+        This function returns True if it is adding the candidate pair
+        to the current partial isomorphism/monomorphism mapping is allowable.
+        The addition is allowable if the inclusion of the candidate pair does
+        not make it impossible for an isomorphism/monomorphism to be found.
+        """
+
+        # The VF2 algorithm was designed to work with graphs having, at most,
+        # one edge connecting any two nodes.  This is not the case when
+        # dealing with an MultiGraphs.
+        #
+        # Basically, when we test the look-ahead rules R_neighbor, we will
+        # make sure that the number of edges are checked. We also add
+        # a R_self check to verify that the number of selfloops is acceptable.
+        #
+        # Users might be comparing Graph instances with MultiGraph instances.
+        # So the generic GraphMatcher class must work with MultiGraphs.
+        # Care must be taken since the value in the innermost dictionary is a
+        # singlet for Graph instances.  For MultiGraphs, the value in the
+        # innermost dictionary is a list.
+
+        ###
+        # Test at each step to get a return value as soon as possible.
+        ###
+
+        # Look ahead 0
+
+        # R_self
+
+        # The number of selfloops for G1_node must equal the number of
+        # self-loops for G2_node. Without this check, we would fail on
+        # R_neighbor at the next recursion level. But it is good to prune the
+        # search tree now.
+
+        if self.test == "mono":
+            if self.G1.number_of_edges(G1_node, G1_node) < self.G2.number_of_edges(
+                G2_node, G2_node
+            ):
+                return False
+        else:
+            if self.G1.number_of_edges(G1_node, G1_node) != self.G2.number_of_edges(
+                G2_node, G2_node
+            ):
+                return False
+
+        # R_neighbor
+
+        # For each neighbor n' of n in the partial mapping, the corresponding
+        # node m' is a neighbor of m, and vice versa. Also, the number of
+        # edges must be equal.
+        if self.test != "mono":
+            for neighbor in self.G1[G1_node]:
+                if neighbor in self.core_1:
+                    if self.core_1[neighbor] not in self.G2[G2_node]:
+                        return False
+                    elif self.G1.number_of_edges(
+                        neighbor, G1_node
+                    ) != self.G2.number_of_edges(self.core_1[neighbor], G2_node):
+                        return False
+
+        for neighbor in self.G2[G2_node]:
+            if neighbor in self.core_2:
+                if self.core_2[neighbor] not in self.G1[G1_node]:
+                    return False
+                elif self.test == "mono":
+                    if self.G1.number_of_edges(
+                        self.core_2[neighbor], G1_node
+                    ) < self.G2.number_of_edges(neighbor, G2_node):
+                        return False
+                else:
+                    if self.G1.number_of_edges(
+                        self.core_2[neighbor], G1_node
+                    ) != self.G2.number_of_edges(neighbor, G2_node):
+                        return False
+
+        if self.test != "mono":
+            # Look ahead 1
+
+            # R_terminout
+            # The number of neighbors of n in T_1^{inout} is equal to the
+            # number of neighbors of m that are in T_2^{inout}, and vice versa.
+            num1 = 0
+            for neighbor in self.G1[G1_node]:
+                if (neighbor in self.inout_1) and (neighbor not in self.core_1):
+                    num1 += 1
+            num2 = 0
+            for neighbor in self.G2[G2_node]:
+                if (neighbor in self.inout_2) and (neighbor not in self.core_2):
+                    num2 += 1
+            if self.test == "graph":
+                if num1 != num2:
+                    return False
+            else:  # self.test == 'subgraph'
+                if not (num1 >= num2):
+                    return False
+
+            # Look ahead 2
+
+            # R_new
+
+            # The number of neighbors of n that are neither in the core_1 nor
+            # T_1^{inout} is equal to the number of neighbors of m
+            # that are neither in core_2 nor T_2^{inout}.
+            num1 = 0
+            for neighbor in self.G1[G1_node]:
+                if neighbor not in self.inout_1:
+                    num1 += 1
+            num2 = 0
+            for neighbor in self.G2[G2_node]:
+                if neighbor not in self.inout_2:
+                    num2 += 1
+            if self.test == "graph":
+                if num1 != num2:
+                    return False
+            else:  # self.test == 'subgraph'
+                if not (num1 >= num2):
+                    return False
+
+        # Otherwise, this node pair is syntactically feasible!
+        return True
+
+
+class DiGraphMatcher(GraphMatcher):
+    """Implementation of VF2 algorithm for matching directed graphs.
+
+    Suitable for DiGraph and MultiDiGraph instances.
+    """
+
+    def __init__(self, G1, G2):
+        """Initialize DiGraphMatcher.
+
+        G1 and G2 should be nx.Graph or nx.MultiGraph instances.
+
+        Examples
+        --------
+        To create a GraphMatcher which checks for syntactic feasibility:
+
+        >>> from networkx.algorithms import isomorphism
+        >>> G1 = nx.DiGraph(nx.path_graph(4, create_using=nx.DiGraph()))
+        >>> G2 = nx.DiGraph(nx.path_graph(4, create_using=nx.DiGraph()))
+        >>> DiGM = isomorphism.DiGraphMatcher(G1, G2)
+        """
+        super().__init__(G1, G2)
+
+    def candidate_pairs_iter(self):
+        """Iterator over candidate pairs of nodes in G1 and G2."""
+
+        # All computations are done using the current state!
+
+        G1_nodes = self.G1_nodes
+        G2_nodes = self.G2_nodes
+        min_key = self.G2_node_order.__getitem__
+
+        # First we compute the out-terminal sets.
+        T1_out = [node for node in self.out_1 if node not in self.core_1]
+        T2_out = [node for node in self.out_2 if node not in self.core_2]
+
+        # If T1_out and T2_out are both nonempty.
+        # P(s) = T1_out x {min T2_out}
+        if T1_out and T2_out:
+            node_2 = min(T2_out, key=min_key)
+            for node_1 in T1_out:
+                yield node_1, node_2
+
+        # If T1_out and T2_out were both empty....
+        # We compute the in-terminal sets.
+
+        # elif not (T1_out or T2_out):   # as suggested by [2], incorrect
+        else:  # as suggested by [1], correct
+            T1_in = [node for node in self.in_1 if node not in self.core_1]
+            T2_in = [node for node in self.in_2 if node not in self.core_2]
+
+            # If T1_in and T2_in are both nonempty.
+            # P(s) = T1_out x {min T2_out}
+            if T1_in and T2_in:
+                node_2 = min(T2_in, key=min_key)
+                for node_1 in T1_in:
+                    yield node_1, node_2
+
+            # If all terminal sets are empty...
+            # P(s) = (N_1 - M_1) x {min (N_2 - M_2)}
+
+            # elif not (T1_in or T2_in):   # as suggested by  [2], incorrect
+            else:  # as inferred from [1], correct
+                node_2 = min(G2_nodes - set(self.core_2), key=min_key)
+                for node_1 in G1_nodes:
+                    if node_1 not in self.core_1:
+                        yield node_1, node_2
+
+        # For all other cases, we don't have any candidate pairs.
+
+    def initialize(self):
+        """Reinitializes the state of the algorithm.
+
+        This method should be redefined if using something other than DiGMState.
+        If only subclassing GraphMatcher, a redefinition is not necessary.
+        """
+
+        # core_1[n] contains the index of the node paired with n, which is m,
+        #           provided n is in the mapping.
+        # core_2[m] contains the index of the node paired with m, which is n,
+        #           provided m is in the mapping.
+        self.core_1 = {}
+        self.core_2 = {}
+
+        # See the paper for definitions of M_x and T_x^{y}
+
+        # in_1[n]  is non-zero if n is in M_1 or in T_1^{in}
+        # out_1[n] is non-zero if n is in M_1 or in T_1^{out}
+        #
+        # in_2[m]  is non-zero if m is in M_2 or in T_2^{in}
+        # out_2[m] is non-zero if m is in M_2 or in T_2^{out}
+        #
+        # The value stored is the depth of the search tree when the node became
+        # part of the corresponding set.
+        self.in_1 = {}
+        self.in_2 = {}
+        self.out_1 = {}
+        self.out_2 = {}
+
+        self.state = DiGMState(self)
+
+        # Provide a convenient way to access the isomorphism mapping.
+        self.mapping = self.core_1.copy()
+
+    def syntactic_feasibility(self, G1_node, G2_node):
+        """Returns True if adding (G1_node, G2_node) is syntactically feasible.
+
+        This function returns True if it is adding the candidate pair
+        to the current partial isomorphism/monomorphism mapping is allowable.
+        The addition is allowable if the inclusion of the candidate pair does
+        not make it impossible for an isomorphism/monomorphism to be found.
+        """
+
+        # The VF2 algorithm was designed to work with graphs having, at most,
+        # one edge connecting any two nodes.  This is not the case when
+        # dealing with an MultiGraphs.
+        #
+        # Basically, when we test the look-ahead rules R_pred and R_succ, we
+        # will make sure that the number of edges are checked.  We also add
+        # a R_self check to verify that the number of selfloops is acceptable.
+
+        # Users might be comparing DiGraph instances with MultiDiGraph
+        # instances. So the generic DiGraphMatcher class must work with
+        # MultiDiGraphs. Care must be taken since the value in the innermost
+        # dictionary is a singlet for DiGraph instances.  For MultiDiGraphs,
+        # the value in the innermost dictionary is a list.
+
+        ###
+        # Test at each step to get a return value as soon as possible.
+        ###
+
+        # Look ahead 0
+
+        # R_self
+
+        # The number of selfloops for G1_node must equal the number of
+        # self-loops for G2_node. Without this check, we would fail on R_pred
+        # at the next recursion level. This should prune the tree even further.
+        if self.test == "mono":
+            if self.G1.number_of_edges(G1_node, G1_node) < self.G2.number_of_edges(
+                G2_node, G2_node
+            ):
+                return False
+        else:
+            if self.G1.number_of_edges(G1_node, G1_node) != self.G2.number_of_edges(
+                G2_node, G2_node
+            ):
+                return False
+
+        # R_pred
+
+        # For each predecessor n' of n in the partial mapping, the
+        # corresponding node m' is a predecessor of m, and vice versa. Also,
+        # the number of edges must be equal
+        if self.test != "mono":
+            for predecessor in self.G1.pred[G1_node]:
+                if predecessor in self.core_1:
+                    if self.core_1[predecessor] not in self.G2.pred[G2_node]:
+                        return False
+                    elif self.G1.number_of_edges(
+                        predecessor, G1_node
+                    ) != self.G2.number_of_edges(self.core_1[predecessor], G2_node):
+                        return False
+
+        for predecessor in self.G2.pred[G2_node]:
+            if predecessor in self.core_2:
+                if self.core_2[predecessor] not in self.G1.pred[G1_node]:
+                    return False
+                elif self.test == "mono":
+                    if self.G1.number_of_edges(
+                        self.core_2[predecessor], G1_node
+                    ) < self.G2.number_of_edges(predecessor, G2_node):
+                        return False
+                else:
+                    if self.G1.number_of_edges(
+                        self.core_2[predecessor], G1_node
+                    ) != self.G2.number_of_edges(predecessor, G2_node):
+                        return False
+
+        # R_succ
+
+        # For each successor n' of n in the partial mapping, the corresponding
+        # node m' is a successor of m, and vice versa. Also, the number of
+        # edges must be equal.
+        if self.test != "mono":
+            for successor in self.G1[G1_node]:
+                if successor in self.core_1:
+                    if self.core_1[successor] not in self.G2[G2_node]:
+                        return False
+                    elif self.G1.number_of_edges(
+                        G1_node, successor
+                    ) != self.G2.number_of_edges(G2_node, self.core_1[successor]):
+                        return False
+
+        for successor in self.G2[G2_node]:
+            if successor in self.core_2:
+                if self.core_2[successor] not in self.G1[G1_node]:
+                    return False
+                elif self.test == "mono":
+                    if self.G1.number_of_edges(
+                        G1_node, self.core_2[successor]
+                    ) < self.G2.number_of_edges(G2_node, successor):
+                        return False
+                else:
+                    if self.G1.number_of_edges(
+                        G1_node, self.core_2[successor]
+                    ) != self.G2.number_of_edges(G2_node, successor):
+                        return False
+
+        if self.test != "mono":
+            # Look ahead 1
+
+            # R_termin
+            # The number of predecessors of n that are in T_1^{in} is equal to the
+            # number of predecessors of m that are in T_2^{in}.
+            num1 = 0
+            for predecessor in self.G1.pred[G1_node]:
+                if (predecessor in self.in_1) and (predecessor not in self.core_1):
+                    num1 += 1
+            num2 = 0
+            for predecessor in self.G2.pred[G2_node]:
+                if (predecessor in self.in_2) and (predecessor not in self.core_2):
+                    num2 += 1
+            if self.test == "graph":
+                if num1 != num2:
+                    return False
+            else:  # self.test == 'subgraph'
+                if not (num1 >= num2):
+                    return False
+
+            # The number of successors of n that are in T_1^{in} is equal to the
+            # number of successors of m that are in T_2^{in}.
+            num1 = 0
+            for successor in self.G1[G1_node]:
+                if (successor in self.in_1) and (successor not in self.core_1):
+                    num1 += 1
+            num2 = 0
+            for successor in self.G2[G2_node]:
+                if (successor in self.in_2) and (successor not in self.core_2):
+                    num2 += 1
+            if self.test == "graph":
+                if num1 != num2:
+                    return False
+            else:  # self.test == 'subgraph'
+                if not (num1 >= num2):
+                    return False
+
+            # R_termout
+
+            # The number of predecessors of n that are in T_1^{out} is equal to the
+            # number of predecessors of m that are in T_2^{out}.
+            num1 = 0
+            for predecessor in self.G1.pred[G1_node]:
+                if (predecessor in self.out_1) and (predecessor not in self.core_1):
+                    num1 += 1
+            num2 = 0
+            for predecessor in self.G2.pred[G2_node]:
+                if (predecessor in self.out_2) and (predecessor not in self.core_2):
+                    num2 += 1
+            if self.test == "graph":
+                if num1 != num2:
+                    return False
+            else:  # self.test == 'subgraph'
+                if not (num1 >= num2):
+                    return False
+
+            # The number of successors of n that are in T_1^{out} is equal to the
+            # number of successors of m that are in T_2^{out}.
+            num1 = 0
+            for successor in self.G1[G1_node]:
+                if (successor in self.out_1) and (successor not in self.core_1):
+                    num1 += 1
+            num2 = 0
+            for successor in self.G2[G2_node]:
+                if (successor in self.out_2) and (successor not in self.core_2):
+                    num2 += 1
+            if self.test == "graph":
+                if num1 != num2:
+                    return False
+            else:  # self.test == 'subgraph'
+                if not (num1 >= num2):
+                    return False
+
+            # Look ahead 2
+
+            # R_new
+
+            # The number of predecessors of n that are neither in the core_1 nor
+            # T_1^{in} nor T_1^{out} is equal to the number of predecessors of m
+            # that are neither in core_2 nor T_2^{in} nor T_2^{out}.
+            num1 = 0
+            for predecessor in self.G1.pred[G1_node]:
+                if (predecessor not in self.in_1) and (predecessor not in self.out_1):
+                    num1 += 1
+            num2 = 0
+            for predecessor in self.G2.pred[G2_node]:
+                if (predecessor not in self.in_2) and (predecessor not in self.out_2):
+                    num2 += 1
+            if self.test == "graph":
+                if num1 != num2:
+                    return False
+            else:  # self.test == 'subgraph'
+                if not (num1 >= num2):
+                    return False
+
+            # The number of successors of n that are neither in the core_1 nor
+            # T_1^{in} nor T_1^{out} is equal to the number of successors of m
+            # that are neither in core_2 nor T_2^{in} nor T_2^{out}.
+            num1 = 0
+            for successor in self.G1[G1_node]:
+                if (successor not in self.in_1) and (successor not in self.out_1):
+                    num1 += 1
+            num2 = 0
+            for successor in self.G2[G2_node]:
+                if (successor not in self.in_2) and (successor not in self.out_2):
+                    num2 += 1
+            if self.test == "graph":
+                if num1 != num2:
+                    return False
+            else:  # self.test == 'subgraph'
+                if not (num1 >= num2):
+                    return False
+
+        # Otherwise, this node pair is syntactically feasible!
+        return True
+
+
+class GMState:
+    """Internal representation of state for the GraphMatcher class.
+
+    This class is used internally by the GraphMatcher class.  It is used
+    only to store state specific data. There will be at most G2.order() of
+    these objects in memory at a time, due to the depth-first search
+    strategy employed by the VF2 algorithm.
+    """
+
+    def __init__(self, GM, G1_node=None, G2_node=None):
+        """Initializes GMState object.
+
+        Pass in the GraphMatcher to which this GMState belongs and the
+        new node pair that will be added to the GraphMatcher's current
+        isomorphism mapping.
+        """
+        self.GM = GM
+
+        # Initialize the last stored node pair.
+        self.G1_node = None
+        self.G2_node = None
+        self.depth = len(GM.core_1)
+
+        if G1_node is None or G2_node is None:
+            # Then we reset the class variables
+            GM.core_1 = {}
+            GM.core_2 = {}
+            GM.inout_1 = {}
+            GM.inout_2 = {}
+
+        # Watch out! G1_node == 0 should evaluate to True.
+        if G1_node is not None and G2_node is not None:
+            # Add the node pair to the isomorphism mapping.
+            GM.core_1[G1_node] = G2_node
+            GM.core_2[G2_node] = G1_node
+
+            # Store the node that was added last.
+            self.G1_node = G1_node
+            self.G2_node = G2_node
+
+            # Now we must update the other two vectors.
+            # We will add only if it is not in there already!
+            self.depth = len(GM.core_1)
+
+            # First we add the new nodes...
+            if G1_node not in GM.inout_1:
+                GM.inout_1[G1_node] = self.depth
+            if G2_node not in GM.inout_2:
+                GM.inout_2[G2_node] = self.depth
+
+            # Now we add every other node...
+
+            # Updates for T_1^{inout}
+            new_nodes = set()
+            for node in GM.core_1:
+                new_nodes.update(
+                    [neighbor for neighbor in GM.G1[node] if neighbor not in GM.core_1]
+                )
+            for node in new_nodes:
+                if node not in GM.inout_1:
+                    GM.inout_1[node] = self.depth
+
+            # Updates for T_2^{inout}
+            new_nodes = set()
+            for node in GM.core_2:
+                new_nodes.update(
+                    [neighbor for neighbor in GM.G2[node] if neighbor not in GM.core_2]
+                )
+            for node in new_nodes:
+                if node not in GM.inout_2:
+                    GM.inout_2[node] = self.depth
+
+    def restore(self):
+        """Deletes the GMState object and restores the class variables."""
+        # First we remove the node that was added from the core vectors.
+        # Watch out! G1_node == 0 should evaluate to True.
+        if self.G1_node is not None and self.G2_node is not None:
+            del self.GM.core_1[self.G1_node]
+            del self.GM.core_2[self.G2_node]
+
+        # Now we revert the other two vectors.
+        # Thus, we delete all entries which have this depth level.
+        for vector in (self.GM.inout_1, self.GM.inout_2):
+            for node in list(vector.keys()):
+                if vector[node] == self.depth:
+                    del vector[node]
+
+
+class DiGMState:
+    """Internal representation of state for the DiGraphMatcher class.
+
+    This class is used internally by the DiGraphMatcher class.  It is used
+    only to store state specific data. There will be at most G2.order() of
+    these objects in memory at a time, due to the depth-first search
+    strategy employed by the VF2 algorithm.
+
+    """
+
+    def __init__(self, GM, G1_node=None, G2_node=None):
+        """Initializes DiGMState object.
+
+        Pass in the DiGraphMatcher to which this DiGMState belongs and the
+        new node pair that will be added to the GraphMatcher's current
+        isomorphism mapping.
+        """
+        self.GM = GM
+
+        # Initialize the last stored node pair.
+        self.G1_node = None
+        self.G2_node = None
+        self.depth = len(GM.core_1)
+
+        if G1_node is None or G2_node is None:
+            # Then we reset the class variables
+            GM.core_1 = {}
+            GM.core_2 = {}
+            GM.in_1 = {}
+            GM.in_2 = {}
+            GM.out_1 = {}
+            GM.out_2 = {}
+
+        # Watch out! G1_node == 0 should evaluate to True.
+        if G1_node is not None and G2_node is not None:
+            # Add the node pair to the isomorphism mapping.
+            GM.core_1[G1_node] = G2_node
+            GM.core_2[G2_node] = G1_node
+
+            # Store the node that was added last.
+            self.G1_node = G1_node
+            self.G2_node = G2_node
+
+            # Now we must update the other four vectors.
+            # We will add only if it is not in there already!
+            self.depth = len(GM.core_1)
+
+            # First we add the new nodes...
+            for vector in (GM.in_1, GM.out_1):
+                if G1_node not in vector:
+                    vector[G1_node] = self.depth
+            for vector in (GM.in_2, GM.out_2):
+                if G2_node not in vector:
+                    vector[G2_node] = self.depth
+
+            # Now we add every other node...
+
+            # Updates for T_1^{in}
+            new_nodes = set()
+            for node in GM.core_1:
+                new_nodes.update(
+                    [
+                        predecessor
+                        for predecessor in GM.G1.predecessors(node)
+                        if predecessor not in GM.core_1
+                    ]
+                )
+            for node in new_nodes:
+                if node not in GM.in_1:
+                    GM.in_1[node] = self.depth
+
+            # Updates for T_2^{in}
+            new_nodes = set()
+            for node in GM.core_2:
+                new_nodes.update(
+                    [
+                        predecessor
+                        for predecessor in GM.G2.predecessors(node)
+                        if predecessor not in GM.core_2
+                    ]
+                )
+            for node in new_nodes:
+                if node not in GM.in_2:
+                    GM.in_2[node] = self.depth
+
+            # Updates for T_1^{out}
+            new_nodes = set()
+            for node in GM.core_1:
+                new_nodes.update(
+                    [
+                        successor
+                        for successor in GM.G1.successors(node)
+                        if successor not in GM.core_1
+                    ]
+                )
+            for node in new_nodes:
+                if node not in GM.out_1:
+                    GM.out_1[node] = self.depth
+
+            # Updates for T_2^{out}
+            new_nodes = set()
+            for node in GM.core_2:
+                new_nodes.update(
+                    [
+                        successor
+                        for successor in GM.G2.successors(node)
+                        if successor not in GM.core_2
+                    ]
+                )
+            for node in new_nodes:
+                if node not in GM.out_2:
+                    GM.out_2[node] = self.depth
+
+    def restore(self):
+        """Deletes the DiGMState object and restores the class variables."""
+
+        # First we remove the node that was added from the core vectors.
+        # Watch out! G1_node == 0 should evaluate to True.
+        if self.G1_node is not None and self.G2_node is not None:
+            del self.GM.core_1[self.G1_node]
+            del self.GM.core_2[self.G2_node]
+
+        # Now we revert the other four vectors.
+        # Thus, we delete all entries which have this depth level.
+        for vector in (self.GM.in_1, self.GM.in_2, self.GM.out_1, self.GM.out_2):
+            for node in list(vector.keys()):
+                if vector[node] == self.depth:
+                    del vector[node]

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/isomorphism/matchhelpers.py

@@ -0,0 +1,351 @@
+"""Functions which help end users define customize node_match and
+edge_match functions to use during isomorphism checks.
+"""
+import math
+import types
+from itertools import permutations
+
+__all__ = [
+    "categorical_node_match",
+    "categorical_edge_match",
+    "categorical_multiedge_match",
+    "numerical_node_match",
+    "numerical_edge_match",
+    "numerical_multiedge_match",
+    "generic_node_match",
+    "generic_edge_match",
+    "generic_multiedge_match",
+]
+
+
+def copyfunc(f, name=None):
+    """Returns a deepcopy of a function."""
+    return types.FunctionType(
+        f.__code__, f.__globals__, name or f.__name__, f.__defaults__, f.__closure__
+    )
+
+
+def allclose(x, y, rtol=1.0000000000000001e-05, atol=1e-08):
+    """Returns True if x and y are sufficiently close, elementwise.
+
+    Parameters
+    ----------
+    rtol : float
+        The relative error tolerance.
+    atol : float
+        The absolute error tolerance.
+
+    """
+    # assume finite weights, see numpy.allclose() for reference
+    return all(math.isclose(xi, yi, rel_tol=rtol, abs_tol=atol) for xi, yi in zip(x, y))
+
+
+categorical_doc = """
+Returns a comparison function for a categorical node attribute.
+
+The value(s) of the attr(s) must be hashable and comparable via the ==
+operator since they are placed into a set([]) object.  If the sets from
+G1 and G2 are the same, then the constructed function returns True.
+
+Parameters
+----------
+attr : string | list
+    The categorical node attribute to compare, or a list of categorical
+    node attributes to compare.
+default : value | list
+    The default value for the categorical node attribute, or a list of
+    default values for the categorical node attributes.
+
+Returns
+-------
+match : function
+    The customized, categorical `node_match` function.
+
+Examples
+--------
+>>> import networkx.algorithms.isomorphism as iso
+>>> nm = iso.categorical_node_match("size", 1)
+>>> nm = iso.categorical_node_match(["color", "size"], ["red", 2])
+
+"""
+
+
+def categorical_node_match(attr, default):
+    if isinstance(attr, str):
+
+        def match(data1, data2):
+            return data1.get(attr, default) == data2.get(attr, default)
+
+    else:
+        attrs = list(zip(attr, default))  # Python 3
+
+        def match(data1, data2):
+            return all(data1.get(attr, d) == data2.get(attr, d) for attr, d in attrs)
+
+    return match
+
+
+categorical_edge_match = copyfunc(categorical_node_match, "categorical_edge_match")
+
+
+def categorical_multiedge_match(attr, default):
+    if isinstance(attr, str):
+
+        def match(datasets1, datasets2):
+            values1 = {data.get(attr, default) for data in datasets1.values()}
+            values2 = {data.get(attr, default) for data in datasets2.values()}
+            return values1 == values2
+
+    else:
+        attrs = list(zip(attr, default))  # Python 3
+
+        def match(datasets1, datasets2):
+            values1 = set()
+            for data1 in datasets1.values():
+                x = tuple(data1.get(attr, d) for attr, d in attrs)
+                values1.add(x)
+            values2 = set()
+            for data2 in datasets2.values():
+                x = tuple(data2.get(attr, d) for attr, d in attrs)
+                values2.add(x)
+            return values1 == values2
+
+    return match
+
+
+# Docstrings for categorical functions.
+categorical_node_match.__doc__ = categorical_doc
+categorical_edge_match.__doc__ = categorical_doc.replace("node", "edge")
+tmpdoc = categorical_doc.replace("node", "edge")
+tmpdoc = tmpdoc.replace("categorical_edge_match", "categorical_multiedge_match")
+categorical_multiedge_match.__doc__ = tmpdoc
+
+
+numerical_doc = """
+Returns a comparison function for a numerical node attribute.
+
+The value(s) of the attr(s) must be numerical and sortable.  If the
+sorted list of values from G1 and G2 are the same within some
+tolerance, then the constructed function returns True.
+
+Parameters
+----------
+attr : string | list
+    The numerical node attribute to compare, or a list of numerical
+    node attributes to compare.
+default : value | list
+    The default value for the numerical node attribute, or a list of
+    default values for the numerical node attributes.
+rtol : float
+    The relative error tolerance.
+atol : float
+    The absolute error tolerance.
+
+Returns
+-------
+match : function
+    The customized, numerical `node_match` function.
+
+Examples
+--------
+>>> import networkx.algorithms.isomorphism as iso
+>>> nm = iso.numerical_node_match("weight", 1.0)
+>>> nm = iso.numerical_node_match(["weight", "linewidth"], [0.25, 0.5])
+
+"""
+
+
+def numerical_node_match(attr, default, rtol=1.0000000000000001e-05, atol=1e-08):
+    if isinstance(attr, str):
+
+        def match(data1, data2):
+            return math.isclose(
+                data1.get(attr, default),
+                data2.get(attr, default),
+                rel_tol=rtol,
+                abs_tol=atol,
+            )
+
+    else:
+        attrs = list(zip(attr, default))  # Python 3
+
+        def match(data1, data2):
+            values1 = [data1.get(attr, d) for attr, d in attrs]
+            values2 = [data2.get(attr, d) for attr, d in attrs]
+            return allclose(values1, values2, rtol=rtol, atol=atol)
+
+    return match
+
+
+numerical_edge_match = copyfunc(numerical_node_match, "numerical_edge_match")
+
+
+def numerical_multiedge_match(attr, default, rtol=1.0000000000000001e-05, atol=1e-08):
+    if isinstance(attr, str):
+
+        def match(datasets1, datasets2):
+            values1 = sorted(data.get(attr, default) for data in datasets1.values())
+            values2 = sorted(data.get(attr, default) for data in datasets2.values())
+            return allclose(values1, values2, rtol=rtol, atol=atol)
+
+    else:
+        attrs = list(zip(attr, default))  # Python 3
+
+        def match(datasets1, datasets2):
+            values1 = []
+            for data1 in datasets1.values():
+                x = tuple(data1.get(attr, d) for attr, d in attrs)
+                values1.append(x)
+            values2 = []
+            for data2 in datasets2.values():
+                x = tuple(data2.get(attr, d) for attr, d in attrs)
+                values2.append(x)
+            values1.sort()
+            values2.sort()
+            for xi, yi in zip(values1, values2):
+                if not allclose(xi, yi, rtol=rtol, atol=atol):
+                    return False
+            else:
+                return True
+
+    return match
+
+
+# Docstrings for numerical functions.
+numerical_node_match.__doc__ = numerical_doc
+numerical_edge_match.__doc__ = numerical_doc.replace("node", "edge")
+tmpdoc = numerical_doc.replace("node", "edge")
+tmpdoc = tmpdoc.replace("numerical_edge_match", "numerical_multiedge_match")
+numerical_multiedge_match.__doc__ = tmpdoc
+
+
+generic_doc = """
+Returns a comparison function for a generic attribute.
+
+The value(s) of the attr(s) are compared using the specified
+operators. If all the attributes are equal, then the constructed
+function returns True.
+
+Parameters
+----------
+attr : string | list
+    The node attribute to compare, or a list of node attributes
+    to compare.
+default : value | list
+    The default value for the node attribute, or a list of
+    default values for the node attributes.
+op : callable | list
+    The operator to use when comparing attribute values, or a list
+    of operators to use when comparing values for each attribute.
+
+Returns
+-------
+match : function
+    The customized, generic `node_match` function.
+
+Examples
+--------
+>>> from operator import eq
+>>> from math import isclose
+>>> from networkx.algorithms.isomorphism import generic_node_match
+>>> nm = generic_node_match("weight", 1.0, isclose)
+>>> nm = generic_node_match("color", "red", eq)
+>>> nm = generic_node_match(["weight", "color"], [1.0, "red"], [isclose, eq])
+
+"""
+
+
+def generic_node_match(attr, default, op):
+    if isinstance(attr, str):
+
+        def match(data1, data2):
+            return op(data1.get(attr, default), data2.get(attr, default))
+
+    else:
+        attrs = list(zip(attr, default, op))  # Python 3
+
+        def match(data1, data2):
+            for attr, d, operator in attrs:
+                if not operator(data1.get(attr, d), data2.get(attr, d)):
+                    return False
+            else:
+                return True
+
+    return match
+
+
+generic_edge_match = copyfunc(generic_node_match, "generic_edge_match")
+
+
+def generic_multiedge_match(attr, default, op):
+    """Returns a comparison function for a generic attribute.
+
+    The value(s) of the attr(s) are compared using the specified
+    operators. If all the attributes are equal, then the constructed
+    function returns True. Potentially, the constructed edge_match
+    function can be slow since it must verify that no isomorphism
+    exists between the multiedges before it returns False.
+
+    Parameters
+    ----------
+    attr : string | list
+        The edge attribute to compare, or a list of node attributes
+        to compare.
+    default : value | list
+        The default value for the edge attribute, or a list of
+        default values for the edgeattributes.
+    op : callable | list
+        The operator to use when comparing attribute values, or a list
+        of operators to use when comparing values for each attribute.
+
+    Returns
+    -------
+    match : function
+        The customized, generic `edge_match` function.
+
+    Examples
+    --------
+    >>> from operator import eq
+    >>> from math import isclose
+    >>> from networkx.algorithms.isomorphism import generic_node_match
+    >>> nm = generic_node_match("weight", 1.0, isclose)
+    >>> nm = generic_node_match("color", "red", eq)
+    >>> nm = generic_node_match(["weight", "color"], [1.0, "red"], [isclose, eq])
+
+    """
+
+    # This is slow, but generic.
+    # We must test every possible isomorphism between the edges.
+    if isinstance(attr, str):
+        attr = [attr]
+        default = [default]
+        op = [op]
+    attrs = list(zip(attr, default))  # Python 3
+
+    def match(datasets1, datasets2):
+        values1 = []
+        for data1 in datasets1.values():
+            x = tuple(data1.get(attr, d) for attr, d in attrs)
+            values1.append(x)
+        values2 = []
+        for data2 in datasets2.values():
+            x = tuple(data2.get(attr, d) for attr, d in attrs)
+            values2.append(x)
+        for vals2 in permutations(values2):
+            for xi, yi in zip(values1, vals2):
+                if not all(map(lambda x, y, z: z(x, y), xi, yi, op)):
+                    # This is not an isomorphism, go to next permutation.
+                    break
+            else:
+                # Then we found an isomorphism.
+                return True
+        else:
+            # Then there are no isomorphisms between the multiedges.
+            return False
+
+    return match
+
+
+# Docstrings for numerical functions.
+generic_node_match.__doc__ = generic_doc
+generic_edge_match.__doc__ = generic_doc.replace("node", "edge")

env-llmeval/lib/python3.10/site-packages/networkx/algorithms/isomorphism/temporalisomorphvf2.py

@@ -0,0 +1,304 @@
+"""
+*****************************
+Time-respecting VF2 Algorithm
+*****************************
+
+An extension of the VF2 algorithm for time-respecting graph isomorphism
+testing in temporal graphs.
+
+A temporal graph is one in which edges contain a datetime attribute,
+denoting when interaction occurred between the incident nodes. A
+time-respecting subgraph of a temporal graph is a subgraph such that
+all interactions incident to a node occurred within a time threshold,
+delta, of each other. A directed time-respecting subgraph has the
+added constraint that incoming interactions to a node must precede
+outgoing interactions from the same node - this enforces a sense of
+directed flow.
+
+Introduction
+------------
+
+The TimeRespectingGraphMatcher and TimeRespectingDiGraphMatcher
+extend the GraphMatcher and DiGraphMatcher classes, respectively,
+to include temporal constraints on matches. This is achieved through
+a semantic check, via the semantic_feasibility() function.
+
+As well as including G1 (the graph in which to seek embeddings) and
+G2 (the subgraph structure of interest), the name of the temporal
+attribute on the edges and the time threshold, delta, must be supplied
+as arguments to the matching constructors.
+
+A delta of zero is the strictest temporal constraint on the match -
+only embeddings in which all interactions occur at the same time will
+be returned. A delta of one day will allow embeddings in which
+adjacent interactions occur up to a day apart.
+
+Examples
+--------
+
+Examples will be provided when the datetime type has been incorporated.
+
+
+Temporal Subgraph Isomorphism
+-----------------------------
+
+A brief discussion of the somewhat diverse current literature will be
+included here.
+
+References
+----------
+
+[1] Redmond, U. and Cunningham, P. Temporal subgraph isomorphism. In:
+The 2013 IEEE/ACM International Conference on Advances in Social
+Networks Analysis and Mining (ASONAM). Niagara Falls, Canada; 2013:
+pages 1451 - 1452. [65]
+
+For a discussion of the literature on temporal networks:
+
+[3] P. Holme and J. Saramaki. Temporal networks. Physics Reports,
+519(3):97–125, 2012.
+
+Notes
+-----
+
+Handles directed and undirected graphs and graphs with parallel edges.
+
+"""
+
+import networkx as nx
+
+from .isomorphvf2 import DiGraphMatcher, GraphMatcher
+
+__all__ = ["TimeRespectingGraphMatcher", "TimeRespectingDiGraphMatcher"]
+
+
+class TimeRespectingGraphMatcher(GraphMatcher):
+    def __init__(self, G1, G2, temporal_attribute_name, delta):
+        """Initialize TimeRespectingGraphMatcher.
+
+        G1 and G2 should be nx.Graph or nx.MultiGraph instances.
+
+        Examples
+        --------
+        To create a TimeRespectingGraphMatcher which checks for
+        syntactic and semantic feasibility:
+
+        >>> from networkx.algorithms import isomorphism
+        >>> from datetime import timedelta
+        >>> G1 = nx.Graph(nx.path_graph(4, create_using=nx.Graph()))
+
+        >>> G2 = nx.Graph(nx.path_graph(4, create_using=nx.Graph()))
+
+        >>> GM = isomorphism.TimeRespectingGraphMatcher(G1, G2, "date", timedelta(days=1))
+        """
+        self.temporal_attribute_name = temporal_attribute_name
+        self.delta = delta
+        super().__init__(G1, G2)
+
+    def one_hop(self, Gx, Gx_node, neighbors):
+        """
+        Edges one hop out from a node in the mapping should be
+        time-respecting with respect to each other.
+        """
+        dates = []
+        for n in neighbors:
+            if isinstance(Gx, nx.Graph):  # Graph G[u][v] returns the data dictionary.
+                dates.append(Gx[Gx_node][n][self.temporal_attribute_name])
+            else:  # MultiGraph G[u][v] returns a dictionary of key -> data dictionary.
+                for edge in Gx[Gx_node][
+                    n
+                ].values():  # Iterates all edges between node pair.
+                    dates.append(edge[self.temporal_attribute_name])
+        if any(x is None for x in dates):
+            raise ValueError("Datetime not supplied for at least one edge.")
+        return not dates or max(dates) - min(dates) <= self.delta
+
+    def two_hop(self, Gx, core_x, Gx_node, neighbors):
+        """
+        Paths of length 2 from Gx_node should be time-respecting.
+        """
+        return all(
+            self.one_hop(Gx, v, [n for n in Gx[v] if n in core_x] + [Gx_node])
+            for v in neighbors
+        )
+
+    def semantic_feasibility(self, G1_node, G2_node):
+        """Returns True if adding (G1_node, G2_node) is semantically
+        feasible.
+
+        Any subclass which redefines semantic_feasibility() must
+        maintain the self.tests if needed, to keep the match() method
+        functional. Implementations should consider multigraphs.
+        """
+        neighbors = [n for n in self.G1[G1_node] if n in self.core_1]
+        if not self.one_hop(self.G1, G1_node, neighbors):  # Fail fast on first node.
+            return False
+        if not self.two_hop(self.G1, self.core_1, G1_node, neighbors):
+            return False
+        # Otherwise, this node is semantically feasible!
+        return True
+
+
+class TimeRespectingDiGraphMatcher(DiGraphMatcher):
+    def __init__(self, G1, G2, temporal_attribute_name, delta):
+        """Initialize TimeRespectingDiGraphMatcher.
+
+        G1 and G2 should be nx.DiGraph or nx.MultiDiGraph instances.
+
+        Examples
+        --------
+        To create a TimeRespectingDiGraphMatcher which checks for
+        syntactic and semantic feasibility:
+
+        >>> from networkx.algorithms import isomorphism
+        >>> from datetime import timedelta
+        >>> G1 = nx.DiGraph(nx.path_graph(4, create_using=nx.DiGraph()))
+
+        >>> G2 = nx.DiGraph(nx.path_graph(4, create_using=nx.DiGraph()))
+
+        >>> GM = isomorphism.TimeRespectingDiGraphMatcher(G1, G2, "date", timedelta(days=1))
+        """
+        self.temporal_attribute_name = temporal_attribute_name
+        self.delta = delta
+        super().__init__(G1, G2)
+
+    def get_pred_dates(self, Gx, Gx_node, core_x, pred):
+        """
+        Get the dates of edges from predecessors.
+        """
+        pred_dates = []
+        if isinstance(Gx, nx.DiGraph):  # Graph G[u][v] returns the data dictionary.
+            for n in pred:
+                pred_dates.append(Gx[n][Gx_node][self.temporal_attribute_name])
+        else:  # MultiGraph G[u][v] returns a dictionary of key -> data dictionary.
+            for n in pred:
+                for edge in Gx[n][
+                    Gx_node
+                ].values():  # Iterates all edge data between node pair.
+                    pred_dates.append(edge[self.temporal_attribute_name])
+        return pred_dates
+
+    def get_succ_dates(self, Gx, Gx_node, core_x, succ):
+        """
+        Get the dates of edges to successors.
+        """
+        succ_dates = []
+        if isinstance(Gx, nx.DiGraph):  # Graph G[u][v] returns the data dictionary.
+            for n in succ:
+                succ_dates.append(Gx[Gx_node][n][self.temporal_attribute_name])
+        else:  # MultiGraph G[u][v] returns a dictionary of key -> data dictionary.
+            for n in succ:
+                for edge in Gx[Gx_node][
+                    n
+                ].values():  # Iterates all edge data between node pair.
+                    succ_dates.append(edge[self.temporal_attribute_name])
+        return succ_dates
+
+    def one_hop(self, Gx, Gx_node, core_x, pred, succ):
+        """
+        The ego node.
+        """
+        pred_dates = self.get_pred_dates(Gx, Gx_node, core_x, pred)
+        succ_dates = self.get_succ_dates(Gx, Gx_node, core_x, succ)
+        return self.test_one(pred_dates, succ_dates) and self.test_two(
+            pred_dates, succ_dates
+        )
+
+    def two_hop_pred(self, Gx, Gx_node, core_x, pred):
+        """
+        The predecessors of the ego node.
+        """
+        return all(
+            self.one_hop(
+                Gx,
+                p,
+                core_x,
+                self.preds(Gx, core_x, p),
+                self.succs(Gx, core_x, p, Gx_node),
+            )
+            for p in pred
+        )
+
+    def two_hop_succ(self, Gx, Gx_node, core_x, succ):
+        """
+        The successors of the ego node.
+        """
+        return all(
+            self.one_hop(
+                Gx,
+                s,
+                core_x,
+                self.preds(Gx, core_x, s, Gx_node),
+                self.succs(Gx, core_x, s),
+            )
+            for s in succ
+        )
+
+    def preds(self, Gx, core_x, v, Gx_node=None):
+        pred = [n for n in Gx.predecessors(v) if n in core_x]
+        if Gx_node:
+            pred.append(Gx_node)
+        return pred
+
+    def succs(self, Gx, core_x, v, Gx_node=None):
+        succ = [n for n in Gx.successors(v) if n in core_x]
+        if Gx_node:
+            succ.append(Gx_node)
+        return succ
+
+    def test_one(self, pred_dates, succ_dates):
+        """
+        Edges one hop out from Gx_node in the mapping should be
+        time-respecting with respect to each other, regardless of
+        direction.
+        """
+        time_respecting = True
+        dates = pred_dates + succ_dates
+
+        if any(x is None for x in dates):
+            raise ValueError("Date or datetime not supplied for at least one edge.")
+
+        dates.sort()  # Small to large.
+        if 0 < len(dates) and not (dates[-1] - dates[0] <= self.delta):
+            time_respecting = False
+        return time_respecting
+
+    def test_two(self, pred_dates, succ_dates):
+        """
+        Edges from a dual Gx_node in the mapping should be ordered in
+        a time-respecting manner.
+        """
+        time_respecting = True
+        pred_dates.sort()
+        succ_dates.sort()
+        # First out before last in; negative of the necessary condition for time-respect.
+        if (
+            0 < len(succ_dates)
+            and 0 < len(pred_dates)
+            and succ_dates[0] < pred_dates[-1]
+        ):
+            time_respecting = False
+        return time_respecting
+
+    def semantic_feasibility(self, G1_node, G2_node):
+        """Returns True if adding (G1_node, G2_node) is semantically
+        feasible.
+
+        Any subclass which redefines semantic_feasibility() must
+        maintain the self.tests if needed, to keep the match() method
+        functional. Implementations should consider multigraphs.
+        """
+        pred, succ = (
+            [n for n in self.G1.predecessors(G1_node) if n in self.core_1],
+            [n for n in self.G1.successors(G1_node) if n in self.core_1],
+        )
+        if not self.one_hop(
+            self.G1, G1_node, self.core_1, pred, succ
+        ):  # Fail fast on first node.
+            return False
+        if not self.two_hop_pred(self.G1, G1_node, self.core_1, pred):
+            return False
+        if not self.two_hop_succ(self.G1, G1_node, self.core_1, succ):
+            return False
+        # Otherwise, this node is semantically feasible!
+        return True