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# Source code for networkx.algorithms.isomorphism.vf2userfunc

    """
    Module to simplify the specification of user-defined equality functions for
    node and edge attributes during isomorphism checks.

    During the construction of an isomorphism, the algorithm considers two
    candidate nodes n1 in G1 and n2 in G2.  The graphs G1 and G2 are then
    compared with respect to properties involving n1 and n2, and if the outcome
    is good, then the candidate nodes are considered isomorphic. NetworkX
    provides a simple mechanism for users to extend the comparisons to include
    node and edge attributes.

    Node attributes are handled by the node_match keyword. When considering
    n1 and n2, the algorithm passes their node attribute dictionaries to
    node_match, and if it returns False, then n1 and n2 cannot be
    considered to be isomorphic.

    Edge attributes are handled by the edge_match keyword. When considering
    n1 and n2, the algorithm must verify that outgoing edges from n1 are
    commensurate with the outgoing edges for n2. If the graph is directed,
    then a similar check is also performed for incoming edges.

    Focusing only on outgoing edges, we consider pairs of nodes (n1, v1) from
    G1 and (n2, v2) from G2. For graphs and digraphs, there is only one edge
    between (n1, v1) and only one edge between (n2, v2). Those edge attribute
    dictionaries are passed to edge_match, and if it returns False, then
    n1 and n2 cannot be considered isomorphic. For multigraphs and
    multidigraphs, there can be multiple edges between (n1, v1) and also
    multiple edges between (n2, v2).  Now, there must exist an isomorphism
    from "all the edges between (n1, v1)" to "all the edges between (n2, v2)".
    So, all of the edge attribute dictionaries are passed to edge_match, and
    it must determine if there is an isomorphism between the two sets of edges.
    """

    from . import isomorphvf2 as vf2

    __all__ = ["GraphMatcher", "DiGraphMatcher", "MultiGraphMatcher", "MultiDiGraphMatcher"]

    def _semantic_feasibility(self, G1_node, G2_node):
        """Returns True if mapping G1_node to G2_node is semantically feasible."""
        # Make sure the nodes match
        if self.node_match is not None:
            nm = self.node_match(self.G1.nodes[G1_node], self.G2.nodes[G2_node])
            if not nm:
                return False

        # Make sure the edges match
        if self.edge_match is not None:
            # Cached lookups
            G1nbrs = self.G1_adj[G1_node]
            G2nbrs = self.G2_adj[G2_node]
            core_1 = self.core_1
            edge_match = self.edge_match

            for neighbor in G1nbrs:
                # G1_node is not in core_1, so we must handle R_self separately
                if neighbor == G1_node:
                    if G2_node in G2nbrs and not edge_match(
                        G1nbrs[G1_node], G2nbrs[G2_node]
                    ):
                        return False
                elif neighbor in core_1:
                    G2_nbr = core_1[neighbor]
                    if G2_nbr in G2nbrs and not edge_match(
                        G1nbrs[neighbor], G2nbrs[G2_nbr]
                    ):
                        return False
            # syntactic check has already verified that neighbors are symmetric

        return True

    class GraphMatcher(vf2.GraphMatcher):
        """VF2 isomorphism checker for undirected graphs."""

        def __init__(self, G1, G2, node_match=None, edge_match=None):
            """Initialize graph matcher.

            Parameters
            ----------
            G1, G2: graph
                The graphs to be tested.

            node_match: callable
                A function that returns True iff node n1 in G1 and n2 in G2
                should be considered equal during the isomorphism test. The
                function will be called like::

                   node_match(G1.nodes[n1], G2.nodes[n2])

                That is, the function will receive the node attribute dictionaries
                of the nodes under consideration. If None, then no attributes are
                considered when testing for an isomorphism.

            edge_match: callable
                A function that returns True iff 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. 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. If None, then no attributes are
                considered when testing for an isomorphism.

            """
            vf2.GraphMatcher.__init__(self, G1, G2)

            self.node_match = node_match
            self.edge_match = edge_match

            # These will be modified during checks to minimize code repeat.
            self.G1_adj = self.G1.adj
            self.G2_adj = self.G2.adj

        semantic_feasibility = _semantic_feasibility

    class DiGraphMatcher(vf2.DiGraphMatcher):
        """VF2 isomorphism checker for directed graphs."""

        def __init__(self, G1, G2, node_match=None, edge_match=None):
            """Initialize graph matcher.

            Parameters
            ----------
            G1, G2 : graph
                The graphs to be tested.

            node_match : callable
                A function that returns True iff node n1 in G1 and n2 in G2
                should be considered equal during the isomorphism test. The
                function will be called like::

                   node_match(G1.nodes[n1], G2.nodes[n2])

                That is, the function will receive the node attribute dictionaries
                of the nodes under consideration. If None, then no attributes are
                considered when testing for an isomorphism.

            edge_match : callable
                A function that returns True iff 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. 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. If None, then no attributes are
                considered when testing for an isomorphism.

            """
            vf2.DiGraphMatcher.__init__(self, G1, G2)

            self.node_match = node_match
            self.edge_match = edge_match

            # These will be modified during checks to minimize code repeat.
            self.G1_adj = self.G1.adj
            self.G2_adj = self.G2.adj

        def semantic_feasibility(self, G1_node, G2_node):
            """Returns True if mapping G1_node to G2_node is semantically feasible."""

            # Test node_match and also test edge_match on successors
            feasible = _semantic_feasibility(self, G1_node, G2_node)
            if not feasible:
                return False

            # Test edge_match on predecessors
            self.G1_adj = self.G1.pred
            self.G2_adj = self.G2.pred
            feasible = _semantic_feasibility(self, G1_node, G2_node)
            self.G1_adj = self.G1.adj
            self.G2_adj = self.G2.adj

            return feasible

    # The "semantics" of edge_match are different for multi(di)graphs, but
    # the implementation is the same.  So, technically we do not need to
    # provide "multi" versions, but we do so to match NetworkX's base classes.

    class MultiGraphMatcher(GraphMatcher):
        """VF2 isomorphism checker for undirected multigraphs."""

    class MultiDiGraphMatcher(DiGraphMatcher):
        """VF2 isomorphism checker for directed multigraphs."""