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# Source code for networkx.algorithms.community.divisive

    import functools

    import networkx as nx

    __all__ = [
        "edge_betweenness_partition",
        "edge_current_flow_betweenness_partition",
    ]

    @nx._dispatchable(edge_attrs="weight")
    def edge_betweenness_partition(G, number_of_sets, *, weight=None):
        """Partition created by iteratively removing the highest edge betweenness edge.

        This algorithm works by calculating the edge betweenness for all
        edges and removing the edge with the highest value. It is then
        determined whether the graph has been broken into at least
        `number_of_sets` connected components.
        If not the process is repeated.

        Parameters
        ----------
        G : NetworkX Graph, DiGraph or MultiGraph
          Graph to be partitioned

        number_of_sets : int
          Number of sets in the desired partition of the graph

        weight : key, optional, default=None
          The key to use if using weights for edge betweenness calculation

        Returns
        -------
        C : list of sets
          Partition of the nodes of G

        Raises
        ------
        NetworkXError
          If number_of_sets is <= 0 or if number_of_sets > len(G)

        Examples
        --------
        >>> G = nx.karate_club_graph()
        >>> part = nx.community.edge_betweenness_partition(G, 2)
        >>> {0, 1, 3, 4, 5, 6, 7, 10, 11, 12, 13, 16, 17, 19, 21} in part
        True
        >>> {
        ...     2,
        ...     8,
        ...     9,
        ...     14,
        ...     15,
        ...     18,
        ...     20,
        ...     22,
        ...     23,
        ...     24,
        ...     25,
        ...     26,
        ...     27,
        ...     28,
        ...     29,
        ...     30,
        ...     31,
        ...     32,
        ...     33,
        ... } in part
        True

        See Also
        --------
        edge_current_flow_betweenness_partition

        Notes
        -----
        This algorithm is fairly slow, as both the calculation of connected
        components and edge betweenness relies on all pairs shortest
        path algorithms. They could potentially be combined to cut down
        on overall computation time.

        References
        ----------
        .. [1] Santo Fortunato 'Community Detection in Graphs' Physical Reports
           Volume 486, Issue 3-5 p. 75-174
           http://arxiv.org/abs/0906.0612
        """
        if number_of_sets <= 0:
            raise nx.NetworkXError("number_of_sets must be >0")
        if number_of_sets == 1:
            return [set(G)]
        if number_of_sets == len(G):
            return [{n} for n in G]
        if number_of_sets > len(G):
            raise nx.NetworkXError("number_of_sets must be <= len(G)")

        H = G.copy()
        partition = list(nx.connected_components(H))
        while len(partition) < number_of_sets:
            ranking = nx.edge_betweenness_centrality(H, weight=weight)
            edge = max(ranking, key=ranking.get)
            H.remove_edge(*edge)
            partition = list(nx.connected_components(H))
        return partition

    @nx._dispatchable(edge_attrs="weight")
    def edge_current_flow_betweenness_partition(G, number_of_sets, *, weight=None):
        """Partition created by removing the highest edge current flow betweenness edge.

        This algorithm works by calculating the edge current flow
        betweenness for all edges and removing the edge with the
        highest value. It is then determined whether the graph has
        been broken into at least `number_of_sets` connected
        components. If not the process is repeated.

        Parameters
        ----------
        G : NetworkX Graph, DiGraph or MultiGraph
          Graph to be partitioned

        number_of_sets : int
          Number of sets in the desired partition of the graph

        weight : key, optional (default=None)
          The edge attribute key to use as weights for
          edge current flow betweenness calculations

        Returns
        -------
        C : list of sets
          Partition of G

        Raises
        ------
        NetworkXError
          If number_of_sets is <= 0 or number_of_sets > len(G)

        Examples
        --------
        >>> G = nx.karate_club_graph()
        >>> part = nx.community.edge_current_flow_betweenness_partition(G, 2)
        >>> {0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 16, 17, 19, 21} in part
        True
        >>> {8, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33} in part
        True

        See Also
        --------
        edge_betweenness_partition

        Notes
        -----
        This algorithm is extremely slow, as the recalculation of the edge
        current flow betweenness is extremely slow.

        References
        ----------
        .. [1] Santo Fortunato 'Community Detection in Graphs' Physical Reports
           Volume 486, Issue 3-5 p. 75-174
           http://arxiv.org/abs/0906.0612
        """
        if number_of_sets <= 0:
            raise nx.NetworkXError("number_of_sets must be >0")
        elif number_of_sets == 1:
            return [set(G)]
        elif number_of_sets == len(G):
            return [{n} for n in G]
        elif number_of_sets > len(G):
            raise nx.NetworkXError("number_of_sets must be <= len(G)")

        rank = functools.partial(
            nx.edge_current_flow_betweenness_centrality, normalized=False, weight=weight
        )

        # current flow requires a connected network so we track the components explicitly
        H = G.copy()
        partition = list(nx.connected_components(H))
        if len(partition) > 1:
            Hcc_subgraphs = [H.subgraph(cc).copy() for cc in partition]
        else:
            Hcc_subgraphs = [H]

        ranking = {}
        for Hcc in Hcc_subgraphs:
            ranking.update(rank(Hcc))

        while len(partition) < number_of_sets:
            edge = max(ranking, key=ranking.get)
            for cc, Hcc in zip(partition, Hcc_subgraphs):
                if edge[0] in cc:
                    Hcc.remove_edge(*edge)
                    del ranking[edge]
                    splitcc_list = list(nx.connected_components(Hcc))
                    if len(splitcc_list) > 1:
                        # there are 2 connected components. split off smaller one
                        cc_new = min(splitcc_list, key=len)
                        Hcc_new = Hcc.subgraph(cc_new).copy()
                        # update edge rankings for Hcc_new
                        newranks = rank(Hcc_new)
                        for e, r in newranks.items():
                            ranking[e if e in ranking else e[::-1]] = r
                        # append new cc and Hcc to their lists.
                        partition.append(cc_new)
                        Hcc_subgraphs.append(Hcc_new)

                        # leave existing cc and Hcc in their lists, but shrink them
                        Hcc.remove_nodes_from(cc_new)
                        cc.difference_update(cc_new)
                    # update edge rankings for Hcc whether it was split or not
                    newranks = rank(Hcc)
                    for e, r in newranks.items():
                        ranking[e if e in ranking else e[::-1]] = r
                    break
        return partition