xhs-note-crawling/python/py/Lib/site-packages/networkx/algorithms/community/divisive.py

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