mightyscape-1.1-deprecated/extensions/networkx/algorithms/centrality/load.py

# -*- coding: utf-8 -*-
#    Copyright (C) 2004-2019 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
#
# Authors: Aric Hagberg (hagberg@lanl.gov)
#          Pieter Swart (swart@lanl.gov)
#          Sasha Gutfraind (ag362@cornell.edu)
"""Load centrality."""
from operator import itemgetter

import networkx as nx

__all__ = ['load_centrality', 'edge_load_centrality']


def newman_betweenness_centrality(G, v=None, cutoff=None,
                                  normalized=True, weight=None):
    """Compute load centrality for nodes.

    The load centrality of a node is the fraction of all shortest
    paths that pass through that node.

    Parameters
    ----------
    G : graph
      A networkx graph.

    normalized : bool, optional (default=True)
      If True the betweenness values are normalized by b=b/(n-1)(n-2) where
      n is the number of nodes in G.

    weight : None or string, optional (default=None)
      If None, edge weights are ignored.
      Otherwise holds the name of the edge attribute used as weight.

    cutoff : bool, optional (default=None)
      If specified, only consider paths of length <= cutoff.

    Returns
    -------
    nodes : dictionary
       Dictionary of nodes with centrality as the value.

    See Also
    --------
    betweenness_centrality()

    Notes
    -----
    Load centrality is slightly different than betweenness. It was originally
    introduced by [2]_. For this load algorithm see [1]_.

    References
    ----------
    .. [1] Mark E. J. Newman:
       Scientific collaboration networks. II.
       Shortest paths, weighted networks, and centrality.
       Physical Review E 64, 016132, 2001.
       http://journals.aps.org/pre/abstract/10.1103/PhysRevE.64.016132
    .. [2] Kwang-Il Goh, Byungnam Kahng and Doochul Kim
       Universal behavior of Load Distribution in Scale-Free Networks.
       Physical Review Letters 87(27):1–4, 2001.
       http://phya.snu.ac.kr/~dkim/PRL87278701.pdf
    """
    if v is not None:   # only one node
        betweenness = 0.0
        for source in G:
            ubetween = _node_betweenness(G, source, cutoff, False, weight)
            betweenness += ubetween[v] if v in ubetween else 0
        if normalized:
            order = G.order()
            if order <= 2:
                return betweenness  # no normalization b=0 for all nodes
            betweenness *= 1.0 / ((order - 1) * (order - 2))
        return betweenness
    else:
        betweenness = {}.fromkeys(G, 0.0)
        for source in betweenness:
            ubetween = _node_betweenness(G, source, cutoff, False, weight)
            for vk in ubetween:
                betweenness[vk] += ubetween[vk]
        if normalized:
            order = G.order()
            if order <= 2:
                return betweenness  # no normalization b=0 for all nodes
            scale = 1.0 / ((order - 1) * (order - 2))
            for v in betweenness:
                betweenness[v] *= scale
        return betweenness  # all nodes


def _node_betweenness(G, source, cutoff=False, normalized=True,
                      weight=None):
    """Node betweenness_centrality helper:

    See betweenness_centrality for what you probably want.
    This actually computes "load" and not betweenness.
    See https://networkx.lanl.gov/ticket/103

    This calculates the load of each node for paths from a single source.
    (The fraction of number of shortests paths from source that go
    through each node.)

    To get the load for a node you need to do all-pairs shortest paths.

    If weight is not None then use Dijkstra for finding shortest paths.
    """
    # get the predecessor and path length data
    if weight is None:
        (pred, length) = nx.predecessor(G, source, cutoff=cutoff,
                                        return_seen=True)
    else:
        (pred, length) = nx.dijkstra_predecessor_and_distance(G, source,
                                                              cutoff, weight)

    # order the nodes by path length
    onodes = [(l, vert) for (vert, l) in length.items()]
    onodes.sort()
    onodes[:] = [vert for (l, vert) in onodes if l > 0]

    # initialize betweenness
    between = {}.fromkeys(length, 1.0)

    while onodes:
        v = onodes.pop()
        if v in pred:
            num_paths = len(pred[v])  # Discount betweenness if more than
            for x in pred[v]:         # one shortest path.
                if x == source:  # stop if hit source because all remaining v
                    break        # also have pred[v]==[source]
                between[x] += between[v] / float(num_paths)
    #  remove source
    for v in between:
        between[v] -= 1
    # rescale to be between 0 and 1
    if normalized:
        l = len(between)
        if l > 2:
            # scale by 1/the number of possible paths
            scale = 1.0 / float((l - 1) * (l - 2))
            for v in between:
                between[v] *= scale
    return between


load_centrality = newman_betweenness_centrality


def edge_load_centrality(G, cutoff=False):
    """Compute edge load.

    WARNING: This concept of edge load has not been analysed
    or discussed outside of NetworkX that we know of.
    It is based loosely on load_centrality in the sense that
    it counts the number of shortest paths which cross each edge.
    This function is for demonstration and testing purposes.

    Parameters
    ----------
    G : graph
        A networkx graph

    cutoff : bool, optional (default=False)
        If specified, only consider paths of length <= cutoff.

    Returns
    -------
    A dict keyed by edge 2-tuple to the number of shortest paths
    which use that edge. Where more than one path is shortest
    the count is divided equally among paths.
    """
    betweenness = {}
    for u, v in G.edges():
        betweenness[(u, v)] = 0.0
        betweenness[(v, u)] = 0.0

    for source in G:
        ubetween = _edge_betweenness(G, source, cutoff=cutoff)
        for e, ubetweenv in ubetween.items():
            betweenness[e] += ubetweenv  # cumulative total
    return betweenness


def _edge_betweenness(G, source, nodes=None, cutoff=False):
    """Edge betweenness helper."""
    # get the predecessor data
    (pred, length) = nx.predecessor(G, source, cutoff=cutoff, return_seen=True)
    # order the nodes by path length
    onodes = [n for n, d in sorted(length.items(), key=itemgetter(1))]
    # initialize betweenness, doesn't account for any edge weights
    between = {}
    for u, v in G.edges(nodes):
        between[(u, v)] = 1.0
        between[(v, u)] = 1.0

    while onodes:           # work through all paths
        v = onodes.pop()
        if v in pred:
            # Discount betweenness if more than one shortest path.
            num_paths = len(pred[v])
            for w in pred[v]:
                if w in pred:
                    # Discount betweenness, mult path
                    num_paths = len(pred[w])
                    for x in pred[w]:
                        between[(w, x)] += between[(v, w)] / num_paths
                        between[(x, w)] += between[(w, v)] / num_paths
    return between