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Source code for networkx.algorithms.centrality.load

# coding=utf8
Load centrality.

#    Copyright (C) 2004-2015 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
__author__ = "\n".join(['Aric Hagberg (hagberg@lanl.gov)',
                        'Pieter Swart (swart@lanl.gov)',
                        'Sasha Gutfraind (ag362@cornell.edu)'])

__all__ = ['load_centrality',

import networkx as nx

def newman_betweenness_centrality(G,v=None,cutoff=None,
    """Compute load centrality for nodes.

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

    G : graph
      A networkx graph

    normalized : bool, optional
      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
      If None, edge weights are ignored.
      Otherwise holds the name of the edge attribute used as weight.

    cutoff : bool, optional
      If specified, only consider paths of length <= cutoff.

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

    See Also

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

    .. [1] Mark E. J. Newman:
       Scientific collaboration networks. II.
       Shortest paths, weighted networks, and centrality.
       Physical Review E 64, 016132, 2001.
    .. [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.
    if v is not None:   # only one node
        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
        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 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.
    In this case a cutoff is not implemented and so is ignored.


    # get the predecessor and path length data
    if weight is None:

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

    # intialize betweenness

    while onodes:
        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]
    #  remove source
    for v in between:
    # rescale to be between 0 and 1
    if normalized:
        if l > 2:
            scale=1.0/float((l-1)*(l-2)) # 1/the number of possible paths
            for v in between:
                between[v] *= scale
    return between


[docs]def edge_load(G,nodes=None,cutoff=False): """Compute edge load. WARNING: This module is for demonstration and testing purposes. """ betweenness={} if not nodes: # find betweenness for every node in graph nodes=G.nodes() # that probably is what you want... for source in nodes: ubetween=_edge_betweenness(G,source,nodes,cutoff=cutoff) for v in ubetween.keys(): b=betweenness.setdefault(v,0) # get or set default betweenness[v]=ubetween[v]+b # cumulative total return betweenness
def _edge_betweenness(G,source,nodes,cutoff=False): """ Edge betweenness helper. """ between={} # get the predecessor data #(pred,length)=_fast_predecessor(G,source,cutoff=cutoff) (pred,length)=nx.predecessor(G,source,cutoff=cutoff,return_seen=True) # order the nodes by path length onodes = [ nn for dd,nn in sorted( (dist,n) for n,dist in length.items() )] # intialize betweenness, doesn't account for any edge weights 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: num_paths=len(pred[v]) # Discount betweenness if more than for w in pred[v]: # one shortest path. if w in pred: num_paths=len(pred[w]) # Discount betweenness, mult path for x in pred[w]: between[(w,x)]+=between[(v,w)]/num_paths between[(x,w)]+=between[(w,v)]/num_paths return between