networkx.algorithms.load_centrality

networkx.algorithms.load_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

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.

Returns:

nodes : dictionary

Dictionary of nodes with centrality as the value.

Notes

Load centrality is slightly different than betweenness. It was originally introduced by [R768]. For this load algorithm see [R767].

References

[R767](1, 2) 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
[R768](1, 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