Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

networkx.algorithms.centrality.load_centrality

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
Ggraph

A networkx graph.

normalizedbool, 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.

weightNone or string, optional (default=None)

If None, edge weights are ignored. Otherwise holds the name of the edge attribute used as weight. The weight of an edge is treated as the length or distance between the two sides.

cutoffbool, optional (default=None)

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

Returns
nodesdictionary

Dictionary of nodes with centrality as the value.

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