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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

• 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 of nodes with centrality as the value.

Return type

dictionary

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