load_centrality(G, v=None, cutoff=None, normalized=True, weight=None)

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

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