networkx.algorithms.centrality.betweenness.betweenness_centrality

betweenness_centrality(G, normalized=True, weighted_edges=False, endpoints=False)

Compute betweenness centrality for nodes.

Betweenness 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.

weighted_edges : bool, optional

Consider the edge weights in determining the shortest paths. The edge weights must be greater than zero. If False, all edge weights are considered equal.

Returns:

nodes : dictionary

Dictionary of nodes with betweenness centrality as the value.

See also

edge_betweenness_centrality, load_centrality

Notes

The algorithm is from Ulrik Brandes [R35].

For weighted graphs the edge weights must be greater than zero. Zero edge weights can produce an infinite number of equal length paths between pairs of nodes.

References

[R35]

(1, 2) A Faster Algorithm for Betweenness Centrality. Ulrik Brandes, Journal of Mathematical Sociology 25(2):163-177, 2001. http://www.inf.uni-konstanz.de/algo/publications/b-fabc-01.pdf