edge_betweenness_centrality(G, k=None, normalized=True, weight=None, seed=None)¶
Compute betweenness centrality for edges.
Betweenness centrality of an edge is the sum of the fraction of all-pairs shortest paths that pass through :
where is the set of nodes,`sigma(s, t)` is the number of shortest -paths, and is the number of those paths passing through edge .
- G (graph) – A NetworkX graph
- k (int, optional (default=None)) – If k is not None use k node samples to estimate betweenness. The value of k <= n where n is the number of nodes in the graph. Higher values give better approximation.
- normalized (bool, optional) – If True the betweenness values are normalized by for graphs, and for directed graphs where is the number of nodes in G.
- weight (None or string, optional) – If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight.
edges – Dictionary of edges with betweenness centrality as the value.
The algorithm is from Ulrik Brandes .
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.
 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  Ulrik Brandes: On Variants of Shortest-Path Betweenness Centrality and their Generic Computation. Social Networks 30(2):136-145, 2008. http://www.inf.uni-konstanz.de/algo/publications/b-vspbc-08.pdf