# edge_betweenness_centrality¶

edge_betweenness_centrality(G, normalized=True, weight=None)

Compute betweenness centrality for edges.

Betweenness centrality of an edge $$e$$ is the sum of the fraction of all-pairs shortest paths that pass through $$e$$:

$c_B(v) =\sum_{s,t \in V} \frac{\sigma(s, t|e)}{\sigma(s, t)}$

where $$V$$ is the set of nodes,sigma(s, t) is the number of shortest $$(s, t)$$-paths, and $$\sigma(s, t|e)$$ is the number of those paths passing through edge $$e$$ [R186].

Parameters : G : graph A NetworkX graph normalized : bool, optional If True the betweenness values are normalized by $$2/(n(n-1))$$ for graphs, and $$1/(n(n-1))$$ for directed graphs where $$n$$ 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 Dictionary of edges with betweenness centrality as the value.