networkx.algorithms.centrality.edge_betweenness_centrality¶

networkx.algorithms.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 $e$ [R93].

Parameters :

G : graph

A NetworkX graph

normalized : bool, optional

If True the betweenness values are normalized by $1/(n-1)(n-2)$ where $n$ is the number of nodes in G.

weight : None, True or string, optional

If None, all edge weights are considered equal. If True, edge attribute ‘weight’ is used as weight of each edge. Otherwise holds the name of the edge attribute used as weight.

Returns :

edges : dictionary

Dictionary of edges with betweenness centrality as the value.

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