edge_betweenness_centrality¶

edge_betweenness_centrality(G, normalized=True, weight=None)[source]¶

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 $e$ [R189].

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.

Returns:

edges : dictionary

Dictionary of edges with betweenness centrality as the value.