networkx.algorithms.centrality.betweenness_centrality¶

networkx.algorithms.centrality.betweenness_centrality(G, normalized=True, weighted_edges=False, endpoints=False)¶

Compute the shortest-path betweenness centrality for nodes.

Betweenness centrality of a node $v$ is the sum of the fraction of all-pairs shortest paths that pass through $v$ :

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

where $V$ is the set of nodes, $\sigma(s, t)$ is the number of shortest $(s, t)$ -paths, and $\sigma(s, t|v)$ is the number of those paths passing through some node $v$ other than $s, t$ . If $s = t$ , $\sigma(s, t) = 1$ , and if $v \in {s, t}$ , $\sigma(s, t|v) = 0$ [R53].

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.

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.

endpoints : bool, optional

If True include the endpoints in the shortest path counts.

Returns :

nodes : dictionary

Dictionary of nodes with betweenness centrality as the value.

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