networkx.algorithms.centrality.betweenness_centrality¶

networkx.algorithms.centrality.betweenness_centrality(G, normalized=True, weight=None, 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 $v \in {s, t}$ , $\sigma(s, t|v) = 0$ [R87].

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.

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.

Previous topic

Next topic

networkx.algorithms.centrality.betweenness_centrality¶

Navigation

Previous topic

Next topic

Quick search

networkx.algorithms.centrality.betweenness_centrality¶

Navigation