betweenness centrality计算公式

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 $v\in s,t$,$\sigma (s,t|v)=0$