Betweenness Centrality (Vertex Centrality)

Description

Given a graph $G = (V, E)$ and a vertex $v \in V$, calculate the betweenness centrality of vertex $v$ (or the proportion of shortest paths that go through $v$), i.e. $BC(v) := \sum\limits_{s\neq t \neq v \in V} \frac{\sigma_{st}(v)}{\sigma_{st}}$ where $\sigma_{st}(v)$ is the number of shortest paths from $s$ to $t$ that go through $v$ and $\sigma_{st}$ is the number of shortest paths from $s$ to $t$.

Related Problems

Subproblem: Approximate Betweenness Centrality, Positive Betweenness Centrality

Related: Eccentricity, All-Nodes Median Parity, Positive Betweenness Centrality, Directed All-Nodes Positive Betweenness Centrality, Undirected All-Nodes Positive Betweenness Centrality, Reach Centrality, Directed All-Nodes Reach Centrality, Undirected All-Nodes Reach Centrality, Approximate Reach Centrality

Parameters

$n$: number of nodes

$m$: number of edges

Table of Algorithms

Currently no algorithms in our database for the given problem.