Betweenness Centrality: Difference between revisions
(Created page with "{{DISPLAYTITLE: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...") |
No edit summary |
||
| Line 12: | Line 12: | ||
== Parameters == | == Parameters == | ||
n: number of nodes | |||
m: number of edges | |||
m: number of edges | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Currently no algorithms in our database for the given problem. | Currently no algorithms in our database for the given problem. | ||
Revision as of 12:04, 15 February 2023
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.