Betweenness centrality of a node $v$ is measurement of how likely the shortest path between two nodes $u_s$ and $u_t$ is gonna pass through node $v$,

$$c(v) = \sum_{v\neq u_s\neq u_t} \frac{\sigma_{u_su_t}(v) }{\sigma_{u_su_t}},$$

where $\sigma_{u_su_t}(v)$ is the number of shortest path between $u_s$ and $u_t$, and passing through $u$, while $\sigma_{u_su_t}$ is the number of shortest path between $u_s$ and $u_t$.

A figure from wikipedia demonstrates this idea well. The nodes on the outreach have smaller betweenness centrality, while the nodes in the core have higher betweenness centrality.

Outreach and Core

It is almost like cheating using the work “outreach” and “core” here. They are somewhat defined by betweenness centrality.

Planted: by ;

L Ma (2021). 'Betweenness Centrality of a Graph', Datumorphism, 09 April. Available at: https://datumorphism.leima.is/cards/graph/graph-betweenness-centrality/.