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Betweenness

Betweenness is a centrality measure of a vertex within a graph. Vertices that occur on many shortest paths between other vertices have higher betweenness than those that do not.

Definition

For a graph $G : = (V, E)$ with n vertices, the betweenness $C B (v)$ for vertex $v$ is:

$C_B(v)= \frac{\sum_{s \neq v \neq t \in V}\sigma_{st}(v)}{(n-1)(n-2)}$

Where $σ s t (v) = 1$ if the shortest path from s to t passes through v and 0 otherwise.

References

Freeman, L. C. (1977) A set of measures of centrality based on betweenness. Sociometry 40, 35--41.

Categories: Graph theory

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03-10-2013 05:06:04
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