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

\sigma_{st}(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.

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Betweenness

Definition

See also

References