Betweenness

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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.

Contents

[edit] Definition

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

C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}

where σst is the number of shortest geodesic paths from s to t, and σst(v) the number of shortest geodesic paths from s to t that pass through a vertex v. This may be normalised by dividing through by the number of pairs of vertices not including v, which is (n − 1)(n − 2).

[edit] See also

[edit] References

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

[edit] External links

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