From Wikipedia, the free encyclopedia
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
)
{\displaystyle G:=(V,E)}
n vertices, the betweenness
C
B
(
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)
{\displaystyle C_{B}(v)}
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{\displaystyle v}
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{\displaystyle C_{B}(v)={\frac {\sigma _{s\neq v\neq t\in V}(\sigma _{st}(v))}{(n-1)(n-2}}}
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{\displaystyle \sigma _{st}(v)=1<math>iftheshortestpathfrom''s''to''t''passesthrough''v''and0otherwise.Seealso[[graphtheory]]measuresof[[distance(graphtheory)|distance]].==References==Freeman,L.C.(1977)Asetofmeasuresofcentralitybasedonbetweenness.''Sociometry'''''40''',35--41.}
![{\displaystyle \sigma _{st}(v)=1<math>iftheshortestpathfrom''s''to''t''passesthrough''v''and0otherwise.Seealso[[graphtheory]]measuresof[[distance(graphtheory)|distance]].==References==Freeman,L.C.(1977)Asetofmeasuresofcentralitybasedonbetweenness.''Sociometry'''''40''',35--41.}](/media/api/rest_v1/media/math/render/svg/0c2230e824190406f0bb146b44e129b6acbce5b7)