Brandes.betweenness.centrality
computes the betweenness centrality of
each vertex or each edge in the graph, using an algorithm by U. Brandes.Betweenness centrality of a vertex v
is calculated as follows:
N_st(v)
= no. of shortest paths from s
to t
that pass through v
,
N_st
= no. of shortest paths from s
to t
,
betweenness centrality of v
= sum(N_st(v)/N_st)
for all vertices s
!= v
!= t
.
Betweenness centrality of an edge is calculated similarly.
The relative betweenness centrality for a vertex is to scale the betweenness
centrality of the given vertex by 2/(n**2 - 3n + 2)
where n
is
the no. of vertices in the graph.
Central point dominance measures the maximum betweenness of any vertex
in the graph.
See documentation on brandes betweenness centrality in Boost Graph Library
for more details.