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κBetweenness Centrality (BoundedDistance Betweenness)Definition
κbetweenness centrality is given by:
For an arbitrary graph G(V,E), let d(s, t) denote
the length of the shortest path between vertices s and t. Define σ_{stk} to be the number of paths between s and t whose
length is less than or equal to d(s, t) + κ. Likewise, σ_{st}(v)
is the count of the subset of paths that pass through vertex v.
This definition of κbetweenness centrality subsumes Freeman’s definition of betweenness centrality for κ = 0. SoftwareReferences
