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κ-Betweenness Centrality (Bounded-Distance Betweenness)


Definition

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

Software

References

  • Borgatti, S.P. and Everett, M.G., 2006. A graph-theoretic perspective on centrality. Social networks, 28(4), pp.466-484.
  • JIANG, K., EDIGER, D. & BADER, D. A. Generalizing k-Betweenness centrality using short paths and a parallel multithreaded implementation. Parallel Processing, 2009. ICPP'09. International Conference on, 2009. IEEE, 542-549.


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