Betweenness Centrality – Incremental and Faster

  • Meghana Nasre
  • Matteo Pontecorvi
  • Vijaya Ramachandran
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8635)

Abstract

We present an incremental algorithm that updates the betweenness centrality (BC) score of all vertices in a graph G when a new edge is added to G, or the weight of an existing edge is reduced. Our incremental algorithm runs in O(v * · n) time, where v * is bounded by m *, the number of edges that lie on a shortest path in G. We achieve the same bound for the more general incremental vertex update problem. Even for a single edge update, our incremental algorithm is the first algorithm that is provably faster on sparse graphs than recomputing with the well-known static Brandes algorithm. It is also likely to be much faster than Brandes on dense graphs since m * is often close to linear in n. Our incremental algorithm is very simple, and we give an efficient cache-oblivious implementation that incurs O(n · sort(v *)) cache misses, where sort is a well-known measure for caching efficiency.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Meghana Nasre
    • 1
  • Matteo Pontecorvi
    • 2
  • Vijaya Ramachandran
    • 2
  1. 1.Indian Institute of Technology MadrasIndia
  2. 2.University of Texas at AustinUSA

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