Approximating betweenness centrality

  • Authors:
  • David A. Bader;Shiva Kintali;Kamesh Madduri;Milena Mihail

  • Affiliations:
  • College of Computing, Georgia Institute of Technology;College of Computing, Georgia Institute of Technology;College of Computing, Georgia Institute of Technology;College of Computing, Georgia Institute of Technology

  • Venue:
  • WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
  • Year:
  • 2007

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Abstract

Betweenness is a centrality measure based on shortest paths, widely used in complex network analysis. It is computationally-expensive to exactly determine betweenness; currently the fastest-known algorithm by Brandes requires O(nm) time for unweighted graphs and O(nm + n2 log n) time for weighted graphs, where n is the number of vertices and m is the number of edges in the network. These are also the worstcase time bounds for computing the betweenness score of a single vertex. In this paper, we present a novel approximation algorithm for computing betweenness centrality of a given vertex, for both weighted and unweighted graphs. Our approximation algorithm is based on an adaptive sampling technique that significantly reduces the number of single-source shortest path computations for vertices with high centrality. We conduct an extensive experimental study on real-world graph instances, and observe that our random sampling algorithm gives very good betweenness approximations for biological networks, road networks and web crawls.