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On the radius of centrality in evolving communication networks

Author

Listed:
  • Danica Vukadinović Greetham

    (University of Reading)

  • Zhivko Stoyanov

    (University of Reading)

  • Peter Grindrod

    (University of Oxford, Andrew Wiles Building)

Abstract

In this article, we investigate how the choice of the attenuation factor in an extended version of Katz centrality influences the centrality of the nodes in evolving communication networks. For given snapshots of a network, observed over a period of time, recently developed communicability indices aim to identify the best broadcasters and listeners (receivers) in the network. Here we explore the attenuation factor constraint, in relation to the spectral radius (the largest eigenvalue) of the network at any point in time and its computation in the case of large networks. We compare three different communicability measures: standard, exponential, and relaxed (where the spectral radius bound on the attenuation factor is relaxed and the adjacency matrix is normalised, in order to maintain the convergence of the measure). Furthermore, using a vitality-based measure of both standard and relaxed communicability indices, we look at the ways of establishing the most important individuals for broadcasting and receiving of messages related to community bridging roles. We compare those measures with the scores produced by an iterative version of the PageRank algorithm and illustrate our findings with three examples of real-life evolving networks: the MIT reality mining data set, consisting of daily communications between 106 individuals over the period of 1 year, a UK Twitter mentions network, constructed from the direct tweets between $$12.4$$ 12.4 k individuals during 1 week, and a subset of the Enron email data set.

Suggested Citation

  • Danica Vukadinović Greetham & Zhivko Stoyanov & Peter Grindrod, 2014. "On the radius of centrality in evolving communication networks," Journal of Combinatorial Optimization, Springer, vol. 28(3), pages 540-560, October.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:3:d:10.1007_s10878-014-9726-0
    DOI: 10.1007/s10878-014-9726-0
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    References listed on IDEAS

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    1. Jamakovic, A. & Kooij, R.E. & van Mieghem, P. & van Dam, E.R., 2006. "Robustness of networks against viruses : The role of the spectral raduis," Other publications TiSEM 1b372c5c-dc77-45bd-824d-3, Tilburg University, School of Economics and Management.
    2. Anurat Chapanond & Mukkai S. Krishnamoorthy & Bülent Yener, 2005. "Graph Theoretic and Spectral Analysis of Enron Email Data," Computational and Mathematical Organization Theory, Springer, vol. 11(3), pages 265-281, October.
    3. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
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