On the radius of centrality in evolving communication networks

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 a...

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Bibliographic Details
Published in:Journal of combinatorial optimization 2014-10, Vol.28 (3), p.540-560
Main Authors: Greetham, Danica Vukadinović, Stoyanov, Zhivko, Grindrod, Peter
Format: Article
Language:English
Subjects:
Combinatorics
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
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Summary: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 k individuals during 1 week, and a subset of the Enron email data set.
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-014-9726-0