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Identifying high betweenness centrality nodes in large social networks

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Abstract

This paper proposes an alternative way to identify nodes with high betweenness centrality. It introduces a new metric, κ-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high κ-path centrality have high node betweenness centrality. The randomized algorithm runs in time O(κ3 n 2−2αlog n) and outputs, for each vertex v, an estimate of its κ-path centrality up to additive error of ±n 1/2+α with probability 1 − 1/n 2. Experimental evaluations on real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared with existing randomized algorithms.

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Notes

  1. The Hoeffding bound (Hoeffding 1963), a classical result in probability theory, states the following: Let \(X_{1}, X_{2}, \ldots, X_{T}\) be independent random variables, such that each X i ranges over the real interval [a i , b i ], and let \(\mu = E[\sum\nolimits_{i=1}^{T} X_{i}/{T}]\) denote the expected value of the average of these variables. Then, for every ξ > 0, \({\rm \hbox{Pr}}[|\frac{\sum_{i=1}^{T} X_{i}}{T} - \mu| \geq \xi] \leq 2e^{-2T^{2}\xi^{2}/\sum_{i=1}^{T} (b_{i} - a_{i})^{2}}. \)

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Acknowledgments

This research was partially supported by the National Science Foundation under Grants No. CNS-0831785 and CNS-0952420. The authors would also like to acknowledge the use of the computing services provided by Research Computing, University of South Florida.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of South Florida, Tampa, FL, USA

    Nicolas Kourtellis, Adriana Iamnitchi & Rahul Tripathi

  2. 2056 Pinnacle Pointe Drive, Norcross, GA, 30071, USA

    Tharaka Alahakoon

  3. Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, USA

    Ramanuja Simha

Authors
  1. Nicolas Kourtellis
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  2. Tharaka Alahakoon
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  3. Ramanuja Simha
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  4. Adriana Iamnitchi
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  5. Rahul Tripathi
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Correspondence to Nicolas Kourtellis.

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Kourtellis, N., Alahakoon, T., Simha, R. et al. Identifying high betweenness centrality nodes in large social networks. Soc. Netw. Anal. Min. 3, 899–914 (2013). https://doi.org/10.1007/s13278-012-0076-6

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