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Modularity maximization using completely positive programming

Author

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  • Yazdanparast, Sakineh
  • Havens, Timothy C.

Abstract

Community detection is one of the most prominent problems of social network analysis. In this paper, a novel method for Modularity Maximization (MM) for community detection is presented which exploits the Alternating Direction Augmented Lagrangian (ADAL) method for maximizing a generalized form of Newman’s modularity function. We first transform Newman’s modularity function into a quadratic program and then use Completely Positive Programming (CPP) to map the quadratic program to a linear program, which provides the globally optimal maximum modularity partition. In order to solve the proposed CPP problem, a closed form solution using the ADAL merged with a rank minimization approach is proposed. The performance of the proposed method is evaluated on several real-world data sets used for benchmarks community detection. Simulation results shows the proposed technique provides outstanding results in terms of modularity value for crisp partitions.

Suggested Citation

  • Yazdanparast, Sakineh & Havens, Timothy C., 2017. "Modularity maximization using completely positive programming," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 20-32.
    • Handle: RePEc:eee:phsmap:v:471:y:2017:i:c:p:20-32
    DOI: 10.1016/j.physa.2016.11.108
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    References listed on IDEAS

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    1. Pablo M. Gleiser & Leon Danon, 2003. "Community Structure In Jazz," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 565-573.
    2. G. Agarwal & D. Kempe, 2008. "Modularity-maximizing graph communities via mathematical programming," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 66(3), pages 409-418, December.
    3. Jian Liu, 2010. "Fuzzy modularity and fuzzy community structure in networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 77(4), pages 547-557, October.
    4. Jiang, Yawen & Jia, Caiyan & Yu, Jian, 2013. "An efficient community detection method based on rank centrality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2182-2194.
    5. Gong, Maoguo & Liu, Jie & Ma, Lijia & Cai, Qing & Jiao, Licheng, 2014. "Novel heuristic density-based method for community detection in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 71-84.
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