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Fuzzy modularity and fuzzy community structure in networks

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  • Jian Liu

Abstract

To find the fuzzy community structure in a complex network, in which each node has a certain probability of belonging to a certain community, is a hard problem and not yet satisfactorily solved over the past years. In this paper, an extension of modularity, the fuzzy modularity is proposed, which can provide a measure of goodness for the fuzzy community structure in networks. The simulated annealing strategy is used to maximize the fuzzy modularity function, associating with an alternating iteration based on our previous work. The proposed algorithm can efficiently identify the probabilities of each node belonging to different communities with random initial fuzzy partition during the cooling process. An appropriate number of communities can be automatically determined without any prior knowledge about the community structure. The computational results on several artificial and real-world networks confirm the capability of the algorithm. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

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  • 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.
    • Handle: RePEc:spr:eurphb:v:77:y:2010:i:4:p:547-557
    DOI: 10.1140/epjb/e2010-00290-3
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    Cited by:

    1. 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.

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