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Z-Score-Based Modularity for Community Detection in Networks

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  • Atsushi Miyauchi
  • Yasushi Kawase

Abstract

Identifying community structure in networks is an issue of particular interest in network science. The modularity introduced by Newman and Girvan is the most popular quality function for community detection in networks. In this study, we identify a problem in the concept of modularity and suggest a solution to overcome this problem. Specifically, we obtain a new quality function for community detection. We refer to the function as Z-modularity because it measures the Z-score of a given partition with respect to the fraction of the number of edges within communities. Our theoretical analysis shows that Z-modularity mitigates the resolution limit of the original modularity in certain cases. Computational experiments using both artificial networks and well-known real-world networks demonstrate the validity and reliability of the proposed quality function.

Suggested Citation

  • Atsushi Miyauchi & Yasushi Kawase, 2016. "Z-Score-Based Modularity for Community Detection in Networks," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-17, January.
    • Handle: RePEc:plo:pone00:0147805
    DOI: 10.1371/journal.pone.0147805
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    References listed on IDEAS

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    3. 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.
    4. Sonia Cafieri & Alberto Costa & Pierre Hansen, 2014. "Reformulation of a model for hierarchical divisive graph modularity maximization," Annals of Operations Research, Springer, vol. 222(1), pages 213-226, November.
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    Cited by:

    1. Jiajing Zhu & Yongguo Liu & Changhong Yang & Wen Yang & Zhi Chen & Yun Zhang & Shangming Yang & Xindong Wu, 2018. "A degree-based block model and a local expansion optimization algorithm for anti-community detection in networks," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-25, April.

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