Quantitative function for community detection

Zhenping Li, Shihua Zhang, Rui-Sheng Wang, Xiang-Sun Zhang, and Luonan Chen

Phys. Rev. E 77, 036109 – Published 10 March 2008; Erratum Phys. Rev. E 91, 019901 (2015)

Abstract

We propose a quantitative function for community partition—i.e., modularity density or $D$ value. We demonstrate that this quantitative function is superior to the widely used modularity $Q$ and also prove its equivalence with the objective function of the kernel $k$ means. Both theoretical and numerical results show that optimizing the new criterion not only can resolve detailed modules that existing approaches cannot achieve, but also can correctly identify the number of communities.

Received 6 October 2007

DOI:https://doi.org/10.1103/PhysRevE.77.036109

Erratum

Erratum: Quantitative function for community detection [Phys. Rev. E 77, 036109 (2008)]

Zhenping Li, Shihua Zhang, Rui-Sheng Wang, Xiang-Sun Zhang, and Luonan Chen

Phys. Rev. E 91, 019901 (2015)

Authors & Affiliations

Zhenping Li^1,2,*, Shihua Zhang^2,3,*, Rui-Sheng Wang⁴, Xiang-Sun Zhang^2,†, and Luonan Chen^5,6,†

¹Beijing Wuzi University, Beijing 101149, China
²Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
³Graduate University of Chinese Academy of Sciences, Beijing 100049, China
⁴School of Information, Renmin University of China, Beijing 100872, China
⁵Institute of Systems Biology, Shanghai University, Shanghai 200444, China
⁶Department of Electrical Engineering and Electronics, Osaka Sangyo University, Osaka 574-8530, Japan

^*The first two authors contributed equally to this paper.
^†Corresponding authors.

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Issue

Vol. 77, Iss. 3 — March 2008

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics