Eur. Phys. J. B (2018) 91: 145
https://doi.org/10.1140/epjb/e2018-90064-2

Regular Article

Constructing null networks for community detection in complex networks

¹ College of Information and Communication Engineering, Dalian Minzu University, Dalian 116600, P.R. China
² Guizhou Provincial Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, P.R. China
³ Computational Communication Collaboratory, School of Journalism and Communication, Nanjing University, Nanjing 210093, P.R. China

^a e-mail: xuxiaoke@foxmail.com

Received: 9 February 2018
Received in final form: 27 April 2018
Published online: 4 July 2018

Abstract

Communities are virtually ubiquitous in real-world networks, and the statistic of modularity index Q is the classical measurement for community detection algorithms. However, the relationship between the modularity property and network multilever micro-scale structures is still not clear. In this paper, we study community detection results both in artificial and real-life complex networks by constructing different order null networks, and the results uncover that how micro-structures (such as degree distribution, assortativity and clustering coefficient) affect community properties. Meanwhile, we also propose two novel null networks (increasing or decreasing community structures) to verify the robustness of different community detection algorithms. Our results indicate that the modularity index Q is not a suitable statistic to measure the weak community property which is widely available in empirical networks. Our findings can not only be used to test the robustness of different community detection methods, but also be helpful to uncover the correlation of network structures between microcosmic and mesoscopic scales.