Community structure detection based on Potts model and network's spectral characterization

¹ Academy of Mathematics and Systems Science, Chinese Academy of Sciences - Beijing 100190, China
² National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences Beijing 100190, China
³ Key Laboratory of Systems Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences Shanghai 200233, China
⁴ Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, University of Tokyo - Tokyo 153-8505, Japan

^a lnchen@sibs.ac.cn
^b zxs@amt.ac.cn

Received: 15 August 2011
Accepted: 10 January 2012

Abstract

The Potts model was used to uncover community structure in complex networks. However, it could not reveal much important information such as the optimal number of communities and the overlapping nodes hidden in networks effectively. Differently from the previous studies, we established a new framework to study the dynamics of Potts model for community structure detection by using the Markov process, which has a clear mathematic explanation. Based on our framework, we showed that the local uniform behavior of spin values could naturally reveal the hierarchical community structure of a given network. Critical topological information regarding the optimal community structure could also be inferred from spectral signatures of the Markov process. A two-stage algorithm to detect community structure is developed. The effectiveness and efficiency of the algorithm has been theoretically analyzed as well as experimentally validated.