Identification of multi-resolution network structures with multi-objective immune algorithm

Community structure is one of the most important properties in complex networks, and the field of community detection has received an enormous amount of attention in the past several years. Many quality metrics and methods have been proposed for revealing community structures at multiple resolution levels, while most existing methods need a tunable parameter in their quality metrics to determine the resolution level in advance. In this study, a multi-objective evolutionary algorithm (MOEA) for revealing multi-resolution community structures is proposed. The proposed MOEA-based community detection algorithm aims to find a set of tradeoff solutions which represent network partitions at different resolution levels in a single run. It adopts an efficient multi-objective immune algorithm to simultaneously optimize two contradictory objective functions, Modified Ratio Association and Ratio Cut. The optimization of Modified Ratio Association tends to divide a network into small communities, while the optimization of Ratio Cut tends to divide a network into large communities. The simultaneous optimization of these two contradictory objectives returns a set of tradeoff solutions between the two objectives. Each of these solutions corresponds to a network partition at one resolution level. Experiments on artificial and real-world networks show that the proposed method has the ability to reveal community structures of networks at different resolution levels in a single run. (C) 2013 Elsevier B. V. All rights reserved.