Modularities maximization in multiplex network analysis using Many-Objective Optimization

Nowadays, social network analysis receives big attention from academia, industries and governments. Some practical applications such as community detection and centrality in economic networks have become main issues in this research area. Community detection algorithm for complex network analysis is mainly accomplished by the Louvain Method that seeks to find communities by heuristically finding a partitioning with maximal modularity. Traditionally, community detection applied for a network that has homogeneous semantics, for instance indicating friend relationship between people or import-export relationships between countries etc. However we increasingly deal with more complex network and also with so-called multiplex networks. In a multiplex network the set of nodes stays the same, while there are multiple sets of edges. In the analysis we would like to identify communities, but different edge sets give rise to different modularity optimizing partitions into communities. We propose to view community detection of such multilayer networks as a many-objective optimization problem. For this apply Evolutionary Many Objective Optimization and compute the Pareto fronts between different modularity layers. Then we group the objective functions into community in order to better understand the relationship and dependence between different layers (conflict, indifference, complementarily). As a case study, we compute the Pareto fronts for model problems and for economic data sets in order to show how to find the network modularity tradeoffs between different layers.