Multilayer overlapping community detection using multi-objective optimization

Abstract Community detection in multilayer networks such as social or information networks, due to its vast practical applications has attracted many attentions in the past years. Although some researches have been done to develop monoplex methods to multilayers, but because of the complexity of multilayer networks they are in their infancy. In this study, initially, the definition of community in single layer networks is extended and a new definition for multilayer community is presented. Then, regarding the importance of overlapping communities in real networks, a comprehensive definition for overlapping multilayer community is presented. Furthermore, in order to address the problem of multilayer community detection, a two-phase approach has been adopted. In the first phase, a multi-objective mathematical model is developed, and optimized using a genetic algorithm based method (NSGA-II) to achieve a set of solutions (Pareto front). Each potential solution represents a partition of the multilayer network. In the second phase, the best solution is chosen from the Pareto fronts, using a novel algorithm. This proposed algorithm, handles the obstacles of genetic representation and is able to detect the optimal multilayer overlapping communities. Experiments on both synthetic mLFR networks with different parameters and six real data networks show the performance of the algorithm in terms of NMI and multilayer modularity.

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