A Multi-Objective Community Detection Algorithm for Directed Network Based on Random Walk

Uncovering community structure is an important technique for studying complex networks. While a large bulk of algorithms have been proposed for community detection in recent years, most of them were designed for undirected networks. Considering many real-world networks are by nature directed, it is necessary to develop community detection methods that can handle directed networks. In this work, we formulates a multi-objective framework for community detection in directed networks and proposes a multi-objective evolutionary algorithm for finding efficient solutions under this framework. Specifically, based on the theory that an efficient partition of directed networks should have larger network information flow within the community than that between different communities, we first designed two conflicting objective functions based on PageRank random walk, one of which is to maximize within-community transition probability, and the other is to minimize between-community transition probability. By optimizing these two objectives simultaneously, we modelled the problem of community detection as a multi-objective optimization problem, and then developed a novel multi-objective evolutionary algorithm to solve it. Particularly, to guarantee the capability of searching the optimal solution, our proposed method designed/adopted the directed-network-specific population initialization method and evolutionary operator by introducing label propagation algorithm into multi-objective genetic algorithm. Comparison with other four art-of-the-state algorithms, our method showed the competitive performance on both synthetic and real-world networks. Moreover, attributing to the multi-objective framework, the proposed method could generate multiple optimal network partitions in a single run, which provides a hierarchical description of community structure of the network.