Detecting composite communities in multiplex networks: A multilevel memetic algorithm

Nowadays, many systems can be well represented by multiplex networks, in which entities can communicate with each other on multiple layers. A multiplex network under each layer has its own communities (i.e., a higher-order organization with a group of similar nodes) while it has a composite structure which is most likely to describe its community structures at all layers. Many algorithms have been proposed to detect communities in unweighted single-layered networks, but most of them cannot be well applied to detect composite communities in multiplex networks. The aim of this paper is to detect composite communities in weighted multiplex networks using a multilevel memetic algorithm. First, a simplified multiplex modularity is adopted for evaluating the fitness of composite communities, and then the community detection problem in multiplex networks is modeled as a combinational optimization problem. Second, we devise a multilevel memetic algorithm that combines a network specific genetic algorithm with problem-specific multilevel local search operators. In the presented algorithm, the network-specific knowledge (i.e., the layer neighborhood and the consensus neighborhood) and the problem specific information (i.e., the fast computation of multiplex modularity under each local refinement) are adopted to guide its search processes. Last, extensive experiments are performed on eight real-world networks ranging from social, transport, financial to genetic areas, and the results demonstrate that our algorithm discoveries composite communities in multiplex networks more accurately than the state-of-the-art.