Community detection using multilayer edge mixture model

Multilayer networks are networks where edges exist in multiple layers that encode different types or sources of interactions. As one of the most important problems in network science, discovering the underlying community structure in multilayer networks has received an increasing amount of attention in recent years. One of the challenging issues is to develop effective community structure quality functions for characterizing the structural or functional properties of the expected community structure. Although several quality functions have been developed for evaluating the detected community structure, little has been explored about how to explicitly bring our knowledge of the desired community structure into such quality functions, in particular for the multilayer networks. To address this issue, we propose the multilayer edge mixture model (MEMM), which is positioned as a general framework that enables us to design a quality function that reflects our knowledge about the desired community structure. The proposed model is based on a mixture of the edges, and the weights reflect their role in the detection process. By decomposing a community structure quality function into the form of MEMM, it becomes clear which type of community structure will be discovered by such quality function. Similarly, after such decomposition we can also modify the weights of the edges to find the desired community structure. In this paper, we apply the quality functions modified with the knowledge of MEMM to different multilayer benchmark networks as well as real-world multilayer networks and the detection results confirm the feasibility of MEMM.