Community detection using multilayer edge mixture model

Abstract

A wide range of complex systems can be modeled as networks with corresponding constraints on the edges and nodes, which have been extensively studied in recent years. Nowadays, with the progress of information technology, systems that contain the information collected from multiple perspectives have been generated. The conventional models designed for single perspective networks fail to depict the diverse topological properties of such systems, so multilayer network models aiming at describing the structure of these networks emerge. As a major concern in network science, decomposing the networks into communities, which usually refers to closely interconnected node groups, extracts valuable information about the structure and interactions of the network. Unlike the contention of dozens of models and methods in conventional single-layer networks, methods aiming at discovering the communities in the multilayer networks are still limited. In order to help explore the community structure in multilayer networks, we propose the multilayer edge mixture model, which explores a relatively general form of a community structure evaluator from an edge combination view. As an example, we demonstrate that the multilayer modularity and stochastic blockmodels can be derived from the proposed model. We also explore the decomposition of community structure evaluators with specific forms to the multilayer edge mixture model representation, which turns out to reveal some new interpretation of the evaluators. The flexibility and performance on different networks of the proposed model are illustrated with applications on a series of benchmark networks.

GHOC: A generative model for hybrid‐order community detection

“…Several variants have been developed by regarding modularity as a basic component or extending it to more general cases. 15,20,21 Another typical community detection method is stochastic block model, 22 which is a random graph model with planted communities. In addition, the generative models have been developed for community detection, 17,23 in which the community membership strength vectors are utilized to represent the community structure.…”

“…One of the most widely adopted methods is modularity, 19 which partitions a network by maximizing the sum of the number of within‐community edges compared with the sum of the expected number of within‐community edges. Several variants have been developed by regarding modularity as a basic component or extending it to more general cases 15,20,21 . Another typical community detection method is stochastic block model, 22 which is a random graph model with planted communities.…”

Motif-based community detection in heterogeneous multilayer networks

“…Most of the current research on the community structure of multilayer networks is based on multiplexing networks, in which the community refers to the structure consisting of homogeneous nodes that are all more tightly connected in different layers 11 . Community detection on multilayer networks is usually implemented based on three methods: the algorithms based on modularity optimization 26 – 28 , network layer aggregation-based algorithms 29 , 30 , and dynamics-based algorithms 31 , 32 , among which modularity is the most widely used 4 , 33 . In 2010, Mucha et al 26 summarized the previous studies to obtain a modularity function for multilayer networks.…”

“…In 2018, Pamfil et al 27 obtained various types of multilayer networks and demonstrated its effectiveness in synthetic and empirical networks. In 2019, Zhang et al 28 proposed a multilayer edge mixture model, and identifies different communities. Although the existing research on community detection of multiplexing networks has been relatively mature, it does not take into account the heterogeneity of nodes.…”