A Multilayer Probit Network Model for Community Detection with Dependent Edges and Layers
Dapeng Shi, Haoran Zhang, Tiandong Wang, Junhui Wang
TL;DR
This work tackles community detection in multilayer networks by introducing a multilayer probit network model that merges a stochastic block model with a multivariate probit formulation to accommodate general inter-layer and intra-layer dependence. A constrained pairwise likelihood, together with an alternating update algorithm, enables scalable parameter estimation and community recovery, underpinned by Fisher-consistency and comprehensive asymptotic results. Theoretical insights reveal how dependence and sparsity affect estimation and clustering accuracy, and empirical studies—both synthetic and on an international trade network—show that the method consistently outperforms existing approaches, particularly in settings with strong cross-layer or intra-layer dependencies. The proposed approach offers a flexible, theoretically grounded toolkit for detecting coherent community structure in complex multilayer systems with dependent edges.
Abstract
Community detection in multilayer networks, which aims to identify groups of nodes exhibiting similar connectivity patterns across multiple network layers, has attracted considerable attention in recent years. Most existing methods are based on the assumption that different layers are either independent or follow specific dependence structures, and edges within the same layer are independent. In this article, we propose a novel method for community detection in multilayer networks that accounts for a broad range of inter-layer and intra-layer dependence structures. The proposed method integrates the multilayer stochastic block model for community detection with a multivariate probit model to capture the structures of inter-layer dependence, which also allows intra-layer dependence. To facilitate parameter estimation, we develop a constrained pairwise likelihood method coupled with an efficient alternating updating algorithm. The asymptotic properties of the proposed method are also established, with a focus on examining the influence of inter-layer and intra-layer dependences on the accuracy of both parameter estimation and community detection. The theoretical results are supported by extensive numerical experiments on both simulated networks and a real-world multilayer trade network.