A Multilayer Probit Network Model for Community Detection with Dependent Edges and Layers

2026-01-14

AI Summary

This work proposes a novel framework that integrates the multilayer stochastic block model with the multivariate probit model to address the limitations of existing community detection methods in multilayer networks, which often rely on restrictive assumptions of independence among intra- or inter-layer edges and thus fail to capture complex dependencies. The proposed approach is the first to jointly model arbitrary dependency structures both within and across layers, thereby overcoming traditional independence constraints. Efficient inference is achieved through a constrained pairwise likelihood estimation procedure combined with an alternating update algorithm. Furthermore, the authors establish asymptotic theory characterizing how dependency structures influence detection accuracy. Both theoretical analysis and empirical evaluations demonstrate that the method significantly improves community detection accuracy on synthetic benchmarks and real-world multilayer trade networks.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Social media analysis through the lenses of networks

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.

Problem

• community detection
• multilayer networks
• dependent edges
• inter-layer dependence
• intra-layer dependence

Innovation

• multilayer network
• community detection
• dependent edges
• multivariate probit model
• stochastic block model