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.

翻译：多层网络中的社区检测旨在识别出在多个网络层中展现出相似连接模式的节点群组，近年来引起了广泛关注。现有方法大多基于不同网络层相互独立或遵循特定依赖结构、且同一层内边独立的假设。本文提出了一种新颖的多层网络社区检测方法，能够处理广泛的层间与层内依赖结构。该方法将用于社区检测的多层随机块模型与多元概率模型相结合，以捕捉层间依赖结构，同时允许层内依赖的存在。为便于参数估计，我们开发了一种约束成对似然方法，并结合高效的交替更新算法。本文还建立了所提方法的渐近性质，重点考察了层间与层内依赖对参数估计和社区检测精度的影响。理论结果通过模拟网络和真实世界多层贸易网络上的大量数值实验得到了验证。