Community detection for multilayer weighted networks

Multilayer networks are used to encode multiple types of relations arising in complex systems and have received significant attention in recent years. Community detection in multilayer networks is an important issue in various fields; hence, stochastic block models have emerged as a popular probabilistic framework over the past decades. However, stochastic block models are suited to binary networks rather than weighted networks. A generalised stochastic block model is proposed herein to address multilayer sparse or dense weighted networks. A variational expectation-maximisation algorithm is derived to estimate the parameters of interest. In addition, an upper bound is derived for the probability of misclassification, which is governed by the Renyi divergence of order 12. Furthermore, our model is compared with four competing methods on synthetic networks. Finally, our approach is examined on financial markets and bicycle sharing systems. (C) 2021 Elsevier Inc. All rights reserved.