Consistent community detection in inter-layer dependent multi-layer networks

Community detection in multi-layer networks, which aims at finding groups of nodes with similar connective patterns among all layers, has attracted tremendous interests in multi-layer network analysis. Most existing methods are extended from those for single-layer networks, which assume that different layers are independent. In this paper, we propose a novel community detection method in multi-layer networks with inter-layer dependence, which integrates the stochastic block model (SBM) and the Ising model. The community structure is modeled by the SBM model and the inter-layer dependence is incorporated via the Ising model. An efficient alternative updating algorithm is developed to tackle the resultant optimization task. Moreover, the asymptotic consistencies of the proposed method in terms of both parameter estimation and community detection are established, which are supported by extensive simulated examples and a real example on a multi-layer malaria parasite gene network.