Covariate-assisted community detection in multi-layer networks

Communities in multi-layer networks consist of nodes with similar connectivity patterns across all layers. This article proposes a tensor-based community detection method in multi-layer networks, which leverages available node-wise covariates to improve community detection accuracy. This is motivated by the network homophily principle, which suggests that nodes with similar covariates tend to reside in the same community. To take advantage of the node-wise covariates, the proposed method augments the multi-layer network with an additional layer constructed from the node similarity matrix with proper scaling, and conducts a Tucker decomposition of the augmented multi-layer network, yielding the spectral embedding vector of each node for community detection. Asymptotic consistencies of the proposed method in terms of community detection are established, which are also supported by numerical experiments on various synthetic networks and two real-life multi-layer networks.