Spectral Clustering on Multilayer Networks with Covariates

Abstract: The community detection problem on multilayer networks have drawn much interest. When the nodal covariates ar also present, few work has been done to integrate information from both sources. To leverage the multilayer networks and the covariates, we propose two new algorithms: the spectral clustering on aggregated networks with covariates (SCANC), and the spectral clustering on aggregated Laplacian with covariates (SCALC). These two algorithms are easy to implement, computationally fast, and feature a data-driven approach for tuning parameter selection. We establish theoretical guarantees for both methods under the Multilayer Stochastic Blockmodel with Covariates (MSBM-C), demonstrating their consistency in recovering community structure. Our analysis reveals that increasing the number of layers, incorporating covariate information, and enhancing network density all contribute to improved clustering accuracy. Notably, SCANC is most effective when all layers exhibit similar assortativity, whereas SCALC performs better when both assortative and disassortative layers are present. On the simulation studies and a primary school contact data analysis, our method outperforms other methods. Our results highlight the advantages of spectral-based aggregation techniques in leveraging both network structure and nodal attributes for robust community detection.