Consistent Community Detection in Inter-Layer Dependent Multi-Layer Networks

Abstract

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 article, 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. Supplementary materials for this article are available online.

Keywords:

• Community detection
• Ising model
• Multi-layer network
• Pseudo-likelihood
• Stochastic block model

Supplementary Materials

Supplementary materials contain more explanations mentioned in the paper and the technical proofs of all lemmas.

Acknowledgments

The authors thank the Editor, Associate Editor, and the anonymous reviewers.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Jingnan Zhang’s research is supported in part by “USTC Research Funds of the Double First-Class Initiative” YD2040002020, Junhui Wang’s research is supported in part by HK RGC Grants GRF-11301521, GRF-11311022, GRF-14306523, and CUHK Startup Grant 4937091, and Xueqin Wang’s research is supported in part by National Natural Science Foundation of China grants No.12231017 and 72171216.