In network analysis, within-community members are more likely to be connected than between-community members, which is reflected in that the edges within a community are intercorrelated. However, existing probabilistic models for community detection such as the stochastic block model (SBM) are not designed to capture the dependence among edges. In this paper, we propose a new community detection approach to incorporate intra-community dependence of connectivities through the Bahadur representation. The proposed method does not require specifying the likelihood function, which could be intractable for correlated binary connectivities. In addition, the proposed method allows for heterogeneity among edges between different communities. In theory, we show that incorporating correlation information can achieve a faster convergence rate compared to the independent SBM, and the proposed algorithm has a lower estimation bias and accelerated convergence compared to the variational EM. Our simulation studies show that the proposed algorithm outperforms the existing multinetwork community detection methods assuming conditional independence among edges. We also demonstrate the application of the proposed method to agricultural product trading networks from different countries and to brain fMRI imaging networks.
The work is supported by NSF grants DMS 1952406 and DMS 1821198.
The authors would like to thank two anonymous referees, the Associate Editor and the Editor for their constructive comments and help feedback that improved the quality of this paper.
"Community detection with dependent connectivity." Ann. Statist. 49 (4) 2378 - 2428, August 2021. https://doi.org/10.1214/20-AOS2042