Community Detection and Network Reconstruction With Dependent Connectivity From Rich but Noisy Network Data

ABSTRACT This paper introduces a novel framework for network reconstruction and community detection, addressing two key challenges in network data analysis. One is to utilise rich but noisy data: in network analysis, observations between nodes typically contain substantial noise rather than directly reflecting network structure. Our framework effectively extracts useful information from this noisy data. Another is to consider the dependence on intracommunity connections: networks often exhibit group heterogeneity, where intracommunity members are more interconnected than intercommunity members. This paper integrates dependencies among intracommunity‐connected edges using Bahadur representations. Using a mixture of two latent conditional distributions shared by nodes with the same community label, this paper offers a flexible and interpretable modelling method that introduces a generalised expectation‐maximisation (EM) algorithm for computing approximate maximum likelihood estimates. The proposed approach provides a new network analysis method particularly suited for dealing with noisy data and complex community structures, and outperforms traditional methods in distinguishing similar communities, as validated by numerical simulations and two empirical data studies.