# Community Detection with Dependent Connectivity

## TL;DR

This paper introduces a new community detection method that models dependent connectivities within communities, improving accuracy over traditional models by capturing edge correlations without requiring likelihood specification.

## Contribution

It proposes a novel approach using Bahadur representation to incorporate within-community edge dependence, addressing limitations of existing models like SBM.

## Key findings

- The method reduces estimation bias.
- It accelerates convergence of algorithms.
- It outperforms variational EM in simulations.

## Abstract

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 within-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 lower estimation bias and accelerate algorithm convergence. Our simulation studies show that the proposed algorithm outperforms the popular variational EM algorithm assuming conditional independence among edges. We also demonstrate the application of the proposed method to agricultural product trading networks from different countries.