Community detection in heterogeneous signed networks

TL;DR

This paper introduces a new statistical model for detecting communities in signed networks with positive and negative edges, addressing a gap in network analysis methods for such data.

Contribution

It proposes a signed block β-model capable of modeling both strong and weak balance in signed networks, with proven identifiability and consistency.

Findings

Model effectively captures signed network structures

Algorithm demonstrates efficient convergence and accuracy

Real-world application validates practical utility

Abstract

Network data has attracted growing interest across scientific domains, prompting the development of various network models. Existing network analysis methods mainly focus on unsigned networks, whereas signed networks, consisting of both positive and negative edges, have been frequently encountered in practice but much less investigated. In this paper, we formally define strong and weak balance in signed networks, and propose a signed block $\beta$-model, which is capable of modeling strong- and weak-balanced signed networks simultaneously. We establish the identifiability of the proposed model by leveraging properties of bipartite graphs, and develop an efficient alternating updating algorithm to optimize the resulting log-likelihood function. More importantly, we establish the asymptotic consistencies of the proposed model in terms of both probability estimation and community detection. Its advantages are also demonstrated through extensive numerical experiments and the application to a real-world international relationship network.