Balanced Stochastic Block Model for Community Detection in Signed Networks

TL;DR

This paper introduces a novel Balanced Stochastic Block Model that integrates structural balance theory into community detection for signed networks, providing a more accurate and theoretically grounded approach.

Contribution

The paper proposes a new BSBM that incorporates balance theory into the generative process and develops a consistent estimation algorithm with provable convergence.

Findings

Estimator achieves strong consistency under weaker conditions

Algorithm demonstrates fast convergence in simulations

Method outperforms existing binary SBM approaches

Abstract

Community detection, discovering the underlying communities within a network from observed connections, is a fundamental problem in network analysis, yet it remains underexplored for signed networks. In signed networks, both edge connection patterns and edge signs are informative, and structural balance theory (e.g., triangles aligned with ``the enemy of my enemy is my friend'' and ``the friend of my friend is my friend'' are more prevalent) provides a global higher-order principle that guides community formation. We propose a Balanced Stochastic Block Model (BSBM), which incorporates balance theory into the network generating process such that balanced triangles are more likely to occur. We develop a fast profile pseudo-likelihood estimation algorithm with provable convergence and establish that our estimator achieves strong consistency under weaker signal conditions than methods for the binary SBM that rely solely on edge connectivity. Extensive simulation studies and two real-world signed networks demonstrate strong empirical performance.