An Efficient Local Search Approach for Polarized Community Discovery in Signed Networks

TL;DR

This paper introduces a scalable local search algorithm for polarized community detection in signed networks, effectively handling neutral vertices and avoiding size imbalance, with proven convergence and superior performance.

Contribution

It presents the first local search method for polarized community detection that includes neutral vertices and guarantees linear convergence, improving over prior approaches.

Findings

Outperforms state-of-the-art baselines in solution quality

Maintains competitive computational efficiency

Successfully handles large real-world and synthetic networks

Abstract

Signed networks, where edges are labeled as positive or negative to represent friendly or antagonistic interactions, provide a natural framework for analyzing polarization, trust, and conflict in social systems. Detecting meaningful group structures in such networks is crucial for understanding online discourse, political divisions, and trust dynamics. A key challenge is to identify communities that are internally cohesive and externally antagonistic, while allowing for neutral or unaligned vertices. In this paper, we propose a method for identifying $k$ polarized communities that addresses a major limitation of prior methods: their tendency to produce highly size-imbalanced solutions. We introduce a novel optimization objective that avoids such imbalance. In addition, it is well known that approximation algorithms based on local search are highly effective for clustering signed networks when neutral vertices are not allowed. We build on this idea and design the first local search algorithm that extends to the setting with neutral vertices while scaling to large networks. By connecting our approach to block-coordinate Frank-Wolfe optimization, we prove a linear convergence rate, enabled by the structure of our objective. Experiments on real-world and synthetic datasets demonstrate that our method consistently outperforms state-of-the-art baselines in solution quality, while remaining competitive in computational efficiency.