An Efficient Local Search Approach for Polarized Community Discovery in Signed Networks
Linus Aronsson, Morteza Haghir Chehreghani
TL;DR
This work tackles polarized community discovery in signed networks by allowing a neutral vertex set $S_0$ and proposing a CC-based objective $f({\bm{x}})=(N^+_{\text{intra}}-N^-_{\text{intra}}) + \alpha(N^-_{\text{inter}}-N^+_{\text{inter}}) - \beta\sum_{m=1}^k |S_m|^2$, which promotes density while avoiding unbalanced partitions. It develops the first scalable local-search approach for PCD by embedding the problem in a block-coordinate Frank–Wolfe (FW) framework with a relaxed simplex representation, proving an equivalence to discrete local search when starting from a discrete solution and achieving a linear $O(1/t)$ convergence rate. The method, LSPCD, employs efficient gradient computations and a precomputed matrix to reduce per-iteration cost to $O(n)$ (after an initial $O(kn^2)$ setup), enabling large-scale experiments. Empirical results on real and synthetic data show that LSPCD delivers high polarity with balanced cluster sizes and competitive runtimes, providing a practical tool for analyzing polarization and trust dynamics in online and offline social systems.
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.