Discovering Polarized Communities in Signed Networks

TL;DR

This paper introduces a novel approach to identify polarized communities in signed networks by formulating the problem as a discrete eigenvector problem, developing spectral algorithms, and validating their effectiveness on real-world data.

Contribution

The paper formulates the polarized community detection as a discrete eigenvector problem and proposes two spectral algorithms with proven quality guarantees.

Findings

Algorithms outperform baselines in quality and speed

Methods scale to large networks

Successfully detect ground-truth polarized communities

Abstract

Signed networks contain edge annotations to indicate whether each interaction is friendly (positive edge) or antagonistic (negative edge). The model is simple but powerful and it can capture novel and interesting structural properties of real-world phenomena. The analysis of signed networks has many applications from modeling discussions in social media, to mining user reviews, and to recommending products in e-commerce sites. In this paper we consider the problem of discovering polarized communities in signed networks. In particular, we search for two communities (subsets of the network vertices) where within communities there are mostly positive edges while across communities there are mostly negative edges. We formulate this novel problem as a "discrete eigenvector" problem, which we show to be NP-hard. We then develop two intuitive spectral algorithms: one deterministic, and one randomized with quality guarantee $\sqrt{n}$ (where $n$ is the number of vertices in the graph), tight up to constant factors. We validate our algorithms against non-trivial baselines on real-world signed networks. Our experiments confirm that our algorithms produce higher quality solutions, are much faster and can scale to much larger networks than the baselines, and are able to detect ground-truth polarized communities.