Efficient Algorithms for Relevant Quantities of Friedkin-Johnsen Opinion Dynamics Model

TL;DR

This paper introduces efficient algorithms for computing equilibrium opinions and related metrics in large-scale social networks modeled by Friedkin-Johnsen dynamics, significantly improving scalability and speed.

Contribution

It presents a deterministic local algorithm with error guarantees and acceleration techniques for large networks, enhancing computational efficiency in opinion dynamics analysis.

Findings

Algorithms scale to networks over ten million nodes.

Significant speedups over traditional methods.

Validated on diverse real-world social networks.

Abstract

Online social networks have become an integral part of modern society, profoundly influencing how individuals form and exchange opinions across diverse domains ranging from politics to public health. The Friedkin-Johnsen model serves as a foundational framework for modeling opinion formation dynamics in such networks. In this paper, we address the computational task of efficiently determining the equilibrium opinion vector and associated metrics including polarization and disagreement, applicable to both directed and undirected social networks. We propose a deterministic local algorithm with relative error guarantees, scaling to networks exceeding ten million nodes. Further acceleration is achieved through integration with successive over-relaxation techniques, where a relaxation factor optimizes convergence rates. Extensive experiments on diverse real-world networks validate the practical effectiveness of our approaches, demonstrating significant improvements in computational efficiency and scalability compared to conventional methods.