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

2025-07-20

AI Summary

This work addresses the computational inefficiency of computing equilibrium opinion vectors, polarization, and disagreement metrics under the Friedkin-Johnsen (FJ) opinion dynamics model on large-scale directed or undirected social networks. We propose a deterministic local iterative algorithm with provable relative-error guarantees, accelerated via Successive Over-Relaxation (SOR) using an analytically optimized relaxation parameter. By eschewing global matrix operations, our method achieves significantly reduced time and space complexity—enabling efficient ε-approximate solutions on networks with up to ten million nodes. Experiments across diverse real-world social networks demonstrate that, compared to exact solvers and existing approximation methods, our approach attains 10×–100× speedup while maintaining high accuracy (i.e., ε-relative error). The algorithm exhibits strong scalability and rigorous theoretical guarantees, establishing a practical new paradigm for large-scale opinion dynamics analysis.

Technology Category

• Search and Optimization: Local Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Sentiment analysis and opinion mining

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.

Problem

• Efficiently compute equilibrium opinions in Friedkin-Johnsen model
• Scale algorithms for large networks over 10M nodes
• Optimize convergence using successive over-relaxation techniques

Innovation

• Deterministic local algorithm with error guarantees
• Integration with successive over-relaxation techniques
• Scalable to networks over ten million nodes