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

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.

References in corpus (8)

• A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part I
• Biased Assimilation, Homophily and the Dynamics of Polarization
• Novel Multidimensional Models of Opinion Dynamics in Social Networks
• The Matrix-Forest Theorem and Measuring Relations in Small Social Groups
• On Proximity Measures for Graph Vertices
• Current Flow Group Closeness Centrality for Complex Networks
• Fast Evaluation for Relevant Quantities of Opinion Dynamics
• A Nearly-Linear Time Algorithm for Minimizing Risk of Conflict in Social Networks