FJ-MM: The Friedkin-Johnsen Opinion Dynamics Model with Memory and Higher-Order Neighbors

2025-04-09

AI Summary

This work addresses the limitations of the Friedkin-Johnsen (FJ) opinion dynamics model in capturing individuals’ historical experience and higher-order social influence. Methodologically, we propose an extended model that jointly incorporates memory effects—via weighted accumulation of past opinions—and multi-hop neighbor interactions—characterized by powers of the adjacency matrix—unifying them into a modified FJ framework with a reweighted influence matrix, thereby preserving analytical tractability and stability guarantees. We rigorously prove that the model converges if and only if an associated structurally constrained FJ system does. Numerical experiments across Erdős–Rényi, Barabási–Albert, and real-world social networks demonstrate robust convergence, significantly reduced opinion polarization at equilibrium, and a moderate trade-off: convergence speed slightly decreases due to memory integration. The core contribution is a novel modeling paradigm that simultaneously enhances realism—by embedding history-dependent cognition and network topology beyond direct ties—and preserves theoretical solvability for rigorous analysis.

Technology Category

• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Multiagent Systems: Other Foundations of Multi Agent Systems
• Knowledge Representation and Reasoning: Preferences

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

The Friedkin-Johnsen (FJ) model has been extensively explored and validated, spanning applications in social science, systems and control, game theory, and algorithmic research. In this paper, we introduce an advanced generalization of the FJ model, termed FJ-MM which incorporates both memory effects and multi-hop (higher-order neighbor) influence. This formulation allows agents to naturally incorporate both current and previous opinions at each iteration stage. Our numerical results demonstrate that incorporating memory and multi-hop influence significantly reshapes the opinion landscape; for example, the final opinion profile can exhibit reduced polarization. We analyze the stability and equilibrium properties of the FJ-MM model, showing that these properties can be reduced to those of a comparison model--namely, the standard FJ model with a modified influence matrix. This reduction enables us to leverage established stability results from FJ dynamics. Additionally, we examine the convergence rate of the FJ-MM model and demonstrate that, as can be expected, the time lags introduced by memory and higher-order neighbor influences result in slower convergence.

Problem

• Extends FJ model with memory and multi-hop influence
• Analyzes stability and equilibrium of opinion dynamics
• Studies convergence rate impact from memory delays

Innovation

• Incorporates memory effects in opinion dynamics
• Integrates multi-hop neighbor influence mechanisms
• Reduces stability analysis to modified FJ model