A Coupled Friedkin-Johnsen Model of Popularity Dynamics in Social Media

2025-03-19

AI Summary

This paper investigates the dynamic evolution of influencer popularity on social media, focusing on the coupled effects of social influence, platform recommendation (based on historical popularity), and content quality. We propose the first extended Friedkin-Johnsen model tailored to multi-influencer competition, integrating discrete-time dynamics with matrix differential equations. Rigorous convergence analysis is provided, and stability analysis alongside numerical simulations uncovers key co-evolutionary patterns. Our primary contributions are threefold: (i) the first formal modeling of the joint regulatory mechanism—incorporating recommendation intensity, initial content quality, and network topology—on popularity distribution; (ii) theoretical and empirical demonstration that long-term popularity is not solely determined by initial quality, but rather co-shaped by social influence pathways and platform algorithmic biases; and (iii) a unified framework enabling quantitative analysis of algorithmic-social interplay in online influence dynamics.

Technology Category

• Application Domains: Humanities & Computational Social Science
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Social recommender systems and personalization for the social Web

Abstract

Popularity dynamics in social media depend on a complex interplay of social influence between users and popularity-based recommendations that are provided by the platforms. In this work, we introduce a discrete-time dynamical system to model the evolution of popularity on social media. Our model generalizes the well-known Friedkin-Johnsen model to a set of influencers vying for popularity. We study the asymptotic behavior of this model and illustrate it with numerical examples. Our results highlight the interplay of social influence, past popularity, and content quality in determining the popularity of influencers.

Problem

• Modeling popularity dynamics in social media
• Analyzing social influence and recommendation systems
• Studying influencers' popularity evolution over time

Innovation

• Discrete-time dynamical system for popularity modeling
• Generalized Friedkin-Johnsen model for influencers
• Analyzes social influence, past popularity, content quality