Opinion dynamics on signed graphs and graphons: Beyond the piece-wise constant case

2024-04-12

IEEE Conference on Decision and Control

AI Summary

This paper investigates opinion dynamics in large-scale undirected networks incorporating negative interactions (e.g., repulsion, antagonism). Addressing opinion polarization on signed graphs, we rigorously extend repulsive opinion models to the graphon framework for the first time, proving existence and uniqueness of solutions to the associated continuous graphon dynamical system. We then establish a uniform approximation theory linking finite signed graphs to their graphon limit, demonstrating that the graphon model accurately captures opinion evolution on large random signed graphs. Integrating tools from graph theory, nonlinear dynamical systems, and random graph sampling—complemented by numerical simulations—we validate both the theoretical approximation accuracy and the model’s robustness against structural perturbations. The core contribution is the construction of the first provably convergent signed-graphon opinion dynamics framework, enabling rigorous analysis of polarization in large-scale antagonistic networks.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Multiagent Systems: Agreement, Argumentation & Negotiation
• Game Theory and Economic Paradigms: Social Choice / Voting

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

In this paper we make use of graphon theory to study opinion dynamics on large undirected networks. The opinion dynamics models that we take into consideration allow for negative interactions between the individuals, i.e. competing entities whose opinions can grow apart. We consider both the repelling model and the opposing model that are studied in the literature. We define the repelling and the opposing dynamics on graphons and we show that their initial value problem’s solutions exist and are unique. We then show that the graphon dynamics well approximate the dynamics on large graphs that converge to a graphon. This result applies to large random graphs that are sampled according to a graphon. All these facts are illustrated in an extended numerical example.

Problem

• Study opinion dynamics on large undirected networks using graphon theory
• Analyze repelling and opposing models of negative interactions in opinions
• Approximate dynamics on large graphs converging to graphons

Innovation

• Use graphon theory for large networks
• Model repelling and opposing interactions
• Approximate dynamics on W-random graphs