Opinion Dynamics on Graphon: the piecewise constant case

TL;DR

This paper introduces a graphon-based approach to model opinion dynamics in large networks, proving existence and uniqueness of the limit system, and analyzing piecewise constant graphons for mean field insights.

Contribution

It applies graphon theory to opinion dynamics, providing new theoretical results and mean field analysis for piecewise constant graphons in large networks.

Findings

Proved existence and uniqueness of the limit opinion dynamics system.

Developed mean field analysis for piecewise constant graphons.

Validated the approach with theoretical and simulation results.

Abstract

The study of network supported opinion dynamics in large groups of autonomous agents is attracting an increasing interest during the last years. In this paper, we proposed the use of the recent graphon theory to model and simulate an interacting system describing the evolution of individual opinions over an arbitrary size networks. Specifically, we prove the existence and uniqueness of the limit problem that approximates a very large networks made by homogeneous groups of agents. The significant new example is the mean field analysis deduced from the graphon limit systems in the case of piecewise constant graphon.