Year: 2025
Type: article
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, whose opinions can thus grow apart. We consider both the repelling and the opposing models of negative interactions, which have been studied in the literature. We define the repelling and the opposing dynamics on signed graphons and we show that their initial value problem solutions exist and are unique. We then show that, in a suitable sense, the graphon dynamics is a good approximation of the dynamics on large graphs that converge to a graphon. This result applies to large random graphs that are sampled according to a graphon (W-random graphs), for which we provide a new convergence result under very general assumptions; in particular, the graphs' average degrees only need to grow faster than$\log n$.
Authors: Raoul Prisant, Federica Garin, Paolo Frasca
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4415003012