@article{Favre2026, 
author = {Gianluca Favre and Gaspard Jankowiak and Sara Merino-Aceituno and Lara Trussardi},
title = {A framework for continuum modeling of opinion dynamics on a network based on the probability of connections},
year = {2026},
journal = {Networks and Heterogeneous Media},
volume = {21},
number = {2},
pages = {594-631},
keywords = {opinion formation, network mediated dynamics, systems of nonlinear conservation laws, large population limits},
url = {https://www.sciopen.com/article/10.3934/nhm.2026027},
doi = {10.3934/nhm.2026027},
abstract = {We propose a modeling framework to develop a continuum description of opinion dynamics on networks as an alternative to other models, like the ones based on graphons. In a nutshell, the continuum model that we propose aimed to approximate the distribution of opinions and the probability that two given opinions are connected. To illustrate our framework, we focused on a simple model of consensus dynamics on a network and derived a continuum description using techniques inspired by mean-field limits. We also discussed the limitations of this approach and suggested extensions to account for dynamic networks with evolving connections, stochastic effects, and directional interactions.}
}