A framework for continuum modeling of opinion dynamics on a network based on the probability of connections

Gianluca Favre; Gaspard Jankowiak; Sara Merino-Aceituno; Lara Trussardi; Gianluca Favre; Gaspard Jankowiak; Sara Merino-Aceituno; Lara Trussardi

doi:10.3934/nhm.2026027

Networks and Heterogeneous Media

2026, Volume 21, Issue 2: 594-631. doi: 10.3934/nhm.2026027

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A framework for continuum modeling of opinion dynamics on a network based on the probability of connections

1.
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
2.
Department of Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, 8010 Graz, Austria

Received: 20 October 2025 Revised: 09 February 2026 Accepted: 09 March 2026 Published: 16 April 2026

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.
- opinion formation,
- network mediated dynamics,
- systems of nonlinear conservation laws,
- large population limits
Citation: Gianluca Favre, Gaspard Jankowiak, Sara Merino-Aceituno, Lara Trussardi. A framework for continuum modeling of opinion dynamics on a network based on the probability of connections[J]. Networks and Heterogeneous Media, 2026, 21(2): 594-631. doi: 10.3934/nhm.2026027

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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.

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