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

TL;DR

This paper introduces a continuum modeling framework for opinion dynamics on networks, approximating opinion distributions and connection probabilities, with applications to consensus models and potential extensions for dynamic and stochastic networks.

Contribution

It presents a novel continuum approach to model opinion dynamics on networks, offering an alternative to graphon-based models and addressing limitations of existing methods.

Findings

Derived a continuum description for consensus dynamics

Identified limitations and potential extensions of the model

Proposed techniques inspired by mean-field limits

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 aims at approximating the distribution of opinions as well as the probability that two given opinions are connected. To illustrate our framework, we focus on a simple model of consensus dynamics on a network and derive a continuum description using techniques inspired by mean-field limits. We also discuss the limitations of this approach and suggest extensions to account for dynamic networks with evolving connections, stochastic effects, and directional interactions.