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

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.