Homogeneous Boltzmann-type equations on graphs: A framework for modelling networked social interactions

TL;DR

This paper explores extending homogeneous Boltzmann-type equations to include graph structures, enabling more accurate modeling of social interactions that are not uniformly random but influenced by network connections.

Contribution

It introduces a framework for integrating graph-based interaction patterns into Boltzmann-type equations, addressing limitations of traditional models in social network contexts.

Findings

Framework for graph-structured Boltzmann equations

Potential for more realistic social interaction modeling

Foundation for future empirical validation

Abstract

Homogeneous Boltzmann-type equations are an established tool for modelling interacting multi-agent systems in sociophysics by means of the principles of statistical mechanics and kinetic theory. A customary implicit assumption is that interactions are "all-to-all", meaning that every pair of randomly sampled agents may potentially interact. However, this legacy of classical kinetic theory, developed for collisions among gas molecules, may not be equally applicable to social interactions, which are often influenced by preferential connections between agents. In this paper, we discuss ongoing research on incorporating graph structures into homogeneous Boltzmann-type equations, thereby accounting for the "some-to-some" nature of social interactions.