Network-based kinetic models: Emergence of a statistical description of the graph topology

Abstract

In this paper, we propose a novel approach that employs kinetic equations to describe the collective dynamics emerging from graph-mediated pairwise interactions in multi-agent systems. We formally show that for large graphs and specific classes of interactions a statistical description of the graph topology, given in terms of the degree distribution embedded in a Boltzmann-type kinetic equation, is sufficient to capture the collective trends of networked interacting systems. This proves the validity of a commonly accepted heuristic assumption in statistically structured graph models, namely that the so-called connectivity of the agents is the only relevant parameter to be retained in a statistical description of the graph topology. Then, we validate our results by testing them numerically against real social network data.

Keywords

• Multi-agent systems
• networked interactions
• degree distribution
• graph-based kinetic equations
• Boltzmann-type equations
• 35Q20
• 82C22
• 05C07