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.

Network-based kinetic models: Emergence of a statistical description of the graph topology / Nurisso, Marco; Raviola, Matteo; Tosin, Andrea. - In: EUROPEAN JOURNAL OF APPLIED MATHEMATICS. - ISSN 0956-7925. - ELETTRONICO. - (2024), pp. 1-22. [10.1017/S0956792524000020]

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

Nurisso, Marco;Tosin, Andrea
2024

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2985819