Network-based kinetic models: Emergence of a statistical description of the graph topology
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866917494635102208 |
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| author | Nurisso, Marco Raviola, Matteo Tosin, Andrea |
| author_facet | Nurisso, Marco Raviola, Matteo Tosin, Andrea |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07843 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Network-based kinetic models: Emergence of a statistical description of the graph topology Nurisso, Marco Raviola, Matteo Tosin, Andrea Physics and Society Mathematical Physics 35Q20, 82C22, 05C07 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. |
| title | Network-based kinetic models: Emergence of a statistical description of the graph topology |
| topic | Physics and Society Mathematical Physics 35Q20, 82C22, 05C07 |
| url | https://arxiv.org/abs/2306.07843 |