Emerging properties of the degree distribution in large non-growing networks
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916835995156480 |
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| author | Franceschi, Jonathan Pareschi, Lorenzo Zanella, Mattia |
| author_facet | Franceschi, Jonathan Pareschi, Lorenzo Zanella, Mattia |
| contents | The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and develop kinetic Boltzmann-type models to capture the emergence of degree distributions that characterize both preferential attachment networks and random networks. Under a suitable mean-field scaling, these models reduce to a Fokker-Planck-type partial differential equation with an affine diffusion coefficient, that is consistent with a well-established master equation for discrete rewiring processes. We further analyze the convergence to equilibrium for this class of Fokker-Planck equations, demonstrating how different regimes -- ranging from exponential to algebraic rates -- depend on network parameters. Our results provide a unified framework for modeling degree distributions in non-growing networks and offer insights into the long-time behavior of such systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Emerging properties of the degree distribution in large non-growing networks Franceschi, Jonathan Pareschi, Lorenzo Zanella, Mattia Physics and Society Adaptation and Self-Organizing Systems The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and develop kinetic Boltzmann-type models to capture the emergence of degree distributions that characterize both preferential attachment networks and random networks. Under a suitable mean-field scaling, these models reduce to a Fokker-Planck-type partial differential equation with an affine diffusion coefficient, that is consistent with a well-established master equation for discrete rewiring processes. We further analyze the convergence to equilibrium for this class of Fokker-Planck equations, demonstrating how different regimes -- ranging from exponential to algebraic rates -- depend on network parameters. Our results provide a unified framework for modeling degree distributions in non-growing networks and offer insights into the long-time behavior of such systems. |
| title | Emerging properties of the degree distribution in large non-growing networks |
| topic | Physics and Society Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2409.06099 |