Centrality and Universality in Scale-Free Networks
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910024056438784 |
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| author | Adami, V. Emdadi-Mahdimahalleh, S. Herrmann, H. J. Najafi, M. N. |
| author_facet | Adami, V. Emdadi-Mahdimahalleh, S. Herrmann, H. J. Najafi, M. N. |
| contents | We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter $0\le p\le 1$) shapes the structure of the evolving network. We reveal the ability to seamlessly explore a vast landscape of scale-free networks, unlocking an entirely new class of complex networks that we call \textit{stars-with-filament} structure. Remarkably, the average degree $\bar k$ of these networks grows like $\log t$ to some power, where $t$ is time and the average shortest path length grows logarithmically with the system size for intermediate $p$ values, offering fresh insights into the structural dynamics of scale-free systems. Our approach is backed by a robust mean-field theory, which nicely captures the dynamics of $\bar{k}$. We further unveil a rich, $p$-dependent phase diagram, encompassing 47 real-world scale-free networks, shedding light on previously hidden patterns. This work opens exciting new avenues for understanding the universal properties of complex networks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_10406 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Centrality and Universality in Scale-Free Networks Adami, V. Emdadi-Mahdimahalleh, S. Herrmann, H. J. Najafi, M. N. Physics and Society Statistical Mechanics Computational Physics Data Analysis, Statistics and Probability We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter $0\le p\le 1$) shapes the structure of the evolving network. We reveal the ability to seamlessly explore a vast landscape of scale-free networks, unlocking an entirely new class of complex networks that we call \textit{stars-with-filament} structure. Remarkably, the average degree $\bar k$ of these networks grows like $\log t$ to some power, where $t$ is time and the average shortest path length grows logarithmically with the system size for intermediate $p$ values, offering fresh insights into the structural dynamics of scale-free systems. Our approach is backed by a robust mean-field theory, which nicely captures the dynamics of $\bar{k}$. We further unveil a rich, $p$-dependent phase diagram, encompassing 47 real-world scale-free networks, shedding light on previously hidden patterns. This work opens exciting new avenues for understanding the universal properties of complex networks. |
| title | Centrality and Universality in Scale-Free Networks |
| topic | Physics and Society Statistical Mechanics Computational Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2412.10406 |