Centrality and Universality in Scale-Free Networks

Fuente: arXiv
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Main Authors: Adami, V., Emdadi-Mahdimahalleh, S., Herrmann, H. J., Najafi, M. N.
Format: Preprint
Published: 2024
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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
id 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