Centrality and Universality in Scale-Free Networks

TL;DR

This paper introduces a new model for scale-free networks driven by combined degree and betweenness centralities, revealing a new class of networks and providing insights into their structural dynamics and universality.

Contribution

It presents a novel network growth paradigm integrating centrality measures, unveiling a new class of 'stars-with-filament' networks and a comprehensive phase diagram with real-world applications.

Findings

Average degree grows like a power of log t

Average shortest path length scales logarithmically with system size

Identifies 47 real-world networks fitting the model

Abstract

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.