Scaling properties of scale-free networks in degree-thresholding renormalization flows

TL;DR

This paper investigates the scaling behavior of observables in scale-free networks under degree-thresholding renormalization flows, revealing universal scaling properties and practical implications for analyzing large networks efficiently.

Contribution

It introduces a finite-size scaling analysis of DTR flows in scale-free networks, demonstrating universal scaling exponents and practical applications for large-scale network analysis.

Findings

Observables exhibit similar scaling behavior across different network sizes.

A single scaling exponent captures the changes in network observables.

DTR snapshots can substitute initial networks for efficient analysis.

Abstract

We study the statistical properties of observables of scale-free networks in the degree-thresholding renormalization (DTR) flows. For BA scale-free networks with different sizes, we find that their structural and dynamical observables have similar scaling behavior in the DTR flow. The finite-size scaling analysis confirms this view and reveals a scaling function with a single scaling exponent that collectively captures the changes of these observables. Furthermore, for the scale-free network with a single initial size, we use its DTR snapshots as the original networks in the DTR flows, then perform a similar finite-size scaling analysis. Interestingly, the initial network and its snapshots share the same scaling exponent as the BA synthetic network. Our findings have important guiding significance for analyzing the structure and dynamic behavior of large-scale networks. Such as, in large-scale simulation scenarios with high time complexity, the DTR snapshot could serve as a substitute or guide for the initial network and then quickly explore the scaling behavior of initial networks.