# Finite-size scaling of geometric renormalization flows in complex networks

arXiv: https://arxiv.org/abs/2001.09875 · HTML: https://mlsanity.com/paper/2001.09875/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2020.

## Built on by (most cited first, 1 of 1)

- [Data driven modeling for self-similar dynamics](https://mlsanity.com/paper/2310.08282/) (2023)

## Abstract (arXiv)

Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of structural and dynamical observables in geometric renormalization flows of synthetic and real evolutionary networks. Our results show that these observables can be well characterized by a certain scaling function. Specifically, we show that the critical exponent implied by the scaling function is independent of these observables but only depends on the small-world properties of the network, namely, all networks located in the small-world phase have a uniform scaling exponent, while those located in the non-small-world phase and in their critical regions have another uniform scaling. More importantly, we perform extensive experiments on real evolutionary networks with small-world characteristics, and our results show that these observables also have uniform scaling in their geometric renormalization flows. Therefore, in a sense this exponent can be used as an effective measure for classifying universal small-world and non-small-world network models.