Scaling properties of complex networks: Toward Wilsonian renormalization for complex networks

TL;DR

This paper introduces a novel two-site scaling method for complex networks, exploring its effects on degree distributions and its potential to develop a Wilsonian renormalization group framework for analyzing network dynamics.

Contribution

The paper proposes a new two-site scaling scheme and investigates its application to defining a Wilsonian renormalization approach for complex networks.

Findings

Degree distribution changes under two-site scaling.

BA networks behave differently from natural networks.

Potential for a new renormalization method for network analysis.

Abstract

Nowadays, scaling methods for general large-scale complex networks have been developed. We proposed a new scaling scheme called "two-site scaling". This scheme was applied iteratively to various networks, and we observed how the degree distribution of the network changes by two-site scaling. In particular, networks constructed by the BA algorithm behave differently from the networks observed in the nature. In addition, an iterative scaling scheme can define a new renormalizing method. We investigated the possibility of defining the Wilsonian renormalization group method on general complex networks and its application to the analysis of the dynamics of complex networks.