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

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.