Transition from fractal to non-fractal scalings in growing scale-free networks

TL;DR

This paper introduces a unifying model for real networks that can transition from fractal to non-fractal scaling by adjusting a parameter, revealing insights into their evolution and properties.

Contribution

A novel model that unifies fractal and non-fractal networks and demonstrates a controllable transition between them.

Findings

Networks transition from fractal to non-fractal as parameter q varies.

The model captures changes in degree distribution, path length, and fractal dimensions.

Crossover from large-world to small-world behavior observed.

Abstract

Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological properties of the network including the degree distribution, average path length, diameter, fractal dimensions, and betweenness centrality distribution, which are controlled by parameter $q$. Interestingly, we show that by adjusting $q$, the networks undergo a transition from fractal to non-fractal scalings, and exhibit a crossover from `large' to small worlds at the same time. Our research may shed some light on understanding the evolution and relationships of fractal and non-fractal networks.