Eur. Phys. J. B 64, 277-283 (2008)
https://doi.org/10.1140/epjb/e2008-00299-1

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

¹ School of Computer Science, Fudan University, Shanghai 200433, P.R. China
² Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai 200433, P.R. China
³ Department of Computer Science and Technology, Tongji University, 4800 Cao'an Road, Shanghai 201804, P.R. China

Corresponding authors: ^a zhangzz@fudan.edu.cn - ^b sgzhou@fudan.edu.cn

Received: 3 March 2008
Revised: 4 June 2008
Published online: 23 July 2008

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.