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

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.

7 pages, 3 figures, definitive version accepted for publication in EPJB

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• Influences of degree inhomogeneity on average path length and random walks in disassortative scale-free networks
• Exact eigenvalue spectrum of a class of fractal scale-free networks
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• Investigating the Origins of Fractality Based on Two Novel Fractal Network Models