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

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

2008-03-26

arxiv.org/abs/0803.3691v2

Eur. Phys. J. B 64, 277-283 (2008)

Physics

Condensed Matter

Other Condensed Matter

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

Scientific paper

10.1140/epjb/e2008-00299-1

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.

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