Fractal and multifractal properties of a family of fractal networks

Li, Bao-Gen, Yu, Zu-Guo, & Zhou, Yu (2014) Fractal and multifractal properties of a family of fractal networks. Journal of Statistical Mechanics: Theory and Experiment, 2014, pp. 1-11.

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Abstract

In this work, we study the fractal and multifractal properties of a family of fractal networks introduced by Gallos et al (2007 Proc. Nat. Acad. Sci. USA 104 7746). In this fractal network model, there is a parameter e which is between 0 and 1, and allows for tuning the level of fractality in the network. Here we examine the multifractal behavior of these networks, the dependence relationship of the fractal dimension and the multifractal parameters on parameter e. First, we find that the empirical fractal dimensions of these networks obtained by our program coincide with the theoretical formula given by Song et al (2006 Nature Phys. 2 275). Then from the shape of the τ(q) and D(q) curves, we find the existence of multifractality in these networks. Last, we find that there exists a linear relationship between the average information dimension 〈D(1)〉 and the parameter e.

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ID Code: 88552
Item Type: Journal Article
Refereed: Yes
DOI: 10.1088/1742-5468/2014/02/P02020
ISSN: 1742-5468
Deposited On: 06 Nov 2015 03:54
Last Modified: 06 Nov 2015 03:54

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