2014/02/17 by Bao-Gen Li, Zu-Guo Yu, Yu Zhou
Physics and Astronomy · #Complex Network Analysis Techniques #Dimension (graph theory) #Fractal #Fractal dimension #Fractal dimension on networks #Multifractal system #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2014/02/p02020
published as J. Stat. Mech.: Theor. Exp., 2014 (2014) P02020 · 12 pages, 7 figures, accepted by J. Stat. Mech
arxiv created 2014/02/17 · openalex publication_date 2014/02/27 · arxiv updated 2015/06/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 .