Determination of multifractal dimensions of complex networks by means of the sandbox algorithm

Chaos
Jin-Long LiuVo Anh

Abstract

Complex networks have attracted much attention in diverse areas of science and technology. Multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we employ the sandbox (SB) algorithm proposed by Tél et al. (Physica A 159, 155-166 (1989)), for MFA of complex networks. First, we compare the SB algorithm with two existing algorithms of MFA for complex networks: the compact-box-burning algorithm proposed by Furuya and Yakubo (Phys. Rev. E 84, 036118 (2011)), and the improved box-counting algorithm proposed by Li et al. (J. Stat. Mech.: Theor. Exp. 2014, P02020 (2014)) by calculating the mass exponents τ(q) of some deterministic model networks. We make a detailed comparison between the numerical and theoretical results of these model networks. The comparison results show that the SB algorithm is the most effective and feasible algorithm to calculate the mass exponents τ(q) and to explore the multifractal behavior of complex networks. Then, we apply the SB algorithm to study the multifractal property of some classic model networks, such as scale-free networks, small-world networks, and random networks. Our results show that...Continue Reading

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Apr 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jin-Long LiuVo Anh

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Citations

Apr 1, 2017·Scientific Reports·Jin-Long LiuXian-Hua Xie
Dec 5, 2015·Scientific Reports·Yu-Qin SongBao-Gen Li
Feb 6, 2017·Scientific Reports·Da-Wen Huang, Zu-Guo Yu
May 22, 2019·Physical Review. E·Didier A Vega-OliverosFrancisco A Rodrigues

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