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 multifractality exists in scale-free networks, that of small-world networks is not obvious, and it almost does not exist in random networks.
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February 2015
Research Article|
February 09 2015
Determination of multifractal dimensions of complex networks by means of the sandbox algorithm
Jin-Long Liu;
Jin-Long Liu
1Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education,
Xiangtan University
, Xiangtan, Hunan 411105, China
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Zu-Guo Yu
;
Zu-Guo Yu
a)
1Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education,
Xiangtan University
, Xiangtan, Hunan 411105, China
2School of Mathematical Sciences,
Queensland University of Technology
, GPO Box 2434, Brisbane Q4001, Australia
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Vo Anh
Vo Anh
2School of Mathematical Sciences,
Queensland University of Technology
, GPO Box 2434, Brisbane Q4001, Australia
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a)
Electronic mail: yuzg1970@yahoo.com
Chaos 25, 023103 (2015)
Article history
Received:
October 26 2014
Accepted:
January 26 2015
Citation
Jin-Long Liu, Zu-Guo Yu, Vo Anh; Determination of multifractal dimensions of complex networks by means of the sandbox algorithm. Chaos 1 February 2015; 25 (2): 023103. https://doi.org/10.1063/1.4907557
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