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Chin. Phys. B, 2012, Vol. 21(8): 080504    DOI: 10.1088/1674-1056/21/8/080504
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Multifractal analysis of complex networks

Wang Dan-Linga b, Yu Zu-Guoa c, Anh Va
a School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Q 4001, Australia;
b School of Mathematics & Physics, University of Science & Technology Beijing, Beijing 10083, China;
c Hunan Key Laboratory for Computation & Simulation in Science & Engineering, and School of Mathematics & Computational Science, Xiangtan University, Xiangtan 411105, China
Abstract  Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal dimensions. Multifractal analysis is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we introduce a new box covering algorithm for multifractal analysis of complex networks. This algorithm is used to calculate the generalized fractal dimensions Dq of some theoretical networks, namely scale-free networks, small world networks, and random networks, and one kind of real networks, namely protein-protein interaction networks of different species. Our numerical results indicate the existence of multifractality in scale-free networks and protein-protein interaction networks, while the multifractal behavior is not clear-cut for small world networks and random networks. The possible variation of Dq due to changes in the parameters of the theoretical network models is also discussed.
Keywords:  complex networks      multifractality      box covering algorithm  
Received:  02 February 2012      Revised:  01 March 2012      Published:  01 July 2012
PACS:  05.45.Df (Fractals)  
  47.53.+n (Fractals in fluid dynamics)  
  89.75.Hc (Networks and genealogical trees)  
Fund: Project supported by the Australian Research Council (Grant No. DP0559807), the National Natural Science Foundation of China (Grant No. 11071282), the Science Fund for Changjiang Scholars and Innovative Research Team in University (PCSIRT) (Grant No. IRT1179), the Program for New Century Excellent Talents in University (Grant No. NCET-08-06867), the Research Foundation of the Education Department of Hunan Province of China (Grant No. 11A122), the Natural Science Foundation of Hunan Province of China (Grant No. 10JJ7001), the Science and Technology Planning Project of Hunan Province of China (Grant No. 2011FJ2011), the Lotus Scholars Program of Hunan Province of China, the Aid Program for Science and Technology Innovative Research Team in Higher Education Institutions of Hunan Province of China, and a China Scholarship Council-Queensland University of Technology Joint Scholarship.
Corresponding Authors:  Yu Zu-Guo     E-mail:  yuzg@hotmail.com

Cite this article: 

Wang Dan-Ling, Yu Zu-Guo, Anh V Multifractal analysis of complex networks 2012 Chin. Phys. B 21 080504

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