Multifractal analysis of complex networks

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 $D_q$ 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 $D_q$ due to changes in the parameters of the theoretical network models is also discussed.

18 pages, 7 figures, 4 tables

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Cited by in corpus (11)

• Determination of multifractal dimensions of complex networks by means of the sandbox algorithm
• Fractal and multifractal properties of a family of fractal networks
• Multifractal analysis of weighted networks by a modified sandbox algorithm
• Topological properties and fractal analysis of recurrence network constructed from fractional Brownian motions
• Fractal and multifractal analysis of complex networks: Estonian network of payments
• Multifractal Characterization of Protein Contact Networks
• A Fixed-Mass multifractal approach for unweighted complex networks
• A computationally-efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes
• Multifractality of complex networks is also due to geometry. The Geometric SandBox algorithm
• Bifractality of fractal scale-free networks
• Random walks on bifractal networks