Multifractal analysis of complex networks

• 来源期刊: 中国物理B（英文版）
• 关键词: complex networks multifractality box covering algorithm
• 年，卷（期）: 2012,（8）
• 页码范围: 85-95
• 页数: 11页
• 语种: 英文
• DOI: 10.1088/1674-1056/21/8/080504

摘要

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 muttifractal 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 network,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.