Statistical Self-Similar Properties of Complex Networks

Abstract

It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability depends on the type of networks. To unravel ubiquitous characteristics that complex networks may have in common, we adopt the clustering coefficient as the probability measure, and present a systematic analysis of various types of complex networks from the perspective of statistical self-similarity. We find that the probability distribution of the clustering coefficient is best characterized by the multifractal; moreover, the support of the measure had a fractal dimension. These two features enable us to describe complex networks in a unified way; at the same time, offer unforeseen possibilities to comprehend complex networks.

11 pages, 4 figures

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Cited by in corpus (6)

• 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 complex networks
• Multifractal analysis of weighted networks by a modified sandbox algorithm
• Multifractal Characterization of Protein Contact Networks
• Structural Properties of Networks Grown via an Achlioptas Process