Self-affine Fractals Embedded in Spectra of Complex Networks

Abstract

The scaling properties of spectra of real world complex networks are studied by using the wavelet transform. It is found that the spectra of networks are multifractal. According to the values of the long-range correlation exponent, the Hust exponent $H$, the networks can be classified into three types, namely, $H>0.5$, $H=0.5$ and $H<0.5$. All real world networks considered belong to the class of $H\ge 0.5$, which may be explained by the hierarchical properties.

4 pages, 1 figure, accepted by Phys. Rev. E as rapid comm

References in corpus (13)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Hierarchical Organization in Complex Networks
• Self-similarity of complex networks
• Multifractality in Human Heartbeat Dynamics
• Origins of fractality in the growth of complex networks
• How to calculate the fractal dimension of a complex network: the box covering algorithm
• Skeleton and fractal scaling in complex networks
• Fractality in complex networks: critical and supercritical skeletons
• Portraits of Complex Networks
• Temporal Series Analysis Approach to Spectra of Complex Networks
• Scaling Invariance in Spectra of Complex Networks: A Diffusion Factorial Moment Approach
• Synchronizabilities of Networks: A New index

Cited by in corpus (3)

• Localizations on Complex Networks
• Spectral Properties of Directed Random Networks with Modular Structure
• Spectral analysis of deformed random networks