Temporal Series Analysis Approach to Spectra of Complex Networks

TL;DR

This paper introduces a novel approach combining MF-DFA and DE to analyze spectral level spacings of complex networks, revealing critical points and correlation behaviors across different network models.

Contribution

It applies combined multifractal and entropy methods to spectral data, identifying phase transitions and correlation properties in complex network models for the first time.

Findings

Identifies a critical rewiring probability in WS networks.

Shows spectral time series behave like fractional Brownian motion.

Most GRN networks have Gaussian spectral distributions.

Abstract

The spacing of nearest levels of the spectrum of a complex network can be regarded as a time series. Joint use of Multi-fractal Detrended Fluctuation Approach (MF-DFA) and Diffusion Entropy (DE) is employed to extract characteristics from this time series. For the WS (Watts and Strogatz) small-world model, there exist a critical point at rewiring probability . For a network generated in the range, the correlation exponent is in the range of . Above this critical point, all the networks behave similar with that at . For the ER model, the time series behaves like FBM (fractional Brownian motion) noise at . For the GRN (growing random network) model, the values of the long-range correlation exponent are in the range of . For most of the GRN networks the PDF of a constructed time series obeys a Gaussian form. In the joint use of MF-DFA and DE, the shuffling procedure in DE is essential to obtain a reliable result. PACS number(s): 89.75.-k, 05.45.-a, 02.60.-x