Temporal series analysis approach to spectra of complex networks

Yang, Huijie; Zhao, Fangcui; Qi, Longyu; Hu, Beilai

doi:10.1103/physreve.69.066104

Cited by 41 publications

(29 citation statements)

References 31 publications

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“…In recent literature, the spectral density function and the time series analysis methods are used to capture properties of complex networks [14][15][16][17][18][19]. One of the most important concepts in RMT is the nearest neighbor level spacing (NNLS) distribution.…”

Section: The Methodsmentioning

confidence: 99%

Collective chaos induced by structures of complex networks

Yang

Zhao

Wang

2006

Physica A: Statistical Mechanics and its Applications

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Mapping a complex network of N coupled identical oscillators to a quantum system, the nearest neighbor level spacing (NNLS) distribution is used to identify collective chaos in the corresponding classical dynamics on the complex network. The classical dynamics on an Erdos-Renyi network with the wiring probability p ER ≤ 1 N is in the state of collective order, while that on an Erdos-Renyi network with p ER > 1 N in the state of collective chaos. The dynamics on a WS Small-world complex network evolves from collective order to collective chaos rapidly in the region of the rewiring probability p r ∈ [0.0, 0.1], and then keeps chaotic up to p r = 1.0. The dynamics on a Growing Random Network (GRN) is in a special state deviates from order significantly in a way opposite to that on WS small-world networks. Each network can be measured by a couple values of two parameters (β, η).

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Section: The Methodsmentioning

confidence: 99%

Collective chaos induced by structures of complex networks

Yang

Zhao

Wang

2006

Physica A: Statistical Mechanics and its Applications

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“…The elements A ij are 1/0 if the nodes i and j are connected/disconnected, respectively. If we consider the nodes as atoms and the edges as bonds, the network can be mapped to a large molecule [16]. For an electron moving in such a molecule, the tight-binding Hamiltonian is,…”

Section: The Localizations On Networkmentioning

confidence: 99%

“…We try to detect the global symmetries from the spectra and the eigenvectors of complex networks. Very recently, much attentions have been focused on detecting global characteristics embedded in spectra of complex networks due to their potential application in understanding the organization mechanisms and the synchronization dynamics of complex networks [8,15,16]. To our best knowledge, it is the first time to detect the global characteristics of complex networks from the eigenvectors which contain more information about the system than eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

Localizations on complex networks

et al. 2008

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We study the structure characteristics of complex networks from the representative eigenvectors of the adjacent matrix. The probability distribution function of the components of the representative eigenvectors are proposed to describe the localizations on networks where the Euclidean distance is invalid. Several quantities are used to describe the localization properties of the representative states, as the participation ratio, the structural entropy, the probability distribution function of the nearest neighbor level spacings for spectra of complex networks. The whole cellular networks in real world, the Watts-Strogatz small world and Barabasi-Albert scale-free networks are considered. The networks have nontrivial localization properties due to the nontrivial topological structures. It is found that the ascend-ranked series of the occurring probabilities at the nodes behave generally multi-fractal. This characteristic can be used as a structure measure of complex networks.

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“…The DEA method has been used to analysis many time series in different research fields, such as the solar induced atmosphere temperature series [22], the intermittency time series in fluid turbulence [23], the spectra of complex networks [24], the output spike trains of neurons [25], the index of financial market [26], and so on.…”

Section: Diffusion Entropy Technique Based On Fourier Analysismentioning

confidence: 99%

Diffusion entropy analysis on the stride interval fluctuation of human gait

Cai

Zhou

Yang

et al. 2007

Physica A: Statistical Mechanics and its Applications

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In this paper, the diffusion entropy technique is applied to investigate the scaling behavior of stride interval fluctuations of human gait. The scaling behavior of the stride interval of human walking at normal, slow and fast rate are similar; with the scale-invariance exponents in the interval [0.663, 0.955], of which the mean value is 0.821 ± 0.011. Dynamical analysis of these stride interval fluctuations reveals a self-similar pattern: Fluctuation at one time scale are statistically similar to those at multiple other time scales, at least over hundreds of steps, while the healthy subjects walk at their normal rate. The long-range correlations are observed during the spontaneous walking after the removal of the trend in the time series with Fourier filter. These findings uncover that the fractal dynamics of stride interval of human gait are normally intrinsic to the locomotor systems.

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Temporal series analysis approach to spectra of complex networks

Abstract: The spacing of nearest levels of the spectrum of a complex network can be regarded as a time

Cited by 41 publications

References 31 publications

Collective chaos induced by structures of complex networks

Collective chaos induced by structures of complex networks

Localizations on complex networks

Diffusion entropy analysis on the stride interval fluctuation of human gait

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