Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

Liu, Jin-Long, Yu, Zu-Guo, & Anh, Vo (2014) Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions. Physical Review E, 89(3), 032814-1.

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Abstract

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2-H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.

Impact and interest:

12 citations in Scopus
14 citations in Web of Science®
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ID Code: 88721
Item Type: Journal Article
Refereed: Yes
DOI: 10.1103/PhysRevE.89.032814
ISSN: 1539-3755
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 30 Oct 2015 01:10
Last Modified: 25 Jun 2017 21:02

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