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Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks |
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| Authors: | Xiao-Hui Ni Zhi-Qiang Jiang Wei-Xing Zhou |
| Institution: | a School of Business, East China University of Science and Technology, Shanghai 200237, China b School of Science, East China University of Science and Technology, Shanghai 200237, China c Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China d Chair of Entrepreneurial Risks, D-MTEC, ETH Zurich, Kreuplatz 5, CH-8032 Zurich, Switzerland e Engineering Research Center of Process Systems Engineering (Ministry of Education), East China University of Science and Technology, Shanghai 200237, China f Research Center on Fictitious Economics & Data Science, Chinese Academy of Sciences, Beijing 100080, China |
| Abstract: | The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship. |
| Keywords: | 89 75 Hc 05 40 -a 05 45 Df 05 45 Tp |
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