Comparative regression analysis to degree distributions of visibility graph

ZHANG Rong; ZOU Yong

doi:10.3969/j.issn.1000-5641.2017.02.010

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Mar. 2017

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ZHANG Rong, ZOU Yong. Comparative regression analysis to degree distributions of visibility graph[J]. Journal of East China Normal University (Natural Sciences), 2017, (2): 75-80. doi: 10.3969/j.issn.1000-5641.2017.02.010

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ZHANG Rong, ZOU Yong. Comparative regression analysis to degree distributions of visibility graph[J]. Journal of East China Normal University (Natural Sciences), 2017, (2): 75-80. doi: 10.3969/j.issn.1000-5641.2017.02.010

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Comparative regression analysis to degree distributions of visibility graph

doi: 10.3969/j.issn.1000-5641.2017.02.010

ZHANG Rong,
ZOU Yong^,

School of Physics and Materials Science, East China Normal University, Shanghai 200241, China

Received Date: 2016-03-18
Publish Date: 2017-03-25

Abstract

Abstract

Visibility graph has provided much insight to study the dynamics of time series from the perspective complex network. We construct visibility graphs for time series from both auto-regressive stochastic and fractional Brownian motions. Our results suggest that degree distributions of the resulted complex networks of auto-regressive processes are characterized by exponential forms, while that of fractional Brownian motions obey power-law forms. Our conclusions hold for both the traditional visibility graph and its variant horizontal visibility graph.
- visibility graph,
- autoregressive stochastic process,
- fractional Brownian motion,
- goodness of fit

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References(18)

References

[1]	WATTS D J, STROGATZ S H. Collective dynamics of 'small-world' networks[J]. Nature, 1998, 6684(393):440-442. http://www.wenkuxiazai.com/doc/e70defefaeaad1f346933fda.html
[2]	ALBERT R, BARABÁSI A L. Statistical mechanics of complex networks[J]. Review of Modern Physics, 2002, 74(1):47-97. doi: 10.1103/RevModPhys.74.47
[3]	汪小帆.复杂网络理论及其应用[M].北京:清华大学出版社, 2006.
[4]	何大韧.复杂系统与复杂网络[M].北京:高等教育出版社, 2009.
[5]	ZHANG J, SMALL M. Complex network from pseudoperiodic time series:topology versus dynamics[J]. Physical Review Letters, 2006, 96(23):238701-238704. doi: 10.1103/PhysRevLett.96.238701
[6]	LACASA L, LUQUE B, BALLESTEROS F, et al. From time series to complex networks:The visibility graph[J]. Proceedings of the National Academy of Sciences, 2008, 105(13):4972-4975. doi: 10.1073/pnas.0709247105
[7]	DONNER R V, ZOU Y, DONGES J F, et al. Recurrence networks-a novel paradigm for nonlinear time series analysis[J]. New Journal of Physics, 2010, 12(2):129-132. http://adsabs.harvard.edu/abs/2010NJPh...12c3025D
[8]	XU X K, ZHANG J, SMALL M. Superfamily phenomena and motifs of networks induced from time series[J]. Proceedings of the National Academy of Sciences, 2008, 105(50):19601-19605. doi: 10.1073/pnas.0806082105
[9]	ZOU Y, SMALL M, LIU Z H, et al. Complex network approach to characterize the statistical features of the sunspot series[J]. New Journal of Physics, 2014, 14(1):1-8. http://adsabs.harvard.edu/abs/2014NJPh...16a3051Z
[10]	ZOU Y, DONNER R V, MARWAN N, et al. Long-term changes in the north-south asymmetry of solar activity:A nonlinear dynamics characterization using visibility graphs[J]. Nonlinear Processes in Geophysics, 2014, 21(1):1113-1126. http://pubman.mpdl.mpg.de/pubman/item/escidoc:2081641:3/component/escidoc:2081640/BGC2180D.pdf
[11]	YANG Y, YANG H. Complex network-based time series analysis[J]. Physica A, 2008, 387(s 5-6):1381-1386.
[12]	LACASA L, TORAL R. Description of stochastic and chaotic series using visibility graphs[J]. Physical Review E, 2010, 82(3):4881-4888. http://www.oalib.com/paper/3619847
[13]	GAO Z K, JIN N D. Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks[J]. Physical Review E, 2009, 79(6):1019-1027. http://www.springer.com/us/book/9783642383724
[14]	YANG Y, WANG J, YANG H, et al. Visibility graph approach to exchange rate series[J]. Physica A, 2009, 388(20):4431-4437. doi: 10.1016/j.physa.2009.07.016
[15]	ELSNER J B, JAGGER T H, FOGARTY E A. Visibility network of United States hurricanes[J]. Geophysical Research Letters, 2009, 36(16):554-570. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.724.6028
[16]	LUQUE B, LACASA L, BALLESTEROS F, et al. Horizontal visibility graphs:exact results for random time series[J]. Physical Review E, 2009, 80(2):593-598.
[17]	GUTIN G, MANSOUR T, SEVERINI S. A characterization of horizontal visibility graphs and combinatorics on words[J]. Physica A, 2011, 390(12):2421-2428. doi: 10.1016/j.physa.2011.02.031
[18]	NUÑEN A, LACASA L, VALERO E, et al. Detecting series periodicit e y with horizontal visibility graphs[J]. International Journal of Bifurcation & Chaos, 2012, 22(7):1250160(10pages). DOI: 10.1142/S021812741250160X.