1 Department of Systems Science, University of Shanghai for Science and Technology, Shanghai 200093, China; 2 Department of Business, Wuxi Taihu University, Wuxi 214064, China
Abstract An extreme event may lead to serious disaster to a complex system. In an extreme event series there exist generally non-trivial patterns covering different time scales. Investigations on extreme events are currently based upon statistics, where the patterns are merged into averages. In this paper from extreme event series we constructed extreme value series and extreme interval series. And the visibility graph is then adopted to display the patterns formed by the increases/decreases of extreme value or interval faster/slower than the linear ones. For the fractional Brownian motions, the properties for the constructed networks are the persistence, threshold, and event-type-independent, , the degree distributions decay exponentially with almost identical speeds, the nodes cluster into modular structures with large and similar modularity degrees, and each specific network has a perfect hierarchical structure. For the volatilities of four stock markets (NSDQ, SZI, FTSE100, and HSI), the properties for the former three's networks are threshold- and market-independent. Comparing with the factional Brownian motions, their degree distributions decay exponentially but with slower speeds, their modularity behaviors are significant but with smaller modularity degrees. The fourth market behaves similar qualitatively but different quantitatively with the three markets. Interestingly, all the transition frequency networks share an identical backbone composed of nine edges and the linked graphlets. The universal behaviors give us a framework to describe extreme events from the viewpoint of network.
(Economics; econophysics, financial markets, business and management)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11805128, 11875042, and 11505114) and the Shanghai Project for Construction of Top Disciplines, China (Grant No. USST-SYSBIO).
Corresponding Authors:
Huijie Yang
E-mail: hjyang@ustc.edu.cn
Cite this article:
Jing Zhang(张晶), Xiaolu Chen(陈晓露), Haiying Wang(王海英), Changgui Gu(顾长贵), and Huijie Yang(杨会杰) Visibility graph approach to extreme event series 2023 Chin. Phys. B 32 100505
[1] Chowdhurya S N, Ray A, Dana S K and Ghosh D 2022 Phys. Rep.966 1 [2] Majumdar S N, Pal A and Schehr F 2020 Phys. Rep.840 1 [3] Scheffer M, Bascompte J, Brock W A, Brovkin V, Carpenter S R, et al. 2009 Nature461 53 [4] Battiston S, Farmer J D, Flache A, Garlaschelli D, Haldane A G, Heesterbee K H, et al. 2016 Science351 818 [5] Arani B M S, Carpenter S R, Lahti L, Nes E H V and Scheffer M 2021 Science372 eaay4895 [6] Bunde A, Eichner J F, Kantelhardt J W and Havlin S 2005 Phys. Rev. Lett.94 048701 [7] Bunde A, Eichner J F, Kantelhardt J W and Havlin S 2006 Phys. Rev. E73 016130 [8] Santhanam M S and Kantz H 2008 Phys. Rev. E78 051113 [9] Nicolis C and Nicolis G 2009 Phys. Rev. E80 061119 [10] Aghamohammadi C and Crutchfield J P 2017 Phys. Rev. E95 032101 [11] Gao Z K, Small M and Kurths J 2016 Europhys. Lett.116 50001 [12] Zou Y, Donner R V, Marwan N, Donges J F and Kurths J 2019 Phys. Rep.787 1 [13] Zhang J and Small M 2006 Phys. Rev. Lett.96 238701 [14] Zhang J, Luo X, Nakamura T, Sun J and Small M 2007 Phys. Rev. E75 016218 [15] Zhang J, Sun J, Luo X, Zhang K, Nakamura T and Small M 2008 Physica D237 2856 [16] Yang Y and Yang H J 2008 Physica A387 1381 [17] Marwan M, Donges J F, Zou Y, Donner R V and Kurths J 2009 Phys. Lett. A373 4246 [18] Donner R, Zou Y, Donges J, Marwan N and Kurths J 2010 New J. Phys.12 033025 [19] Gao Z and Jin N D 2009 Phys. Rev. E79 066303 [20] Pham T D 2017 Europhys. Lett.118 20003 [21] Tumminello M, Aste T, Matteo T D and Mantegna R N 2005 Proc. Natl. Acad. Sci. USA102 10421 [22] Xu X, Zhang and Small M 2008 Proc. Natl. Acad. Sci. USA105 19601 [23] Lacasa L, Luque B, Ballesteros F, Luque J and Nuno C 2008 Proc. Natl. Acad. Sci. USA105 4972 [24] Luque B, Lacasa L, Ballesteros F and Luque J 2009 Phys. Rev. E80 046103 [25] Ni X H, Jiang Z Q and Zhou W X 2009 Phys. Lett. A373 3822 [26] Xiao Q, Pan X, Li X L, Mutua S, Yang H J, Jiang Y, Wang J Y and Zhang Q J 2014 Chin. Phys. B23 078904 [27] Mantegna R N and Stanley H E 2000 Introduction to Econophysics: Correlations Complexity in Finance (Cambridge University Press, Cambridge) [28] https://uk.finance.yahoo.com/world-indices/ Accessed in July 20, 2022 [29] Albert R and Barabasi A L 2002 Rev. Mod. Phys.74 47 [30] Lacasa L, Luque L, Luque B and Nuno J C 2009 Europhys. Lett.86 30001 [31] Girvan M and Newman M E J 2002 Proc. Natl. Acad. Sci. USA99 7821 [32] Newman M E J and Girvan M 2004 Phys. Rev. E69 026113 [33] Ravasz E and Barabasi A L 2003 Phys. Rev. E67 026112 [34] McCullough M, Small M, Stemler T and Iu H C 2015 Chaos25 053101 [35] Stephen M, Gu C G and Yang H J 2015 PLoS ONE10 e0143015 [36] Iacovacci J and Lacasa L 2016 Phys. Rev. E93 042309 [37] Mutua S, Gu C G and Yang H J 2016 Chaos26 053107 [38] Kulp C W, Chobot J M, Freitas H R and Sprechini G D 2016 Chaos26 073114 [39] McCullough M, Small M, Iu H H C and Stemler T 2017 Phil. Trans. Roy. Soc. A375 20170016 [40] McCullough M, Sakellariou K, Stemler T and Small M 2017 Chaos27 035814 [41] Zhang J Y, Zhou J, Tang M, Guo H, Small M and Zou Y 2017 Sci. Rep.7 7795 [42] Guo H, Zhang J Y, Zou Y and Guan S G 2018 Front. Phys.13 130508 [43] Ren H G, Yuan Q S, Semba S, Weng T F, Gu C G and Yang H J 2020 Phys. Lett. A384 126781 [44] Wang Y, Weng T F, Deng S G, Gu C G and Yang H J 2019 Chaos29 023109
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
