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Dynamic structural and topological phase transitions on the Warsaw Stock Exchange: A phenomenological approach


  • A. Sienkiewicz
  • T. Gubiec
  • R. Kutner
  • Z. R. Struzik


We study the crash dynamics of the Warsaw Stock Exchange (WSE) by using the Minimal Spanning Tree (MST) networks. We find the transition of the complex network during its evolution from a (hierarchical) power law MST network, representing the stable state of WSE before the recent worldwide financial crash, to a superstar-like (or superhub) MST network of the market decorated by a hierarchy of trees (being, perhaps, an unstable, intermediate market state). Subsequently, we observed a transition from this complex tree to the topology of the (hierarchical) power law MST network decorated by several star-like trees or hubs. This structure and topology represent, perhaps, the WSE after the worldwide financial crash, and could be considered to be an aftershock. Our results can serve as an empirical foundation for a future theory of dynamic structural and topological phase transitions on financial markets.

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  • A. Sienkiewicz & T. Gubiec & R. Kutner & Z. R. Struzik, 2013. "Dynamic structural and topological phase transitions on the Warsaw Stock Exchange: A phenomenological approach," Papers 1301.6506,
  • Handle: RePEc:arx:papers:1301.6506

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    References listed on IDEAS

    1. G. Bonanno & F. Lillo & R. N. Mantegna, 2001. "High-frequency cross-correlation in a set of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 96-104.
    2. Dong-Ming Song & Michele Tumminello & Wei-Xing Zhou & Rosario N. Mantegna, 2011. "Evolution of worldwide stock markets, correlation structure and correlation based graphs," Papers 1103.5555,
    3. B. M. Tabak & T. R. Serra & D. O. Cajueiro, 2010. "Topological properties of commodities networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 74(2), pages 243-249, March.
    4. N. Vandewalle & F. Brisbois & X. Tordoir, 2001. "Non-random topology of stock markets," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 372-374, March.
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    Cited by:

    1. Wiliński, M. & Sienkiewicz, A. & Gubiec, T. & Kutner, R. & Struzik, Z.R., 2013. "Structural and topological phase transitions on the German Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5963-5973.
    2. Fiedor, Paweł, 2014. "Sector strength and efficiency on developed and emerging financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 180-188.
    3. Huang, Wei-Qiang & Zhuang, Xin-Tian & Yao, Shuang & Uryasev, Stan, 2016. "A financial network perspective of financial institutions’ systemic risk contributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 183-196.
    4. repec:kap:compec:v:51:y:2018:i:2:d:10.1007_s10614-017-9672-x is not listed on IDEAS
    5. Gautier Marti & Frank Nielsen & Miko{l}aj Bi'nkowski & Philippe Donnat, 2017. "A review of two decades of correlations, hierarchies, networks and clustering in financial markets," Papers 1703.00485,, revised May 2018.
    6. Jae Woo Lee & Ashadun Nobi, 2018. "State and Network Structures of Stock Markets around the Global Financial Crisis," Papers 1806.04363,
    7. Pawe{l} Fiedor, 2013. "Structural Changes on Warsaw's Stock Exchange: the end of Financial Crisis," Papers 1311.4230,

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