IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v16y2014i3d10.1007_s11009-012-9311-x.html
   My bibliography  Save this article

Max-Plus Objects to Study the Complexity of Graphs

Author

Listed:
  • Cristiano Bocci

    (Università di Siena)

  • Luca Chiantini

    (Università di Siena)

  • Fabio Rapallo

    (Università del Piemonte Orientale)

Abstract

Given an undirected graph G, we define a new object H G , called the mp-chart of G, in the max-plus algebra. We use it, together with the max-plus permanent, to describe the complexity of graphs. We show how to compute the mean and the variance of H G in terms of the adjacency matrix of G and we give a central limit theorem for H G . Finally, we show that the mp-chart is easily tractable also for the complement graph.

Suggested Citation

  • Cristiano Bocci & Luca Chiantini & Fabio Rapallo, 2014. "Max-Plus Objects to Study the Complexity of Graphs," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 507-525, September.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:3:d:10.1007_s11009-012-9311-x
    DOI: 10.1007/s11009-012-9311-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-012-9311-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-012-9311-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    2. Silver, Jonathan & Slud, Eric & Takamoto, Keiji, 2002. "Statistical Equilibrium Wealth Distributions in an Exchange Economy with Stochastic Preferences," Journal of Economic Theory, Elsevier, vol. 106(2), pages 417-435, October.
    3. Garibaldi,Ubaldo & Scalas,Enrico, 2010. "Finitary Probabilistic Methods in Econophysics," Cambridge Books, Cambridge University Press, number 9780521515597.
    4. Marco Raberto & Fabio Rapallo & Enrico Scalas, 2011. "Semi-Markov Graph Dynamics," PLOS ONE, Public Library of Science, vol. 6(8), pages 1-13, August.
    5. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: I. Empirical facts," Post-Print hal-00621058, HAL.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kiran Sharma & Subhradeep Das & Anirban Chakraborti, 2017. "Global Income Inequality and Savings: A Data Science Perspective," Papers 1801.00253, arXiv.org, revised Aug 2018.
    2. Lallouache, Mehdi & Abergel, Frédéric, 2014. "Tick size reduction and price clustering in a FX order book," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 488-498.
    3. Peng Wu & Marcello Rambaldi & Jean-Franc{c}ois Muzy & Emmanuel Bacry, 2019. "Queue-reactive Hawkes models for the order flow," Papers 1901.08938, arXiv.org.
    4. Ioane Muni Toke & Nakahiro Yoshida, 2020. "Marked point processes and intensity ratios for limit order book modeling," Papers 2001.08442, arXiv.org.
    5. Guevara Hidalgo, Esteban, 2017. "Bin size independence in intra-day seasonalities for relative prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 722-732.
    6. A. O. Glekin & A. Lykov & K. L. Vaninsky, 2014. "On Simulation of Various Effects in Consolidated Order Book," Papers 1402.4150, arXiv.org.
    7. Hong Guo & Jianwu Lin & Fanlin Huang, 2023. "Market Making with Deep Reinforcement Learning from Limit Order Books," Papers 2305.15821, arXiv.org.
    8. Changtai Li & Weihong Huang & Wei-Siang Wang & Wai-Mun Chia, 2023. "Price Change and Trading Volume: Behavioral Heterogeneity in Stock Market," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 677-713, February.
    9. Moura, N.J. & Ribeiro, Marcelo B., 2013. "Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2088-2103.
    10. Pierre Gosselin & Aïleen Lotz & Marc Wambst, 2019. "A Statistical Field Approach to Capital Accumulation," Working Papers hal-02280634, HAL.
    11. Aleksejus Kononovicius & Julius Ruseckas, 2014. "Nonlinear GARCH model and 1/f noise," Papers 1412.6244, arXiv.org, revised Feb 2015.
    12. repec:hal:wpaper:hal-00777941 is not listed on IDEAS
    13. Sandrine Jacob Leal & Mauro Napoletano & Andrea Roventini & Giorgio Fagiolo, 2016. "Rock around the clock: An agent-based model of low- and high-frequency trading," Journal of Evolutionary Economics, Springer, vol. 26(1), pages 49-76, March.
    14. Xiaofei Lu & Frédéric Abergel, 2017. "Limit order book modelling with high dimensional Hawkes processes," Working Papers hal-01512430, HAL.
    15. Ben Hambly & Renyuan Xu & Huining Yang, 2021. "Recent Advances in Reinforcement Learning in Finance," Papers 2112.04553, arXiv.org, revised Feb 2023.
    16. Desislava Chetalova & Thilo A. Schmitt & Rudi Schafer & Thomas Guhr, 2013. "Portfolio return distributions: Sample statistics with non-stationary correlations," Papers 1308.3961, arXiv.org, revised Jun 2014.
    17. Andrea Giuseppe Di Iura & Giulia Terenzi, 2021. "A Bayesian analysis of gain-loss asymmetry," Papers 2104.06044, arXiv.org.
    18. Cem Çağrı Dönmez & Abdulkadir Atalan, 2019. "Developing Statistical Optimization Models for Urban Competitiveness Index: Under the Boundaries of Econophysics Approach," Complexity, Hindawi, vol. 2019, pages 1-11, November.
    19. Buonocore, R.J. & Aste, T. & Di Matteo, T., 2016. "Measuring multiscaling in financial time-series," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 38-47.
    20. Nicolas Huth & Frédéric Abergel, 2011. "High Frequency Lead/lag Relationships - Empirical facts," Working Papers hal-00645685, HAL.
    21. Julius Bonart & Martin D. Gould, 2017. "Latency and liquidity provision in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1601-1616, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:16:y:2014:i:3:d:10.1007_s11009-012-9311-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.