IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v108y2018icp94-103.html

Complexity and heterogeneity in a dynamic network

Author

Listed:
  • Lambert, David
  • Vanni, Fabio

Abstract

We present an approximate analytical solution for the connectivity of a network model with a “non-simultaneous” linking scheme. This model exhibits node-space correlations in the link distribution, anomalous fluctuations in the time series of the connectivity variable, and a finite-size effect: the maximum number of links occurs away from the critical value of the system parameter. We derive an exact Master Equation for this model in the form of an infinitesimal time-evolution operator. Fluctuations are much more important than the mean-field approximation predicts, which we attribute to the heterogeneity in the model. Finally, we give a sketch of possible real world applications where the value of a network is related to the number of links.

Suggested Citation

  • Lambert, David & Vanni, Fabio, 2018. "Complexity and heterogeneity in a dynamic network," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 94-103.
    • Handle: RePEc:eee:chsofr:v:108:y:2018:i:c:p:94-103
    DOI: 10.1016/j.chaos.2018.01.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918300249
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.01.024?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Nicola Jentzsch, 2006. "The Economics and Regulation of Financial Privacy," Contributions to Economics, Springer, number 978-3-7908-1738-6, March.
    2. Nimalan Arinaminpathy & Sujit Kapadia & Robert May, 2012. "Size and complexity in model financial systems," Bank of England working papers 465, Bank of England.
    3. Madureira, António & den Hartog, Frank & Bouwman, Harry & Baken, Nico, 2013. "Empirical validation of Metcalfe’s law: How Internet usage patterns have changed over time," Information Economics and Policy, Elsevier, vol. 25(4), pages 246-256.
    4. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497190, January.
    5. Charles I. Plosser, 2009. "Improving financial stability: a speech at the University of Chicago Booth School of Business, March 31, 2009," Speech 26, Federal Reserve Bank of Philadelphia.
    6. Shivakumar Jolad & Wenjia Liu & B Schmittmann & R K P Zia, 2012. "Epidemic Spreading on Preferred Degree Adaptive Networks," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-11, November.
    7. G. Dosi, 2012. "Economic Coordination and Dynamics: Some Elements of an Alternative “Evolutionary” Paradigm," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 12.
    8. Janet L. Yellen, 2013. "Interconnectedness and Systemic Risk: Lessons from the Financial Crisis and Policy Implications : a speech at the American Economic Association/American Finance Association Joint Luncheon, San Diego, ," Speech 631, Board of Governors of the Federal Reserve System (U.S.).
    9. Anna, Petrenko, . "Мaркування готової продукції як складова частина інформаційного забезпечення маркетингової діяльності підприємств овочепродуктового підкомплексу," Agricultural and Resource Economics: International Scientific E-Journal, Agricultural and Resource Economics: International Scientific E-Journal, vol. 2(01).
    10. Franklin Allen & Douglas Gale, 2000. "Financial Contagion," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 1-33, February.
    11. Giulio Bottazzi & Alessandro De Sanctis & Fabio Vanni, 2016. "Non-performing loans, systemic risk and resilience in financial networks," LEM Papers Series 2016/08, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    12. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497701, January.
    13. Johnson, Neil F. & Jefferies, Paul & Hui, Pak Ming, 2003. "Financial Market Complexity," OUP Catalogue, Oxford University Press, number 9780198526650.
    14. Fabio Vanni & Paolo Barucca, 2017. "Time evolution of an agent-driven network model," LEM Papers Series 2017/16, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    15. Gai, Prasanna & Haldane, Andrew & Kapadia, Sujit, 2011. "Complexity, concentration and contagion," Journal of Monetary Economics, Elsevier, vol. 58(5), pages 453-470.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fabio Vanni & Paolo Barucca, 2019. "Degree-correlations in a bursting dynamic network model," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(3), pages 663-695, September.

    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. David Lambert & Fabio Vanni, 2017. "Complexity and Heterogeneity in a Dynamic Network," LEM Papers Series 2017/22, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    2. Fang, Lei & Cheng, Jiang & Su, Fang, 2019. "Interconnectedness and systemic risk: A comparative study based on systemically important regions," Pacific-Basin Finance Journal, Elsevier, vol. 54(C), pages 147-158.
    3. Wiersema, Garbrand & Kleinnijenhuis, Alissa M. & Wetzer, Thom & Farmer, J. Doyne, 2023. "Scenario-free analysis of financial stability with interacting contagion channels," Journal of Banking & Finance, Elsevier, vol. 146(C).
    4. Roukny, Tarik & Battiston, Stefano & Stiglitz, Joseph E., 2018. "Interconnectedness as a source of uncertainty in systemic risk," Journal of Financial Stability, Elsevier, vol. 35(C), pages 93-106.
    5. Hałaj, Grzegorz, 2018. "System-wide implications of funding risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1151-1181.
    6. Silva, Walmir & Kimura, Herbert & Sobreiro, Vinicius Amorim, 2017. "An analysis of the literature on systemic financial risk: A survey," Journal of Financial Stability, Elsevier, vol. 28(C), pages 91-114.
    7. Giulio Bottazzi & Alessandro De Sanctis & Fabio Vanni, 2016. "Non-performing loans, systemic risk and resilience in financial networks," LEM Papers Series 2016/08, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    8. Toivanen, Mervi, 2013. "Contagion in the interbank network : An epidemiological approach," Research Discussion Papers 19/2013, Bank of Finland.
    9. Green, Christopher & Bai, Ye & Murinde, Victor & Ngoka, Kethi & Maana, Isaya & Tiriongo, Samuel, 2016. "Overnight interbank markets and the determination of the interbank rate: A selective survey," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 149-161.
    10. Shakya, Shasta, 2022. "Geographic networks and spillovers between banks," Journal of Corporate Finance, Elsevier, vol. 77(C).
    11. Goswami, Anindya & Rana, Nimit & Siu, Tak Kuen, 2022. "Regime switching optimal growth model with risk sensitive preferences," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    12. Charles L. Munson & Lan Luo & Xiaohui Huang, 2024. "Predictive Global Sensitivity Analysis: Foundational Concepts, Tools, and Applications," Foundations and Trends(R) in Technology, Information and Operations Management, now publishers, vol. 17(4), pages 235-339, March.
    13. Brunetti, Celso & Harris, Jeffrey H. & Mankad, Shawn & Michailidis, George, 2019. "Interconnectedness in the interbank market," Journal of Financial Economics, Elsevier, vol. 133(2), pages 520-538.
    14. Brett, Craig & Weymark, John A., 2016. "Voting over selfishly optimal nonlinear income tax schedules with a minimum-utility constraint," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 18-31.
    15. Gonzalez, Stéphane & Rostom, Fatma Zahra, 2022. "Sharing the global outcomes of finite natural resource exploitation: A dynamic coalitional stability perspective," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 1-10.
    16. Vits, Jeroen & Gelders, Ludo & Pintelon, Liliane, 2006. "Production process changes: A dynamic programming approach to manage effective capacity and experience," International Journal of Production Economics, Elsevier, vol. 104(2), pages 473-481, December.
    17. Cetina, Jill & Paddrik, Mark & Rajan, Sriram, 2018. "Stressed to the core: Counterparty concentrations and systemic losses in CDS markets," Journal of Financial Stability, Elsevier, vol. 35(C), pages 38-52.
    18. Rasch, Alexander & Wambach, Achim, 2009. "Internal decision-making rules and collusion," Journal of Economic Behavior & Organization, Elsevier, vol. 72(2), pages 703-715, November.
    19. Sawada, Hiroyuki & Yan, Xiu-Tian, 2004. "Application of Gröbner bases and quantifier elimination for insightful engineering design," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 67(1), pages 135-148.
    20. Caccioli, Fabio & Shrestha, Munik & Moore, Cristopher & Farmer, J. Doyne, 2014. "Stability analysis of financial contagion due to overlapping portfolios," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 233-245.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:chsofr:v:108:y:2018:i:c:p:94-103. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.