IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v380y2007icp601-610.html
   My bibliography  Save this article

Discrete scale invariance in scale free graphs

Author

Listed:
  • Graña, Matías
  • Pinasco, Juan Pablo

Abstract

In this work, we introduce an energy function in order to study finite scale free graphs generated with different models. The energy distribution has a fractal pattern and presents log periodic oscillations for high energies. These oscillations are related to a discrete scale invariance of certain graphs, that is, there are preferred scaling ratios suggesting a hierarchical distribution of node degrees. On the other hand, small energies correspond to graphs with evenly distributed degrees.

Suggested Citation

  • Graña, Matías & Pinasco, Juan Pablo, 2007. "Discrete scale invariance in scale free graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 601-610.
    • Handle: RePEc:eee:phsmap:v:380:y:2007:i:c:p:601-610
    DOI: 10.1016/j.physa.2007.02.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437107001665
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2007.02.047?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. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(2), pages 255-258, September.
    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. Fenner, Trevor & Levene, Mark & Loizou, George, 2010. "Predicting the long tail of book sales: Unearthing the power-law exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2416-2421.
    2. Rezvanian, Alireza & Meybodi, Mohammad Reza, 2015. "Sampling social networks using shortest paths," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 254-268.
    3. Rafael González-Val, 2012. "A Nonparametric Estimation of the Local Zipf Exponent for all US Cities," Environment and Planning B, , vol. 39(6), pages 1119-1130, December.
    4. Rafael González-Val, 2021. "The Probability Distribution of Worldwide Forest Areas," Sustainability, MDPI, vol. 13(3), pages 1-19, January.
    5. Rafael González‐Val, 2019. "Historical urban growth in Europe (1300–1800)," Papers in Regional Science, Wiley Blackwell, vol. 98(2), pages 1115-1136, April.
    6. Marcus Berliant & Hiroki Watanabe, 2015. "Explaining the size distribution of cities: Extreme economies," Quantitative Economics, Econometric Society, vol. 6(1), pages 153-187, March.
    7. Klabunde, Anna, 2014. "Computational Economic Modeling of Migration," Ruhr Economic Papers 471, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    8. Fenner, Trevor & Levene, Mark & Loizou, George, 2005. "A stochastic evolutionary model exhibiting power-law behaviour with an exponential cutoff," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 641-656.
    9. Peltonen, Tuomas A. & Scheicher, Martin & Vuillemey, Guillaume, 2014. "The network structure of the CDS market and its determinants," Journal of Financial Stability, Elsevier, vol. 13(C), pages 118-133.
    10. Mike, Szabolcs & Farmer, J. Doyne, 2008. "An empirical behavioral model of liquidity and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 200-234, January.
    11. Politi, Mauro & Scalas, Enrico, 2008. "Fitting the empirical distribution of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2025-2034.
    12. Fan Jiang & Niancai Liu, 2018. "The hierarchical status of international academic awards in social sciences," Scientometrics, Springer;Akadémiai Kiadó, vol. 117(3), pages 2091-2115, December.
    13. Bar-Ilan, Judit, 2008. "Informetrics at the beginning of the 21st century—A review," Journal of Informetrics, Elsevier, vol. 2(1), pages 1-52.
    14. Davide Provenzano, 2014. "Power laws and the market structure of tourism industry," Empirical Economics, Springer, vol. 47(3), pages 1055-1066, November.
    15. Aaron Clauset & Maxwell Young & Kristian Skrede Gleditsch, 2007. "On the Frequency of Severe Terrorist Events," Journal of Conflict Resolution, Peace Science Society (International), vol. 51(1), pages 58-87, February.
    16. Morales, R.V. & da Cunha, C.R. & Rambo, C.R., 2014. "A complex network approach for the growth of aerogels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 131-138.
    17. Mauro Politi & Nicolas Millot & Anirban Chakraborti, 2011. "The near-extreme density of intraday log-returns," Papers 1106.0039, arXiv.org.
    18. Ausloos, Marcel & Cerqueti, Roy & Lupi, Claudio, 2017. "Long-range properties and data validity for hydrogeological time series: The case of the Paglia river," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 39-50.
    19. Qianqian, Li & Yijun, Liu, 2020. "The China-Pakistan economic corridor: The Pakistani media attitudes perspective," Technology in Society, Elsevier, vol. 62(C).
    20. Soramäki, Kimmo & Bech, Morten L. & Arnold, Jeffrey & Glass, Robert J. & Beyeler, Walter E., 2007. "The topology of interbank payment flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 317-333.

    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:phsmap:v:380:y:2007:i:c:p:601-610. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.