IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v378y2020ics0096300320301466.html
   My bibliography  Save this article

On the continuous-time limit of the Barabási–Albert random graph

Author

Listed:
  • Pachon, Angelica
  • Polito, Federico
  • Sacerdote, Laura

Abstract

We prove that, via an appropriate scaling, the degree of a fixed vertex in the Barabási–Albert model appeared at a large enough time converges in distribution to a Yule process. Using this relation we explain why the limit degree distribution of a vertex chosen uniformly at random (as the number of vertices goes to infinity), coincides with the limit distribution of the number of species in a genus selected uniformly at random in a Yule model (as time goes to infinity). To prove this result we do not assume that the number of vertices increases exponentially over time (linear rates). On the contrary, we retain their natural growth with a constant rate superimposing to the overall graph structure a suitable set of processes that we call the planted model and introducing an ad-hoc sampling procedure.

Suggested Citation

  • Pachon, Angelica & Polito, Federico & Sacerdote, Laura, 2020. "On the continuous-time limit of the Barabási–Albert random graph," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    • Handle: RePEc:eee:apmaco:v:378:y:2020:i:c:s0096300320301466
    DOI: 10.1016/j.amc.2020.125177
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320301466
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125177?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. Andreas Klaus & Shan Yu & Dietmar Plenz, 2011. "Statistical Analyses Support Power Law Distributions Found in Neuronal Avalanches," PLOS ONE, Public Library of Science, vol. 6(5), pages 1-12, May.
    2. Derek De Solla Price, 1976. "A general theory of bibliometric and other cumulative advantage processes," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 27(5), pages 292-306, 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. Sarah Shandera & Jes L Matsick & David R Hunter & Louis Leblond, 2021. "RASE: Modeling cumulative disadvantage due to marginalized group status in academia," PLOS ONE, Public Library of Science, vol. 16(12), pages 1-20, December.
    3. Smith, Dallas & Webb, Benjamin, 2019. "Hidden symmetries in real and theoretical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 855-867.
    4. Thor, Andreas & Marx, Werner & Leydesdorff, Loet & Bornmann, Lutz, 2016. "Introducing CitedReferencesExplorer (CRExplorer): A program for reference publication year spectroscopy with cited references standardization," Journal of Informetrics, Elsevier, vol. 10(2), pages 503-515.
    5. Perc, Matjaž, 2010. "Zipf’s law and log-normal distributions in measures of scientific output across fields and institutions: 40 years of Slovenia’s research as an example," Journal of Informetrics, Elsevier, vol. 4(3), pages 358-364.
    6. Loet Leydesdorff, 2015. "Can intellectual processes in the sciences also be simulated? The anticipation and visualization of possible future states," Scientometrics, Springer;Akadémiai Kiadó, vol. 105(3), pages 2197-2214, December.
    7. Cremonini, Marco, 2016. "Introducing serendipity in a social network model of knowledge diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 64-71.
    8. Martín-Martín, Alberto & Orduna-Malea, Enrique & Thelwall, Mike & Delgado López-Cózar, Emilio, 2018. "Google Scholar, Web of Science, and Scopus: A systematic comparison of citations in 252 subject categories," Journal of Informetrics, Elsevier, vol. 12(4), pages 1160-1177.
    9. Marcus Wagner, 2007. "The Link between Environmental Innovation, Patents, and Environmental Management," DRUID Working Papers 07-14, DRUID, Copenhagen Business School, Department of Industrial Economics and Strategy/Aalborg University, Department of Business Studies.
    10. Michel Zitt, 2015. "Meso-level retrieval: IR-bibliometrics interplay and hybrid citation-words methods in scientific fields delineation," Scientometrics, Springer;Akadémiai Kiadó, vol. 102(3), pages 2223-2245, March.
    11. Todd Zorick & Mark A Mandelkern, 2013. "Multifractal Detrended Fluctuation Analysis of Human EEG: Preliminary Investigation and Comparison with the Wavelet Transform Modulus Maxima Technique," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-7, July.
    12. Thelwall, Mike & Fairclough, Ruth, 2015. "The influence of time and discipline on the magnitude of correlations between citation counts and quality scores," Journal of Informetrics, Elsevier, vol. 9(3), pages 529-541.
    13. Guillermo Armando Ronda-Pupo, 2017. "The effect of document types and sizes on the scaling relationship between citations and co-authorship patterns in management journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 110(3), pages 1191-1207, March.
    14. Guillermo Armando Ronda-Pupo, 2020. "The performance of Latin American research on economics & business," Scientometrics, Springer;Akadémiai Kiadó, vol. 122(1), pages 573-590, January.
    15. Matthew O. Jackson & Brian W. Rogers & Yves Zenou, 2017. "The Economic Consequences of Social-Network Structure," Journal of Economic Literature, American Economic Association, vol. 55(1), pages 49-95, March.
    16. Michael P. Leung, 2022. "Dependence‐robust inference using resampled statistics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 270-285, March.
    17. Miia Bask, 2011. "Cumulative Disadvantage and Connections Between Welfare Problems," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 103(3), pages 443-464, September.
    18. Tol, Richard S.J., 2013. "The Matthew effect for cohorts of economists," Journal of Informetrics, Elsevier, vol. 7(2), pages 522-527.
    19. Fetta, A.G. & Harper, P.R. & Knight, V.A. & Vieira, I.T. & Williams, J.E., 2012. "On the Peter Principle: An agent based investigation into the consequential effects of social networks and behavioural factors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(9), pages 2898-2910.
    20. Thelwall, Mike, 2018. "Do females create higher impact research? Scopus citations and Mendeley readers for articles from five countries," Journal of Informetrics, Elsevier, vol. 12(4), pages 1031-1041.

    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:apmaco:v:378:y:2020:i:c:s0096300320301466. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.