IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v80y2018i1d10.1007_s13171-017-0116-4.html
   My bibliography  Save this article

Phase Transition in Inhomogenous Erdős-Rényi Random Graphs via Tree Counting

Author

Listed:
  • Ghurumuruhan Ganesan

    (New York University)

Abstract

Consider the complete graph K n on n vertices where each edge e is independently open with probability p n (e) or closed otherwise. The edge probabilities are not necessarily same but are close to some positive constant C. The resulting random graph G is in general inhomogenous and we use a tree counting argument to establish phase transition in the following sense: For C 1, with high probability, there is at least one giant component and every component is either small or giant. For C > 8, with positive probability, the giant component is unique and every other component is small. An important consequence of our method is that we directly obtain the fraction of vertices present in the giant component in the form of an infinite series.

Suggested Citation

  • Ghurumuruhan Ganesan, 2018. "Phase Transition in Inhomogenous Erdős-Rényi Random Graphs via Tree Counting," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 1-27, February.
    • Handle: RePEc:spr:sankha:v:80:y:2018:i:1:d:10.1007_s13171-017-0116-4
    DOI: 10.1007/s13171-017-0116-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-017-0116-4
    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/s13171-017-0116-4?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.

    Citations

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


    Cited by:

    1. Ganesan, Ghurumuruhan, 2021. "Deviation estimates for Eulerian edit numbers of random graphs," Statistics & Probability Letters, Elsevier, vol. 171(C).

    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:sankha:v:80:y:2018:i:1:d:10.1007_s13171-017-0116-4. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.