IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v125y2015i11p4154-4177.html
   My bibliography  Save this article

Asymptotic structure and singularities in constrained directed graphs

Author

Listed:
  • Aristoff, David
  • Zhu, Lingjiong

Abstract

We study the asymptotics of large directed graphs, constrained to have certain densities of edges and/or outward p-stars. Our models are close cousins of exponential random graph models, in which edges and certain other subgraph densities are controlled by parameters. We find that large graphs have either uniform or bipodal structure. When edge density (resp. p-star density) is fixed and p-star density (resp. edge density) is controlled by a parameter, we find phase transitions corresponding to a change from uniform to bipodal structure. When both edge and p-star density are fixed, we find only bipodal structures and no phase transition.

Suggested Citation

  • Aristoff, David & Zhu, Lingjiong, 2015. "Asymptotic structure and singularities in constrained directed graphs," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4154-4177.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:11:p:4154-4177
    DOI: 10.1016/j.spa.2015.06.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030441491500143X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2015.06.004?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. Yin, Mei & Zhu, Lingjiong, 2016. "Reciprocity in directed networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 71-84.

    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:spapps:v:125:y:2015:i:11:p:4154-4177. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.