IDEAS home Printed from https://ideas.repec.org/a/nat/natcom/v6y2015i1d10.1038_ncomms8723.html
   My bibliography  Save this article

Topological data analysis of contagion maps for examining spreading processes on networks

Author

Listed:
  • Dane Taylor

    (Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, North Carolina 27709, USA
    Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina, Chapel Hill)

  • Florian Klimm

    (Potsdam Institute for Climate Impact Research
    Humboldt-Universität zu Berlin
    Mathematical Institute, University of Oxford)

  • Heather A. Harrington

    (Mathematical Institute, University of Oxford)

  • Miroslav Kramár

    (Rutgers, The State University of New Jersey)

  • Konstantin Mischaikow

    (Rutgers, The State University of New Jersey
    BioMaPS Institute, Rutgers, The State University of New Jersey)

  • Mason A. Porter

    (Mathematical Institute, University of Oxford
    CABDyN Complexity Centre, University of Oxford)

  • Peter J. Mucha

    (Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina, Chapel Hill)

Abstract

Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth’s surface; however, in modern contagions long-range edges—for example, due to airline transportation or communication media—allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct ‘contagion maps’ that use multiple contagions on a network to map the nodes as a point cloud. By analysing the topology, geometry and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modelling, forecast and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.

Suggested Citation

  • Dane Taylor & Florian Klimm & Heather A. Harrington & Miroslav Kramár & Konstantin Mischaikow & Mason A. Porter & Peter J. Mucha, 2015. "Topological data analysis of contagion maps for examining spreading processes on networks," Nature Communications, Nature, vol. 6(1), pages 1-11, November.
  • Handle: RePEc:nat:natcom:v:6:y:2015:i:1:d:10.1038_ncomms8723
    DOI: 10.1038/ncomms8723
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/ncomms8723
    File Function: Abstract
    Download Restriction: no

    File URL: https://libkey.io/10.1038/ncomms8723?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
    ---><---

    Citations

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


    Cited by:

    1. Li, Yan & Jiang, Xiong-Fei & Tian, Yue & Li, Sai-Ping & Zheng, Bo, 2019. "Portfolio optimization based on network topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 671-681.
    2. Krishnagopal, Sanjukta & Bianconi, Ginestra, 2023. "Topology and dynamics of higher-order multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. M Ulmer & Lori Ziegelmeier & Chad M Topaz, 2019. "A topological approach to selecting models of biological experiments," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-18, March.

    More about this item

    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:nat:natcom:v:6:y:2015:i:1:d:10.1038_ncomms8723. 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.nature.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.