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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
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    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. 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.

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