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

Dane Taylor, Florian Klimm, Heather A. Harrington, Miroslav Kramár, Konstantin Mischaikow, Mason A. Porter, Peter J. Mucha

    Research output: Contribution to journalArticlepeer-review

    40 Citations (Scopus)

    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.

    Original languageEnglish
    Article number7723
    JournalNature communications
    Volume6
    DOIs
    Publication statusPublished - 2015 Jul 21

    ASJC Scopus subject areas

    • Chemistry(all)
    • Biochemistry, Genetics and Molecular Biology(all)
    • Physics and Astronomy(all)

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