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

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 Added by Dane Taylor
 Publication date 2014
and research's language is English




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Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earths 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 analyzing the topology, geometry, and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modeling, forecast, and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.



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