Spreading Processes on Networks
In the last decades, the mechanisms for the spread of epidemics and ideas around the world have changed. Previously, they spread as a wavefront across parts of the Earth's surface. Now, due to the presence of airline transportation and communication media, clusters of contagion can suddenly appear in distant locations. We investigated how the spreading of multiple contagions on a network can be used to understand properties of the underlying network, such as the structure of the manifold on which the nodes of the network are embedded, as well as the structure of the long-range connections [1]. These insights could improve spreading processes' modeling, forecasting, and control. The methods that we developed can also be used for dimension reduction and manifold learning.
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D. Taylor, F. Klimm, H.A. Harrington, M. Kramar, K Mischaikow, M.A. Porter and P.J. Mucha
Topological data analysis of contagion maps for examining spreading processes on networks
Nature Communications, 6 (2015).