Journal
NATURE COMMUNICATIONS
Volume 6, Issue -, Pages -Publisher
NATURE PORTFOLIO
DOI: 10.1038/ncomms8723
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Funding
- Eunice Kennedy Shriver National Institute of Child Health & Human Development of the National Institutes of Health [R01HD075712]
- National Science Foundation [DMS-1127914]
- Institute of Mathematics and its Applications
- European Commission FET-Proactive project PLEXMATH [317614]
- EPSRC [EP/J001759/1]
- EPSRC Fellowship [EP/K041096/1]
- King Abdullah University of Science and Technology [KUK-C1-013-04]
- SAMSI Low-Dimensional Structure in High-Dimensional Data workshop travel grant
- AMS Simons travel grant
- NSF [NSF-DMS-0915019, 1125174, 1248071]
- AFOSR
- DARPA
- EPSRC [EP/K041096/1, EP/J001759/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/J001759/1, EP/K041096/1] Funding Source: researchfish
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1125174, 1248071] Funding Source: National Science Foundation
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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 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.
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