Complex contagions for topological data analysis of networks
Year: 2014
Type: preprint
Abstract: Social and biological contagions are often strongly influenced by the spatial embeddedness of networks. In some cases, such as in the Black Death, they can spread as a wave through space. In many modern contagions, however, long-range edges -- e.g., due to airline transportation or communication media -- allow clusters of a contagion to arise in distant locations. We study these competing phenomena for the Watts threshold model (WTM) of complex contagions on empirical and synthetic geometric networks, which are networks that are embedded in a manifold and which consist of both short-range and long-range, noisy edges. Our approach involves using the WTM to construct contagion maps that use multiple contagions to map the nodes as a point cloud, which we analyze using tools from high-dimensional data analysis and computational homology. For contagions that predominantly exhibit wavefront propagation, we identify a geometric network's underlying manifold in the point cloud, highlighting our approach as a tool for inferring low-dimensional structure. Our approach makes it possible to obtain insights to aid in the modeling, forecast, and control of spreading processes, and it simultaneously leads to a novel technique for manifold learning in geometric networks.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1912624343