Complex contagion on noisy geometric networks

The study of contagion on networks is central to our understanding of collective social processes and epidemiology. However, for networks arising from an underlying manifold such as the Earth¿s surface, it remains unclear the extent to which the dynamics will reflect this inherent structure, especially when long-range, ¿noisy¿ edges are present. We study the Watts threshold model (WTM) for complex contagion on noisy geometric networks ¿ a generalization of small world networks in which nodes are embedded on a manifold. To study the extent to which contagion adheres to the manifold versus the network, which can greatly disagree on notions such as node-to-node distance, we present WTM-maps that embed the network nodes as a point cloud for which we study the geometry, topology, and intrinsic dimensionality. Interestingly, this work bridges several research disciplines by aligning the pursuits of network science and epidemiology with those of manifold learning and dimension reduction.