Figure 7: Complex contagions on a London transit system.

(a) London transit network with N=2,217 nodes (that is, intersections), 2,854 roads⁵⁹ (which we interpret as geometric edges) and 15 metropolitan lines⁶⁰ (which we interpret as non-geometric edges). (b) Node activation times for a WTM contagion initialized with cluster seeding illustrate for small T that contagions quickly spread by skipping across the metro lines; this leads to ANC. (c) In contrast, for moderate T, the contagion spreads via slow WFP. (d) Although not all contagions exhibit such extreme sensitivity to T (see Supplementary Note 5), the dependence of ANC and WFP on T is captured by the geometry of WTM maps if one appropriately handles the activation times that are infinite (that is, nodes that never adopt the contagion). See the discussion in the text. The curves with symbols indicate the values of ρ for WTM maps (curves with symbols), and the horizontal dotted and dashed lines, respectively, indicate ρ for the mapping of nodes based on shortest-path distances (that is, as in the Isomap algorithm²²) and a two-dimensional Laplacian eigenmap²³.