Figure 3: Empirical cluster statistics and simulation results.
(a) Empirical connected-component size distribution at different times for the adoption [P(sa), main panel] and stable adoption [P(ss), inset] networks, with sa and ss relative to system size. (b) Empirical connected-component size distribution P(sv) for the relative size of innovator-induced vulnerable trees at different times. (c) Average size of the largest (LC) and 2nd largest (LC2nd) components of the model network (‘Net’), adoption network (‘Casc’), stable network (‘Stab’), and induced vulnerable trees (‘Vuln’) as a function of r. Dashed lines show the observed relative size of the real LC of the adopter network in 2011 [see main panel in (a)] and the predicted r value. (d) Distribution P(d) of depths of induced vulnerable trees in both data and model for several r values, showing a good fit with the data for r = 0.73. The difference in the tail is due to finite-size effects. (e) Correlation 〈sv〉(k) between innovator degree and average size of vulnerable trees in both data and model with the same r values as in (e). Model calculations for (d,e) correspond to networks of size N = 106 and are averaged over 102 realisations.
