Figure 1: Structure and dynamics of online service adoption.

(a) Yearly maximum relative growth rate (RGR) of cumulative adoption (see Appendix) for several online social-communication services⁴⁸, including three Skype paid services (s1 - “subscription”, s2 - “voicemail”, and s3 - “buy credit”). The red bar corresponds to a rapid cascade of adoption suggested by the Watts threshold (WT) model, while the green bar is the model prediction for Skype s3. (b,c) Snowball sample of the Skype social network (gray links) with nodes and links coloured according to their adoption state: multiple innovators (green nodes), induced small vulnerable trees (red nodes and links), and the triggered connected stable cluster (blue nodes and links). Note that some vulnerable and stable clusters seemingly appear without an innovator seed due to the finite distance used in the snowball sampling method. (d) Degree distribution P(k) of the Skype network (gray/blue circles for raw/binned data) on double log-scale with arbitrary base n. P(k) is fitted by a lognormal distribution (see Appendix and SI) with parameters μ_D = 1.2 and σ_D = 1.39, and average z = 8.56 (red line). (e) Distribution P(Φ_k) of integer thresholds Φ_k for several degree groups in Skype s3 (inset). By using P(Φ_k, k) = kP(Φ_k/k), these curves collapse to a master curve approximated by a lognormal function (dashed line in main panel) with parameters μ_T = −2 and σ_T = 1, as constrained by the average threshold w = 0.19 (see Appendix and SI). (f) Adoption rate of innovators [R_i(t)], vulnerable nodes [R_v(t)], and stable nodes [R_s(t)], as well as net service adoption rate [R(t)]. Rates are measured with a 1-month time window, while q and τ are arbitrary constants. The shaded area indicates the regime where innovators adopt approximately with constant rate.