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Adoption of innovations, products or online services is commonly interpretedas a spreading process driven to large extent by social influence andconditioned by the needs and capacities of individuals. To model this processone usually introduces behavioural threshold mechanisms, which can give rise tothe evolution of global cascades if the system satisfies a set of conditions.However, these models do not address temporal aspects of the emerging cascades,which in real systems may evolve through various pathways ranging from slow torapid patterns. Here we fill this gap through the analysis and modelling ofproduct adoption in the world's largest voice over internet service, the socialnetwork of Skype. We provide empirical evidence about the heterogeneousdistribution of fractional behavioural thresholds, which appears to beindependent of the degree of adopting egos. We show that the structure ofreal-world adoption clusters is radically different from previous theoreticalexpectations, since vulnerable adoptions --induced by a single adoptingneighbour-- appear to be important only locally, while spontaneous adoptersarriving at a constant rate and the involvement of unconcerned individualsgovern the global emergence of social spreading.

Local cascades induced global contagion: How heterogeneous thresholds, exogenous effects, and unconcerned behaviour govern online adoption spreading