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Abstract
Adoption of innovations, products or online services is commonly interpreted as a spreading process driven to large extent by social influence and conditioned by the needs and capacities of individuals. To model this process one usually introduces behavioural threshold mechanisms, which can give rise to the 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 to rapid patterns. Here we fill this gap through the analysis and modelling of product adoption in the world’s largest voice over internet service, the social network of Skype. We provide empirical evidence about the heterogeneous distribution of fractional behavioural thresholds, which appears to be independent of the degree of adopting egos. We show that the structure of real-world adoption clusters is radically different from previous theoretical expectations, since vulnerable adoptions—induced by a single adopting neighbour—appear to be important only locally, while spontaneous adopters arriving at a constant rate and the involvement of unconcerned individuals govern the global emergence of social spreading.
Highlights
Matters, in complex contagion the fraction of adopting neighbours relative to the total number of partners determines whether a node adopts or not, capturing the natural mechanisms involved in individuals’ decision makings[21,22,23]
Our aim is to identify the crucial mechanisms necessary to consider in models of complex contagion to match them better with reality, and define a model that incorporates these mechanisms and captures the possible dynamics leading to the emergence of real-world global cascades
In order to avoid the effect of instantaneous group adoptions, we only consider links between nodes who are neighbours in the underlying social network and whose adoption did not happen at the same time
Summary
Matters, in complex contagion the fraction of adopting neighbours relative to the total number of partners determines whether a node adopts or not, capturing the natural mechanisms involved in individuals’ decision makings[21,22,23]. Besides the case of rapid cascading mentioned above, an example of the other extreme is the propagation of products in social networks[18], where adoption evolves gradually even if it is driven by threshold mechanisms and may cover a large fraction of the total population[21] This behaviour characterises the adoption of online services such as Facebook, Twitter, LinkedIn and Skype (Fig. 1a), since their yearly maximum relative growth of cumulative adoption[48] (for definition see Appendix) is lower than in the case of rapid cascades as suggested e.g. by the Watts threshold (WT) model. Model calculations and the analysis of the real social contagion process suggest that the evolving structure of an adoption cluster differs radically from what has been proposed earlier[9], since it is triggered by several spontaneous adoptions arriving at a constant rate, while stable adopters who are initially resisting exposure, are responsible for the emergence of global social adoption (Fig. 1b,c)
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