Modelling complex contagion with tie heterogeneities

Social influence, the effect that the past behaviour of acquaintances has on our daily decisions, is arguably the main driving mechanism of many complex collective phenomena in society, including the spreading of innovations, ideas and fads, or the growth of political and social movements. Many of these processes have been studied empirically in the past, particularly with regards to the existence of so-called adoption cascades, where large number of people adopt the same behaviour in a relatively short time. Moreover, they have been modelled either as simple contagion (where adoption is driven by independent contagion stimuli, like the Bass model of innovation diffusion), or as complex contagion (where a threshold on the number of adopting neighbours in a network determines spreading, like the Watts model of adoption cascades). However, it is still unclear whether real spreading phenomena is regulated by simple or complex contagion (or a combination of both), which makes it difficult to identify cognitive and social mechanisms that may control the collective action of large groups of people. Furthermore, most spreading models disregard one relevant property of real social networks, namely tie heterogeneities in terms of social influence.Influence arriving on social ties may vary from neighbour to neighbour, as it largely dependson the nature and frequency of interaction with a given friend.

 

Here we close this gap on the understanding of social contagion by extending the conventional Watts cascade model to account for tie heterogeneities. We focus on the case of a bimodal weight distribution, such that spreading is determined by the adoption threshold of nodes and the standard deviation of tie weights. We find that the presence of tie heterogeneities induce unexpected dynamical behaviour, as they either speed up or slow down contagion with respect to the unweightedcase, depending on the adoption threshold and weight standard deviation. We found this effect to be present in both synthetic and real social networks, which we verify via numerical simulations and an analytical approach based on approximate master equations. Moreover, we find that our model with tie heterogeneities bridges the theoretical descriptions of simple and complex contagion, and thus hints at the existence of a single mechanism driving social spreading, regardless of the initial hypotheses used to describe contagion stimuli between individuals. These results may be instrumental in developing more accurate spreading models that manage to gauge the rise and extent of real behavioural cascades in society.