Abstract
The dynamic of social networks is driven by the interplay between diverse mechanisms that still challenge our theoretical and modelling efforts. Amongst them, two are known to play a central role in shaping the networks evolution, namely the heterogeneous propensity of individuals to i) be socially active and ii) establish a new social relationships with their alters. Here, we empirically characterise these two mechanisms in seven real networks describing temporal human interactions in three different settings: scientific collaborations, Twitter mentions, and mobile phone calls. We find that the individuals’ social activity and their strategy in choosing ties where to allocate their social interactions can be quantitatively described and encoded in a simple stochastic network modelling framework. The Master Equation of the model can be solved in the asymptotic limit. The analytical solutions provide an explicit description of both the system dynamic and the dynamical scaling laws characterising crucial aspects about the evolution of the networks. The analytical predictions match with accuracy the empirical observations, thus validating the theoretical approach. Our results provide a rigorous dynamical system framework that can be extended to include other processes shaping social dynamics and to generate data driven predictions for the asymptotic behaviour of social networks.
Highlights
We propose a dynamic network model, that generalises the recent modelling scheme of activity-driven-networks[23,50,55]
We considered five scientific collaborations networks obtained from five different journals (PRA, PRB, PRD, PRE, and PRL) of the American Physical Society (APS), one Twitter mentions network (TMN), and one mobile phone network (MPN)
We represent all datasets as time-varying networks, where each node describes an individual and each time-resolved link describes a social interaction
Summary
We propose a dynamic network model, that generalises the recent modelling scheme of activity-driven-networks[23,50,55]. We propose a general functional form for the social allocation mechanism, able to fit empirical observations in seven time-resolved datasets, describing three different types of social interactions: scientific collaborations, Twitter mentions, and mobile phone calls. We provide a thorough statistical characterisation of activity and formation of social ties in each network and we identify the basic parameters defining the dynamics of ties’ evolution. We observe, across all the datasets, that, the larger the degree, the smaller is the probability of creating a new tie Prompted by this statistical analysis, we study the Master Equation (ME) that describes the evolution of the network connectivity structure of the proposed model. The analytical solutions capture very well the empirical behaviour measured in all the analysed datasets They connect explicitly the evolution of social networks to the parameter regulating the emergence of social ties. The presented results have the potential to pave the way for a general asymptotic theory of the dynamics of social networks by progressively integrating further social mechanisms
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