title: Asymptotic theory of time-varying social networks with heterogeneous activity and tie allocation.
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.
authors: Institute for Scientific Interchange Foundation, 10126 Torino, Italy.|Dipartimento di Fisica e Scienza della Terra, Università di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy.|INFN, Gruppo Collegato di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy.
authors: Enrico
authors: E
authors: Ubaldi
authors: Centre for Business Network Analysis, University of Greenwich, Park Row, London SE10 9LS, United Kingdom.|Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston MA 02115 USA.
authors: Nicola
authors: N
authors: Perra
authors: Univ Lyon, ENS de Lyon, Inria, CNRS, UCB Lyon 1, LIP UMR 5668, IXXI, F-69342, Lyon, France.
authors: Márton
authors: M
authors: Karsai
authors: Dipartimento di Fisica e Scienza della Terra, Università di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy.|Centro S3, CNR-Istituto di Nanoscienze, Via Campi 213A, 41125 Modena Italy.
authors: Alessandro
authors: A
authors: Vezzani
authors: Dipartimento di Fisica e Scienza della Terra, Università di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy.|INFN, Gruppo Collegato di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy.
authors: Raffaella
authors: R
authors: Burioni
authors: Institute for Scientific Interchange Foundation, 10126 Torino, Italy.|Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston MA 02115 USA.
authors: Alessandro
authors: A
authors: Vespignani
mesh_terms: D000465:Algorithms; D040421:Cell Phone; D006801:Humans; D008962:Models, Theoretical; D012919:Social Behavior; D060756:Social Networking; D012944:Social Support