Burstiness and tie activation strategies in time-varying social networks

Enrico Ubaldi,Márton Karsai,Nicola Perra,Alessandro Vezzani,Raffaella Burioni

doi:10.1038/srep46225

Abstract

The recent developments in the field of social networks shifted the focus from static to dynamical representations, calling for new methods for their analysis and modelling. Observations in real social systems identified two main mechanisms that play a primary role in networks’ evolution and influence ongoing spreading processes: the strategies individuals adopt when selecting between new or old social ties, and the bursty nature of the social activity setting the pace of these choices. We introduce a time-varying network model accounting both for ties selection and burstiness and we analytically study its phase diagram. The interplay of the two effects is non trivial and, interestingly, the effects of burstiness might be suppressed in regimes where individuals exhibit a strong preference towards previously activated ties. The results are tested against numerical simulations and compared with two empirical datasets with very good agreement. Consequently, the framework provides a principled method to classify the temporal features of real networks, and thus yields new insights to elucidate the effects of social dynamics on spreading processes.

Highlights

The recent availability of longitudinal and time-resolved datasets capturing social behaviour has induced a paradigm shift in the way we study, describe, and model the interactions between individuals
In order to capture this bursty nature of human dynamics, we impose that the inter-event time τi for node i is drawn from a power-law distribution Ψ(τi): Ψ(τi)
We solved the master equation (ME) of the model in the large time regime and in unsaturated degree approximation1 k N, analytically exploring a complex phase space, where changes in the relative importance between the two mechanisms are linked to different degree distributions and emerging dynamics

Summary

Introduction

The recent availability of longitudinal and time-resolved datasets capturing social behaviour has induced a paradigm shift in the way we study, describe, and model the interactions between individuals. It moved the focus from static, time-aggregated, representations to time-varying, dynamical, characterisations of social networks. Thinking in terms of time-varying systems allows to overcome the limitations arising from the depiction of social ties as fixed and immutable in time2,3 It allows to capture a set of complex dynamics driving the evolution of links and to uncover the effects of such dynamics on processes unfolding on the networks’ fabrics Such a framework would allow for the analytical characterization on how the interplay www.nature.com/scientificreports/

Methods

Results

Conclusion