Critical transitions in social network activity

Abstract

A large variety of complex systems in ecology, climate science, biomedicine and engineering have been observed to exhibit tipping points, where the dynamical state of the system abruptly changes. For example, such critical transitions may result in the sudden change of ecological environments and climate conditions. Data and models suggest that detectable warning signs may precede some of these drastic events. This view is also corroborated by abstract mathematical theory for generic bifurcations in stochastic multi-scale systems. Whether such stochastic scaling laws used as warning signs for a priori unknown events in society are present in social networks is an exciting open problem, to which at present only highly speculative answers can be given. Here, we instead provide a first step towards tackling a simpler question by focusing on a priori known events and analyse a social media data set with a focus on classical variance and autocorrelation warning signs. Our results thus pertain to one absolutely fundamental question: Can the stochastic warning signs known from other areas also be detected in large-scale social media data? We answer this question affirmatively as we find that several a priori known events are preceded by variance and autocorrelation growth. Our findings thus clearly establish the necessary starting point to further investigate the relationship between abstract mathematical theory and various classes of critical transitions in social networks.