A large variety of complex systems in ecology, climate science, biomedicine, and engineering have been observed to exhibit so-called tipping points, where the dynamical state of the system abruptly changes. Typical examples are the rapid transition in lakes from clear to turbid conditions or the sudden extinction of species after a slightly change of environmental conditions. Data and models suggest that detectable warning signs may precede some, though clearly not all, of these drastic events. This view is also corroborated by recently developed abstract mathematical theory for systems, where processes evolve at different rates and are subject to internal and/or external stochastic perturbations.
One main idea to derive warning signs is to monitor the fluctuations of the dynamical process by calculating the variance of a suitable monitoring variable. When the tipping point is approached via a slowly-drifting parameter, the stabilizing effects of the system slowly diminish and the noisy fluctuations increase via certain well-defined scaling laws.
Based upon these observations, it is natural to ask, whether these scaling laws are also present in human social networks and can allow us to make predictions about future events. This is an exciting open problem, to which at present only highly speculative answers can be given. It is indeed to predict a priori unknown events in a social system. Therefore, as an initial step, we try to reduce the problem to a much simpler problem to understand whether the same mechanisms, which have been observed in the context of natural sciences and engineering, could also be present in sociological domains.
In our work, we provide a very first step towards tackling a substantially simpler question by focusing on a priori known events. We analyse a social media data set with a focus on classical variance and autocorrelation scaling law warning signs. In particular, we consider a few events, which are known to occur on a specific time of the year, e.g., Christmas, Halloween, and Thanksgiving. Then we consider time series of the frequency of Twitter hashtags related to the considered events a few weeks before the actual event, but excluding the event date itself and some time period before it.
Now suppose we do not know that a dramatic spike in the number of Twitter hashtags, such as #xmas or #thanksgiving, will occur on the actual event date. Are there signs of the same stochastic scaling laws observed in other dynamical systems visible some time before the event? The more fundamental question is: Are there similarities to known warning signs from other areas also present in social media data?
We answer this question affirmatively as we find that the a priori known events mentioned above are preceded by variance and autocorrelation growth (see Figure). Nevertheless, we are still very far from actually using social networks to predict the occurrence of many other drastic events. For example, it can also be shown that many spikes in Twitter activity are not predictable through variance and autocorrelation growth. Hence, a lot more research is needed to distinguish different dynamical processes that lead to large outburst of activity on social media.
The findings suggest that further investigations of dynamical processes in social media would be worthwhile. Currently, a main focus in the research on social networks lies on structural questions, such as: Who connects to whom? How many connections do we have on average? Who are the hubs in social media? However, if one takes dynamical processes on the network, as well as the changing dynamics of the network topology, into account, one may obtain a much clearer picture, how social systems compare and relate to classical problems in physics, chemistry, biology and engineering.