Robust dynamic classes revealed by measuring the response function of a social system

Abstract

We study the relaxation response of a social system after endogenous and exogenous bursts of activity using the time series of daily views for nearly 5 million videos on YouTube. We find that most activity can be described accurately as a Poisson process. However, we also find hundreds of thousands of examples in which a burst of activity is followed by an ubiquitous power-law relaxation governing the timing of views. We find that these relaxation exponents cluster into three distinct classes and allow for the classification of collective human dynamics. This is consistent with an epidemic model on a social network containing two ingredients: a powerlaw distribution of waiting times between cause and action and an complex systems | human dynamics U ncovering rules governing collective human behavior is a difficult task because of the myriad of factors that influence an individual's decision to take action. Investigations into the timing of individual activity, as a basis for understanding more complex collective behavior, have reported statistical evidence that human actions range from random (1) to highly correlated (2). Although most of the time, the aggregated dynamics of our individual activities create seasonal trends or simple patterns, sometimes our collective action results in blockbusters, best sellers, and other large-scale trends in financial and cultural markets.Here, we attempt to understand this nontrivial herding by investigating how the distribution of waiting times describing individuals' activity (3) is modified by the combination of interactions (4) and external influences in a social network. This is achieved by measuring the response function of a social system (5) and distinguishing whether a burst of activity was the result of a cumulative effect of small endogenous factors or, instead, the response to a large exogenous perturbation. Looking for endogenous and exogenous signatures in complex systems provides a useful framework for understanding many complex systems and has been successfully applied in several other contexts (6).As an illustration of this distinction in a social system, consider the example of trends in queries on internet search engines (http://trends.google.com) in Fig. 1, which shows the remarkable differences in the dynamic response of a social network to major social events. For the "exogenous" catastrophic Asian tsunami of December 26th, 2004, we see that the social network responded suddenly. In contrast, the search activity surrounding the release of a Harry Potter movie has the more "endogenous" signature generated by word of mouth, with significant precursory growth and an almost symmetric decay of interest after the release. In both "endo" and "exo" cases, there is a significant burst of activity. However, we expect to be able to distinguish the post peak relaxation dynamics on account of the very different processes that resulted in the bursts. Furthermore, we expect the relaxation process to depend on the interest of the population because this will influence t...

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