Endogenous Versus Exogenous Shocks in Complex Networks: An Empirical Test Using Book Sale Rankings

We study the precursory and recovery signatures accompanying shocks in complex networks, that we test on a unique database of the Amazon.com ranking of book sales. We find clear distinguishing signatures classifying two types of sales peaks. Exogenous peaks occur abruptly and are followed by a power law relaxation, while endogenous peaks occur after a progressively accelerating power law growth followed by an approximately symmetrical power law relaxation which is slower than for exogenous peaks. These results are rationalized quantitatively by a simple model of epidemic propagation of interactions with long memory within a network of acquaintances. The observed relaxation of sales implies that the sales dynamics is dominated by cascades rather than by the direct effects of news or advertisements, indicating that the social network is close to critical.