Endogenous Versus Exogenous Shocks in Complex Networks: an Empirical Test Using Book Sale Ranking

TL;DR

This study distinguishes between endogenous and exogenous shocks in complex networks by analyzing book sales data, revealing different signatures and relaxation patterns that suggest social networks operate near criticality.

Contribution

It provides an empirical method to classify shocks in complex systems and introduces a simple epidemic model to explain the observed signatures.

Findings

Exogenous shocks show abrupt peaks with power law relaxation.

Endogenous shocks exhibit gradual growth and symmetrical power law relaxation.

Sales dynamics are dominated by cascades, indicating near-critical social networks.

Abstract

Are large biological extinctions such as the Cretaceous/Tertiary KT boundary due to a meteorite, extreme volcanic activity or self-organized critical extinction cascades? Are commercial successes due to a progressive reputation cascade or the result of a well orchestrated advertisement? Determining the chain of causality for extreme events in complex systems requires disentangling interwoven exogenous and endogenous contributions with either no clear or too many signatures. Here, we study the precursory and recovery signatures accompanying shocks, that we test on a unique database of the Amazon sales ranking of books. 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 sale 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 slow 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.