This paper investigates the intricate relationship between predictability and reconstructability in complex systems using an information-theoretical approach. The authors quantify codependence between a random graph and a stochastic process using mutual information and uncertainty coefficients. Analytical and numerical methods are presented to evaluate these measures. A key finding is the identification of a duality where predictability and reconstructability can behave differently, even in an opposing manner, particularly when changing the number of steps in the process. The study provides evidence that this duality may exist in real-world networks near criticality.

Charles Murphy, Vincent Thibeault, Antoine Allard, Patrick Desrosiers