Wu, Haochen; Ryan G. James; James P. Crutchfield and Raissa M. D’Souza

Many natural, engineered, and social systems can be represented using the framework of a layered network, where each layer captures a different type of interaction between the same set of nodes. The study of such multiplex networks is a vibrant area of research. Yet, understanding how to quantify the correlations present between pairs of layers, and more so present in their co-evolution, is lacking. Such methods would enable us to address fundamental questions involving issues such as function, redundancy and potential disruptions. Here we show first how the edge-set of a multiplex network can be used to construct an estimator of a joint probability distribution describing edge existence over all layers. We then adapt an information-theoretic measure of general correlation called the conditional mutual information, which uses the estimated joint probability distribution, to quantify the pair-wise correlations present between layers. The pair-wise comparisons can also be temporal, allowing us to identify if knowledge of a certain layer can provide additional information about the evolution of another layer. We analyze datasets from three distinct domains—economic, political, and airline networks—to demonstrate how pair-wise correlation in structure and dynamical evolution between layers can be identified and show that anomalies can serve as potential indicators of major events such as shocks.