Inferring the underlying multivariate structure from bivariate networks with highly correlated nodes

Complex systems are often described mathematically as networks. Inferring the actual interactions from observed dynamics of the nodes of the networks is a challenging inverse task. It is crucial to distinguish direct and indirect interactions to allow for a robust identification of the underlying network. If strong and weak links are simultaneously present in the observed network, typical multivariate approaches to address this challenge fail. By means of correlation and partial correlation, we illustrate the challenges that arise and demonstrate how to overcome these. The challenge of strong and weak links translates into ill-conditioned matrices that need to be inverted to obtain the partial correlations, and therefore the correct network topology. Our novel procedure enables robust identification of multivariate network topologies in the presence of highly correlated processes. In applications, this is crucial to avoid erroneous conclusions about network structures and characteristics. Our novel approach applies to other types of interaction measures between processes in a network.