Abstract
Most systems can be represented as networks that couple a series of nodes to each other via one or more edges, with typically unknown equations governing their quantitative behaviour. A major question then pertains to the importance of each of the elements that act as system inputs in determining the output(s). We show that any such system can be treated as a 'communication channel' for which the associations between inputs and outputs can be quantified via a decomposition of their mutual information into different components characterizing the main effect of individual inputs and their interactions. Unlike variance-based approaches, our novel methodology can easily accommodate correlated inputs.