From the difference of structures to the structure of the difference

Abstract: When dealing with evolving or multi-dimensional complex systems, network theory provides with elegant ways of describing their constituting components, through respectively time-varying and multi-layer complex networks. Nevertheless, the analysis of how these components are related is still an open problem. We here propose a framework for analysing the evolution of a (complex) system, by describing the structure created by the difference between multiple networks by means of the Information Content metric. As opposed to other approaches, as for instance the use of global overlap or entropies, the proposed one allows to understand if the observed changes are due to random noise, or to structural (targeted) modifications. We validate the framework by means of sets of synthetic networks, as well as networks representing real technological, social and biological evolving systems. We further propose a way of reconstructing network correlograms, which allow to convert the system's evolution to the frequency domain.