Spatiotemporal signal propagation in complex networks

A major achievement in the study of complex networks is the realization that diverse systems, from sub-cellular biology to social networks, exhibit universal topological characteristics. Yet, such universality does not naturally translate to the dynamics of these systems, as dynamic behaviour cannot be uniquely predicted from topology alone. Rather, it depends on the interplay of the network's topology with the dynamic mechanisms of interaction between the nodes. Hence, systems with similar structure may exhibit profoundly different dynamic behaviour. We therefore seek a general theoretical framework to help us systematically translate topological elements into their predicted dynamic outcome. Here, we offer such a translation in the context of signal propagation, linking the topology of a network to the observed spatiotemporal spread of perturbative signals across it, thus capturing the network's role in propagating local information. For a range of nonlinear dynamic models, we predict that the propagation rules condense into three highly distinctive dynamic regimes, characterized by the interplay between network paths, degree distribution and the interaction dynamics. As a result, classifying a system's intrinsic interaction mechanisms into the relevant dynamic regime allows us to systematically translate topology into dynamic patterns of information propagation.