Synchronization waves in geometric networks

Abstract

We report synchronization of networked excitable nodes embedded in a metric space, where the connectivity properties are mostly determined by the distance between units. Such a high clustered structure, combined with the lack of long-range connections, prevents full synchronization, and yields, instead, the emergence of synchronization waves. We show that this regime is optimal for information transmission through the system, as it enhances the options of reconstructing the topology from the dynamics. Measurements of topological and functional centralities reveal, indeed, that the wave synchronization state allows to detect the most structurally relevant nodes from a single observation of the dynamics, without any a-priori information on the model equations ruling the evolution of the ensemble.