Network inference from the timing of events in coupled dynamical systems.

Spreading phenomena like opinion formation or disease propagation often follow the links of some underlying network structure. While the effects of network topology on spreading efficiency have already been vastly studied, we here address the inverse problem of whether we can infer an unknown network structure from the timing of events observed at different nodes. For this purpose, we numerically investigate two types of event-based stochastic processes. On the one hand, a generic model of event propagation on networks is considered where the nodes exhibit two types of eventlike activity: spontaneous events reflecting mutually independent Poisson processes and triggered events that occur with a certain probability whenever one of the neighboring nodes exhibits any of these two kinds of events. On the other hand, we study a variant of the well-known SIRS model from epidemiology and record only the timings of state switching events of individual nodes, irrespective of the specific states involved. Based on simulations of both models on different prototypical network architectures, we study the pairwise statistical similarity between the sequences of event timings at all nodes by means of event synchronization and event coincidence analysis (ECA). By taking strong mutual similarities of event sequences (functional connectivity) as proxies for actual physical links (structural connectivity), we demonstrate that both approaches can lead to reasonable prediction accuracy. In general, sparser networks can be reconstructed more accurately than denser ones, especially in the case of larger networks. In such cases, ECA is shown to commonly exhibit the better reconstruction accuracy.