Reconstruction of dynamic networks with time-delayed interactions in the presence of fast-varying noises.

Most complex social, biological and technological systems can be described by dynamic networks. Reconstructing network structures from measurable data is a fundamental problem in almost all interdisciplinary fields. Network nodes interact with each other and those interactions often have diversely distributed time delays. Accurate reconstruction of any targeted interaction to a node requires measured data of all its neighboring nodes together with information on the time delays of interactions from these neighbors. When networks are large, these data are often not available and time-delay factors are deeply hidden. Here we show that fast-varying noise can be of great help in solving these challenging problems. By computing suitable correlations, we can infer the intensity and time delay of any targeted interaction with the data of two related nodes (driving and driven nodes) only while all other nodes in the network are hidden. This method is analytically derived and fully justified by extensive numerical simulations.