Scaling of noisy fluctuations in complex networks and applications to network prediction

We study the collective dynamics of oscillator-network systems in the presence of noise. By focusing on the time-averaged fluctuation of dynamical variable of interest about the mean field, we discover a scaling law relating the average fluctuation to the node degree. The scaling law is quite robust as it holds for a variety of network topologies and node dynamics. Analyses and numerical support for different types of networks and node dynamics are provided. We also point out an immediate application of the scaling law: predicting complex networks based on time series only, and we articulate how this can be done.