Mapping stochastic processes onto complex networks

We introduce a method by which stochastic processes are mapped onto complex networks. As examples, we construct the networks for such time series as those for free-jet and low-temperature helium turbulence, the German stock market index (the DAX), and the white noise. The networks are further studied by contrasting their geometrical properties, such as the mean-length, diameter, clustering, average number of connection per node. By comparing the network properties of the investigated original time series with those for the shuffled and surrogate series, we are able to quantify the effect of the long-range correlations and the fatness of the probability distribution functions of the series on the constructed networks. Most importantly, we demonstrate that the time series can be reconstructed with high precisions by a simple random walk on their corresponding networks.