Uncovering evolutionary ages of nodes in complex networks

In a complex network, different groups of nodes may have existed for different amounts of time. To detect the evolutionary history of a network is of great importance. We present a spectral-analysis based method to address this fundamental question in network science. In particular, we find that there are complex networks in the real-world for which there is a positive correlation between the eigenvalue magnitude and node age. In situations where the network topology is unknown but short time series measured from nodes are available, we suggest to uncover the network topology at the present (or any given time of interest) by using compressive sensing and then perform the spectral analysis. Knowledge of ages of various groups of nodes can provide significant insights into the evolutionary process underpinning the network. It should be noted, however, that at the present the applicability of our method is limited to the networks for which information about the node age has been encoded gradually in the eigen-properties through evolution.