Time-series analysis of networks: Exploring the structure with random walks

We generate time series from scale-free networks based on a finite-memory random walk traversing the network. These time series reveal topological and functional properties of networks via their temporal correlations. Remarkably, networks with different node-degree mixing patterns exhibit distinct self-similar characteristics. In particular, assortative networks are transformed into time series with long-range correlation, while disassortative networks are transformed into time series exhibiting anticorrelation. These relationships are consistent across a diverse variety of real networks. Moreover, we show that multiscale analysis of these time series can describe and classify various physical networks ranging from social and technological to biological networks according to their functional origin. These results suggest that there is a unified dynamical mechanism that governs the structural organization of many seemingly different networks.