Time series of graphs arise in many branches of sciences and applications. We discuss novel techniques for measuring distances between graphs, based on multiscale analysis of random walks, in a way that is both sensitive to localized changes and robust to ``noisy'' perturbations of the graph. From this we derive a framework for analyzing time series of graphs, together with fast algorithms. Finally, we discuss applications to families of graphs with multiscale structure, as well as real data mapped to dynamic graphs.