Multiscale Analysis of Time Series of Graphs

Time series of graphs arise in a variety of applications, from the analysis of network traffic to time-dependent data sets to social networks. We introduce novel techniques for measuring distances between graphs in a multiscale fashion, in such a way that such distances reflect changes at different levels of granularity, are easily localized to regions of the graph, and, when considered at a fixed scale, are robust with respect to changes and finer scales. These distances, or similarity measures, are based on random walks on graphs at multiple time scales. We then employ these notions to analyze time series of graphs, and show that on simple models of graphs that possess a natural multiscale structure, our algorithms have desirable properties of sensitivity and robustness. Keywords— Multiscale analysis, spectral graph theory, dynamic graphs, random walks.