Temporal network analysis using zigzag persistence

Abstract This work presents a framework for studying temporal networks using zigzag persistence, tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to wide variety time-varying graphs. For example, these graphs may correspond system modeled as network with edges whose weights are functions time, or they represent time series complex dynamical system. We use simplicial complexes snapshots that can then be analyzed persistence. show two applications our method dynamic networks: an analysis commuting trends on multiple scales, e.g., daily weekly, in Great Britain transportation network, detection periodic/chaotic transitions due intermittency systems represented by ordinal partition networks. Our findings zero- one-dimensional persistence diagrams detect changes networks’ shapes missed traditional connectivity centrality graph statistics.