Before revision:  To validate our approach, we examine the stability of these metric spaces by performing a comparative analysis of topological and metric space features under perturbations. Finally, we conduct several case studies on real world data sets and show how our method can find cyclic patterns, deviations from those patterns, and one-time events in time-varying graphs  .
After revision:  To validate our approach, we conduct several case studies on real world data sets and show how our method can find cyclic patterns, deviations from those patterns, and one-time events in time-varying graphs .