Classification of Temporal Graphs using Persistent Homology

Abstract: Temporal graphs effectively model dynamic systems by representing interactions as timestamped edges. However, analytical tools for temporal graphs are limited compared to static graphs. We propose a novel method for analyzing temporal graphs using Persistent Homology. Our approach leverages $\delta$-temporal motifs (recurrent subgraphs) to capture temporal dynamics %without aggregation . By evolving these motifs, we define the \textit{average filtration} and compute PH on the associated clique complex. This method captures both local and global temporal structures and is stable with respect to reference models. We demonstrate the applicability of our approach to the temporal graph classification task. Experiments verify the effectiveness of our approach, achieving over 92\% accuracy, with some cases reaching 100\%. Unlike existing methods that require node classes, our approach is node class free, offering flexibility for a wide range of temporal graph analysis.