Understanding and Predicting Links in Graphs: A Persistent Homology Perspective

Abstract: Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data items (nodes) is an essential means of characterizing their properties. In this paper, we propose the use of persistent homology methods to capture structural and topological properties of graphs and use it to address the problem of link prediction. We evaluate our approach on seven different real-world datasets and offer directions for future work.