  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.
