Understanding and Predicting Links in Graphs: A Persistent Homology Perspective

TL;DR

This paper introduces a novel approach using persistent homology from Topological Data Analysis to predict links in graphs by capturing their structural and topological properties, evaluated on multiple real-world datasets.

Contribution

It applies persistent homology techniques to graph data for link prediction, offering a new topological perspective in this domain.

Findings

Effective link prediction across diverse datasets

Persistent homology captures meaningful structural features

Provides directions for future research in topological graph analysis

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.