# Topology Based Scalable Graph Kernels

## TL;DR

This paper introduces a scalable graph kernel based on Ollivier Ricci curvature, enabling graph classification and comparison solely from topology, especially useful when node attributes are unavailable.

## Contribution

It presents a novel curvature-based graph kernel leveraging Ollivier Ricci curvature for topology-only graph analysis.

## Key findings

- Effective in classifying and clustering graphs based on curvature distributions.
- Operates solely on graph topology, no node attributes needed.
- Applicable to various graph comparison tasks.

## Abstract

We propose a new graph kernel for graph classification and comparison using Ollivier Ricci curvature. The Ricci curvature of an edge in a graph describes the connectivity in the local neighborhood. An edge in a densely connected neighborhood has positive curvature and an edge serving as a local bridge has negative curvature. We use the edge curvature distribution to form a graph kernel which is then used to compare and cluster graphs. The curvature kernel uses purely the graph topology and thereby works for settings when node attributes are not available.