Scaling up graph homomorphism for classification via sampling

TL;DR

This paper introduces a scalable sampling-based method for computing graph homomorphism density features, enabling effective graph classification with simple models on large datasets.

Contribution

It proposes a high-performance sampling algorithm for homomorphism densities that scales to large graphs and retains key theoretical properties.

Findings

Sampling-based features achieve comparable performance to GNNs.

Algorithm scales to very large graphs using Bloom filters.

Simple linear models perform well on standard datasets.

Abstract

Feature generation is an open topic of investigation in graph machine learning. In this paper, we study the use of graph homomorphism density features as a scalable alternative to homomorphism numbers which retain similar theoretical properties and ability to take into account inductive bias. For this, we propose a high-performance implementation of a simple sampling algorithm which computes additive approximations of homomorphism densities. In the context of graph machine learning, we demonstrate in experiments that simple linear models trained on sample homomorphism densities can achieve performance comparable to graph neural networks on standard graph classification datasets. Finally, we show in experiments on synthetic data that this algorithm scales to very large graphs when implemented with Bloom filters.