The Power of the Weisfeiler-Leman Algorithm for Machine Learning with Graphs

TL;DR

This paper reviews how the Weisfeiler-Leman algorithm enhances machine learning on graphs, covering theoretical foundations, neural connections, and practical applications, highlighting its significance in graph classification tasks.

Contribution

It provides a comprehensive overview of the Weisfeiler-Leman algorithm's role in graph machine learning, including recent extensions and neural architecture connections.

Findings

Effective for supervised graph and node classification

Theoretical insights into the algorithm's capabilities

Overview of applications and future research directions

Abstract

In recent years, algorithms and neural architectures based on the Weisfeiler-Leman algorithm, a well-known heuristic for the graph isomorphism problem, emerged as a powerful tool for (supervised) machine learning with graphs and relational data. Here, we give a comprehensive overview of the algorithm's use in a machine learning setting. We discuss the theoretical background, show how to use it for supervised graph- and node classification, discuss recent extensions, and its connection to neural architectures. Moreover, we give an overview of current applications and future directions to stimulate research.