Weisfeiler and Leman’s Unlikely Journey from Graph Isomorphism to Neural Networks (Invited Talk)

Author Martin Grohe

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Martin Grohe
  • RWTH Aachen University, Germany

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Martin Grohe. Weisfeiler and Leman’s Unlikely Journey from Graph Isomorphism to Neural Networks (Invited Talk). In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


The Weisfeiler-Leman algorithm is a well-known combinatorial graph isomorphism test going back to work of Weisfeiler and Leman in the late 1960s. The algorithm has a surprising number of seemingly unrelated characterisations in terms of logic, algebra, linear and semi-definite programming, and graph homomorphisms. Due to its simplicity and efficiency, it is an important subroutine of all modern graph isomorphism tools. In recent years, further applications in linear optimisation, probabilistic inference, and machine learning have surfaced. In the first part of my talk, I will give an introduction to the Weisfeiler-Leman algorithm and its various characterisations. In the second part I will speak about its applications, in particular about recent work relating the algorithm to graph neural networks.

Subject Classification

ACM Subject Classification
  • Theory of computation → Discrete optimization
  • Mathematics of computing → Graph algorithms
  • Weisfeiler adn Leman algorithm
  • Graph isomorphism
  • Neural network
  • logic
  • algebra
  • linear and semi-definite programming


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