Weisfeiler Leman graph isomorphism test

In graph theory, the Weisfeiler Leman graph isomorphism test is a heuristic test for the existence of an isomorphism between two graphs G and H.^[1] It is based on a normal form for graphs first described in an article by Weisfeiler and Leman in 1968.^[2]

The basic Weisfeiler Leman graph isomorphism test

Graph G0	Graph G1	Graph G2

Weisfeiler Leman graph kernels

Generalizations

More powerful variations of the algorithm

Generalizations to τ-structures)

Applications

The theory behind the Weisfeiler Leman test is applied in graph neural networks.

References

^ Huang, Ningyuan; Villar, Soledad (2022), "A Short Tutorial on the Weisfeiler-Lehman Test and Its Variants", ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 8533–8537, arXiv:2201.07083, doi:10.1109/ICASSP39728.2021.9413523, ISBN 978-1-7281-7605-5, S2CID 235780517
^ Weisfeiler, B. Yu.; Leman, A. A. (1968). "A Reduction of a Graph to a Canonical Form and an Algebra Arising during This Reduction" (PDF). Nauchno-Technicheskaya Informatsia. 2 (9): 12–16. Retrieved 2023-10-28.

[1] Huang, Ningyuan; Villar, Soledad (2022), "A Short Tutorial on the Weisfeiler-Lehman Test and Its Variants", ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 8533–8537, arXiv:2201.07083, doi:10.1109/ICASSP39728.2021.9413523, ISBN 978-1-7281-7605-5, S2CID 235780517

[WL-2] Weisfeiler, B. Yu.; Leman, A. A. (1968). "A Reduction of a Graph to a Canonical Form and an Algebra Arising during This Reduction" (PDF). Nauchno-Technicheskaya Informatsia. 2 (9): 12–16. Retrieved 2023-10-28.

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