Papers › Gradual Weisfeiler-Leman: Slow and Steady Wins the Race

Gradual Weisfeiler-Leman: Slow and Steady Wins the Race

19 Sep 2022arXiv:2209.09048archive 2025-07-28

Franka Bause, Nils M. Kriege

The classical Weisfeiler-Leman algorithm aka color refinement is fundamental for graph learning with kernels and neural networks. Originally developed for graph isomorphism testing, the algorithm iteratively refines vertex colors. On many datasets, the stable coloring is reached after a few iterations and the optimal number of iterations for machine learning tasks is typically even lower. This suggests that the colors diverge too fast, defining a similarity that is too coarse. We generalize the concept of color refinement and propose a framework for gradual neighborhood refinement, which allows a slower convergence to the stable coloring and thus provides a more fine-grained refinement hierarchy and vertex similarity. We assign new colors by clustering vertex neighborhoods, replacing the original injective color assignment function. Our approach is used to derive new variants of existing graph kernels and to approximate the graph edit distance via optimal assignments regarding vertex similarity. We show that in both tasks, our method outperforms the original color refinement with only a moderate increase in running time advancing the state of the art.

PaperPDFCode

In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.

Code

frareba/gradualweisfeilerleman officialmentioned in papermentioned on GitHub report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Tasks

Graph LearningIsomorphism Testing

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections