Weisfeiler–Leman Graph Isomorphism Test

The 1-WL (color refinement) test iteratively recolors each vertex based on its current color and the multiset of neighbor colors. Two graphs are WL-distinguishable if their color histograms diverge. WL is complete for trees and other graph classes, but fails on non-isomorphic regular graphs (e.g., two 3-regular graphs with same degree sequence). Modern GNNs are exactly as powerful as 1-WL.

Graph G₁
Graph G₂
Round: 0
G₁ color multiset:
G₂ color multiset:
WL result:
Select a graph pair and step through WL refinement.