Weisfeiler-Lehman Test

The problem, from first principles

The Weisfeiler-Lehman (WL) test is a graph isomorphism heuristic. It iteratively refines node labels based on neighbor labels. Two graphs are deemed non-isomorphic if their label distributions differ at any iteration.

From theory to code

Implement:

weisfeiler_lehman(adj, num_iterations=3)

Performs WL iterations and returns final node color distributions.

Constraints

• adj shape: (num_nodes, num_nodes), binary.
• num_iterations: number of WL refinement steps.
• Return shape: (num_nodes,), integer color labels.