Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning
This work addresses graph representation learning for researchers and practitioners, offering a novel method that improves expressiveness over existing approaches.
The paper tackles the problem of graph isomorphism testing and representation learning by introducing a new hierarchy, $r$-loopy Weisfeiler-Leman, which can count cycles up to length $r+2$ and homomorphisms of cactus graphs, extending classical methods. It shows state-of-the-art predictive performance on real-world datasets.
We introduce $r$-loopy Weisfeiler-Leman ($r$-$\ell{}$WL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, $r$-$\ell{}$MPNN, that can count cycles up to length $r + 2$. Most notably, we show that $r$-$\ell{}$WL can count homomorphisms of cactus graphs. This strictly extends classical 1-WL, which can only count homomorphisms of trees and, in fact, is incomparable to $k$-WL for any fixed $k$. We empirically validate the expressive and counting power of the proposed $r$-$\ell{}$MPNN on several synthetic datasets and present state-of-the-art predictive performance on various real-world datasets. The code is available at https://github.com/RPaolino/loopy