Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning Pascal Welke 3

We introduce r-loopy Weisfeiler-Leman (r-lWL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, r-lMPNN, that can count cycles up to length r+2. Most notably, we show that r-lWL can count homomorphisms of cactus graphs. This extends 1-WL, which can only count homomorphisms of trees and, in fact, we prove that r-lWL is incomparable to k-WL for any fixed k. We empirically validate the expressive and counting power of r-lMPNN on several synthetic datasets and demonstrate the scalability and strong performance on various real-world datasets, particularly on sparse graphs. Our code is available on GitHub.