Papers › Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks
Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks
Christopher Morris, Martin Ritzert, Matthias Fey, William L. Hamilton, Jan Eric Lenssen, Gaurav Rattan, Martin Grohe
In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion. Up to now, GNNs have only been evaluated empirically -- showing promising results. The following work investigates GNNs from a theoretical point of view and relates them to the $1$-dimensional Weisfeiler-Leman graph isomorphism heuristic ($1$-WL). We show that GNNs have the same expressiveness as the $1$-WL in terms of distinguishing non-isomorphic (sub-)graphs. Hence, both algorithms also have the same shortcomings. Based on this, we propose a generalization of GNNs, so-called k-dimensional GNNs (k-GNNs), which can take higher-order graph structures at multiple scales into account. These higher-order structures play an essential role in the characterization of social networks and molecule graphs. Our experimental evaluation confirms our theoretical findings as well as confirms that higher-order information is useful in the task of graph classification and regression.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
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
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Graph Classification | IMDb-B | k-GNN | Accuracy | 74.2% | #28 of 51 | Archive leaderboard | report |
| Graph Classification | IMDb-B | 3-WL Kernel | Accuracy | 73.5% | #30 of 51 | Archive leaderboard | report |
| Graph Classification | IMDb-M | 1-WL Kernel | Accuracy | 51.5% | #14 of 36 | Archive leaderboard | report |
| Graph Classification | IMDb-M | k-GNN | Accuracy | 49.5% | #27 of 36 | Archive leaderboard | report |
| Graph Classification | MUTAG | Graphlet Kernel | Accuracy | 87.7% | #44 of 74 | Archive leaderboard | report |
| Graph Classification | MUTAG | k-GNN | Accuracy | 86.1% | #58 of 74 | Archive leaderboard | report |
| Graph Classification | NCI1 | WL-OA Kernel | Accuracy | 86.1% | #5 of 69 | Archive leaderboard | report |
| Graph Classification | NCI1 | k-GNN | Accuracy | 76.2% | #49 of 69 | Archive leaderboard | report |
| Graph Classification | PROTEINS | Shortest-Path Kernel | Accuracy | 76.4% | #46 of 103 | Archive leaderboard | report |
| Graph Classification | PROTEINS | k-GNN | Accuracy | 75.9% | #59 of 103 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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