Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks

  • Christopher Morris TU Dortmund University
  • Martin Ritzert RWTH Aachen University
  • Matthias Fey TU Dortmund University
  • William L. Hamilton Stanford University
  • Jan Eric Lenssen TU Dortmund University
  • Gaurav Rattan RWTH Aachen University
  • Martin Grohe RWTH Aachen University


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.

AAAI Technical Track: Machine Learning