Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting

While Graph Neural Networks (GNNs) have achieved remarkable results in a variety of applications, recent studies exposed important shortcomings in their ability to capture the structure of the underlying graph. It has been shown that the expressive power of standard GNNs is bounded by the Weisfeiler-Lehman (WL) graph isomorphism test, from which they inherit proven limitations such as the inability to detect and count graph substructures. On the other hand, there is significant empirical evidence, e.g. in network science and bioinformatics, that substructures are often informative for downstream tasks, suggesting that it is desirable to design GNNs capable of leveraging this important source of information. To this end, we propose a novel topologically-aware message passing scheme based on subgraph isomorphism counting. We show that our architecture allows incorporating domain-specific inductive biases and that it is strictly more expressive than the WL test. Importantly, in contrast to recent works on the expressivity of GNNs, we do not attempt to adhere to the WL hierarchy; this allows us to retain multiple attractive properties of standard GNNs such as locality and linear complexity, while being able to disambiguate even hard instances of graph isomorphism. We extensively evaluate our method on graph classification and regression tasks and show state-of-the-art results on multiple datasets including molecular graphs and social networks.