A New Perspective on "How Graph Neural Networks Go Beyond Weisfeiler-Lehman?"

We propose a new perspective on designing powerful Graph Neural Networks (GNNs). In a nutshell, this enables a general solution to inject structural properties of graphs into a message-passing aggregation scheme of GNNs. As a theoretical basis, we first develop a new hierarchy of local isomorphism on neighborhood subgraphs. Then, we generalise the message-passing aggregation scheme to theoretically characterize how GNNs can be designed to be more expressive beyond the Weisfeiler Lehman test. To elaborate this framework, we propose a novel neural model, called GraphSNN, and prove that this model is strictly more expressive than the Weisfeiler Lehman test in distinguishing graph structures. We empirically verify the strength of our model on different graph learning tasks. It is shown that our model consistently improves the state-of-the-art methods on the benchmark tasks without sacrificing computational simplicity and efficiency.