Substructure Aware Graph Neural Networks.

Despite the great achievements of Graph Neural Networks (GNNs) in graph learning, conventional GNNs struggle to break through the upper limit of the expressiveness of firstorder Weisfeiler-Leman graph isomorphism test algorithm (1-WL) due to the consistency of the propagation paradigm of GNNs with the 1-WL. Based on the fact that it is easier to distinguish the original graph through subgraphs, we propose a novel framework neural network framework called Substructure Aware Graph Neural Networks (SAGNN) to address these issues. We first propose a Cut subgraph which can be obtained from the original graph by continuously and selectively removing edges. Then we extend the random walk encoding paradigm to the return probability of the rooted node on the subgraph to capture the structural information and use it as a node feature to improve the expressiveness of GNNs. We theoretically prove that our framework is more powerful than 1-WL, and is superior in structure perception. Our extensive experiments demonstrate the effectiveness of our framework, achieving state-of-the-art performance on a variety of well-proven graph tasks, and GNNs equipped with our framework perform flawlessly even in 3-WL failed graphs. Specifically, our framework achieves a maximum performance improvement of 83% compared to the base models and 32% compared to the previous state-of-the-art methods.