Towards Better Evaluation of GNN Expressiveness with BREC Dataset

Research on the theoretical expressiveness of Graph Neural Networks (GNNs) has developed rapidly, and many methods have been proposed to enhance the expressiveness. However, most methods do not have a uniform expressiveness measure except for a few that strictly follow the $k$-dimensional Weisfeiler-Lehman ($k$-WL) test hierarchy. Their theoretical analyses are often limited to distinguishing certain families of non-isomorphic graphs, leading to difficulties in quantitatively comparing their expressiveness. In contrast to theoretical analysis, another way to measure expressiveness is by evaluating model performance on certain datasets containing 1-WL-indistinguishable graphs. Previous datasets specifically designed for this purpose, however, face problems with difficulty (any model surpassing 1-WL has nearly 100% accuracy), granularity (models tend to be either 100% correct or near random guess), and scale (only a few essentially different graphs in each dataset). To address these limitations, we propose a new expressiveness dataset, $\textbf{BREC}$, which includes 400 pairs of non-isomorphic graphs carefully selected from four primary categories (Basic, Regular, Extension, and CFI). These graphs have higher difficulty (up to 4-WL-indistinguishable), finer granularity (able to compare models between 1-WL and 3-WL), and a larger scale (400 pairs). Further, we synthetically test 16 models with higher-than-1-WL expressiveness on our BREC dataset. Our experiment gives the first thorough comparison of the expressiveness of those state-of-the-art beyond-1-WL GNN models. We expect this dataset to serve as a benchmark for testing the expressiveness of future GNNs. Our dataset and evaluation code are released at: https://github.com/GraphPKU/BREC.