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), 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.

翻译：关于图神经网络（GNN）理论表达能力的研究发展迅速，目前已提出多种增强表达能力的方法。然而，除少数严格遵循k维Weisfeiler-Lehman（k-WL）测试层级的方法外，大多数方法缺乏统一的表达能力度量标准。其理论分析往往局限于区分特定类别的非同构图，导致难以定量比较不同方法的表达能力。与理论分析不同，另一种衡量表达能力的方式是通过评估模型在某些包含1-WL不可区分图的数据集上的表现。但此前专门为此设计的数据集存在以下问题：难度不足（任何超越1-WL的模型几乎都能达到100%准确率）、粒度粗糙（模型要么完全正确要么近乎随机猜测）、规模较小（每个数据集仅包含少数本质不同的图）。为解决这些局限，我们提出新的表达能力数据集——$\textbf{BREC}$，该数据集从四大类别（基础图、正则图、扩展图与CFI图）中精心筛选出400对非同构图。这些图具有更高难度（最高可达4-WL）、更细粒度（可比较1-WL至3-WL之间的模型）以及更大规模（400对）。进一步，我们在BREC数据集上对16种表达能力超过1-WL的模型进行了全面测试。实验首次系统比较了这些超越1-WL的最先进GNN模型的表达能力。我们期待该数据集能成为未来GNN表达能力测试的基准。数据集及评估代码已发布于：https://github.com/GraphPKU/BREC。