Graph Neural Networks (GNNs) have emerged as a powerful tool for learning from graph-structured data. However, even state-of-the-art architectures have limitations on what structures they can distinguish, imposing theoretical limits on what the networks can achieve on different datasets. In this paper, we provide a new tool called Graphtester for a comprehensive analysis of the theoretical capabilities of GNNs for various datasets, tasks, and scores. We use Graphtester to analyze over 40 different graph datasets, determining upper bounds on the performance of various GNNs based on the number of layers. Further, we show that the tool can also be used for Graph Transformers using positional node encodings, thereby expanding its scope. Finally, we demonstrate that features generated by Graphtester can be used for practical applications such as Graph Transformers, and provide a synthetic dataset to benchmark node and edge features, such as positional encodings. The package is freely available at the following URL: https://github.com/meakbiyik/graphtester.

翻译：图神经网络（GNNs）已成为从图结构数据中学习的强大工具。然而，即便是最先进的架构，在区分不同结构的能力上仍存在局限性，这为网络在不同数据集上的表现施加了理论上的上限。本文提出一种名为Graphtester的新工具，用于全面分析GNNs在不同数据集、任务及评分指标下的理论能力。我们利用Graphtester分析了超过40种不同的图数据集，基于网络层数确定了各类GNNs的性能上限。此外，我们证明该工具还可用于使用位置节点编码的图Transformer（Graph Transformers），从而拓展其应用范围。最后，我们展示了Graphtester生成的特征可应用于Graph Transformers等实际场景，并提供了一个用于基准测试节点和边特征（如位置编码）的合成数据集。该工具包可免费获取，网址为：https://github.com/meakbiyik/graphtester。