Graphtester: Exploring Theoretical Boundaries of GNNs on Graph Datasets

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.