Do graph neural network states contain graph properties?

Graph learning models achieve state-of-the-art performance on many tasks, but this often requires increasingly large model sizes. Accordingly, the complexity of their representations increase. Explainability techniques (XAI) have made remarkable progress in the interpretability of ML models. However, the non-relational nature of Graph Neural Networks (GNNs) make it difficult to reuse already existing XAI methods. While other works have focused on instance-based explanation methods for GNNs, very few have investigated model-based methods and, to our knowledge, none have tried to probe the embedding of the GNNs for well-known structural graph properties. In this paper we present a model agnostic explainability pipeline for Graph Neural Networks (GNNs) employing diagnostic classifiers. This pipeline aims to probe and interpret the learned representations in GNNs across various architectures and datasets, refining our understanding and trust in these models.