Analyzing Explanations of Deep Graph Networks Through Node Centrality and Connectivity

This chapter delves into the analysis of explanations for Deep Graph Networks (DGNs) by leveraging node centrality and connectivity measures from network science. It begins by introducing the flexibility of graphs in representing complex data structures and the capabilities of DGNs in learning from these structures. The authors then highlight the challenge of understanding DGNs due to their black-box nature and the subsequent development of Explainable AI (XAI) techniques to shed light on their inner workings. The core of the chapter focuses on investigating the inductive biases of recursive and convolutional DGNs through the alignment of explanations with centrality measures like Katz centrality and connectivity measures like the Fiedler eigenvector. The results reveal that recursive DGNs tend to focus on low-order structures, while convolutional DGNs are more inclined towards high-order structures. This analysis provides practitioners with valuable insights into selecting the most suitable DGN for their specific learning tasks. The chapter concludes with a discussion on the practical implications of these findings and proposes future directions for extending the investigation into temporal networks and the full spectrum of the Laplacian.