On Reconstructability of Graph Neural Networks

Recently, the expressive power of GNNs has been analyzed based on their ability to determine if two given graphs are isomorphic using the WL-test. However, previous analyses only establish the expressiveness of GNNs for graph-level tasks from a global perspective. In this paper, we analyze the expressive power of GNNs in terms of Graph Reconstructability, which aims to examine whether the topological information of graphs can be recovered from a local (node-level) perspective. We answer this question by analyzing how the output node embeddings extracted from GNNs may maintain important information for reconstructing the input graph structure. Moreover, we generalize GNNs in the form of Graph Reconstructable Neural Network (GRNN) and explore Nearly Orthogonal Random Features (NORF) to retain graph reconstructability. Experimental results demonstrate that GRNN outperforms representative baselines in reconstructability and efficiency.