Multi-Level Task-Agnostic Graph Representation Learning With Isomorphic-Consistent Variational Graph Auto-Encoders

Graph representation learning is a fundamental research theme and can be generalized to benefit multiple downstream tasks from the node and link levels to the higher graph level. In practice, it is desirable to develop task-agnostic graph representation learning methods that are typically trained in an unsupervised manner. However, existing unsupervised graph models, represented by the variational graph auto-encoders (VGAEs), can only address node- and link-level tasks while manifesting poor generalizability on the more difficult graph-level tasks because they can only keep low-order isomorphic consistency within the subgraphs of one-hop neighborhoods. To overcome the limitations of existing methods, in this paper, we propose the Isomorphic-Consistent VGAE (IsoC-VGAE) for multi-level task-agnostic graph representation learning. We first devise an unsupervised decoding scheme to provide a theoretical guarantee of keeping the high-order isomorphic consistency within the VGAE framework. We then propose the Inverse Graph Neural Network (Inv-GNN) decoder as its intuitive realization, which trains the model via reconstructing the node embeddings and neighborhood distributions learned by the GNN encoder. Extensive experiments on multi-level graph learning tasks verify that our model achieves superior or comparable performance compared to both the state-of-the-art unsupervised methods and representative supervised methods with distinct advantages on the graph-level tasks.