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Graph representation learning is a fundamental research theme and can begeneralized to benefit multiple downstream tasks from the node and link levelsto the higher graph level. In practice, it is desirable to developtask-agnostic general graph representation learning methods that are typicallytrained in an unsupervised manner. Related research reveals that the power ofgraph representation learning methods depends on whether they can differentiatedistinct graph structures as different embeddings and map isomorphic graphs toconsistent embeddings (i.e., the isomorphic consistency of graph models).However, for task-agnostic general graph representation learning, existingunsupervised graph models, represented by the variational graph auto-encoders(VGAEs), can only keep the isomorphic consistency within the subgraphs of 1-hopneighborhoods and thus usually manifest inferior performance on the moredifficult higher-level tasks. To overcome the limitations of existingunsupervised methods, in this paper, we propose the Isomorphic-Consistent VGAE(IsoC-VGAE) for multi-level task-agnostic graph representation learning. Wefirst devise a decoding scheme to provide a theoretical guarantee of keepingthe isomorphic consistency under the settings of unsupervised learning. We thenpropose the Inverse Graph Neural Network (Inv-GNN) decoder as its intuitiverealization, which trains the model via reconstructing the GNN node embeddingswith multi-hop neighborhood information, so as to maintain the high-orderisomorphic consistency within the VGAE framework. We conduct extensiveexperiments on the representative graph learning tasks at different levels,including node classification, link prediction and graph classification, andthe results verify that our proposed model generally outperforms both thestate-of-the-art unsupervised methods and representative supervised methods.

Isomorphic-Consistent Variational Graph Auto-Encoders for Multi-Level Graph Representation Learning