Unsupervised/self-supervised graph neural networks (GNN) are vulnerable to inherent randomness in the input graph data which greatly affects the performance of the model in downstream tasks. In this paper, we alleviate the interference of graph randomness and learn appropriate representations of nodes without label information. To this end, we propose USER, an unsupervised robust version of graph neural networks that is based on structural entropy. We analyze the property of intrinsic connectivity and define intrinsic connectivity graph. We also identify the rank of the adjacency matrix as a crucial factor in revealing a graph that provides the same embeddings as the intrinsic connectivity graph. We then introduce structural entropy in the objective function to capture such a graph. Extensive experiments conducted on clustering and link prediction tasks under random-noises and meta-attack over three datasets show USER outperforms benchmarks and is robust to heavier randomness.
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