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Graph neural networks~(GNNs) apply deep learning techniques to graph-structured data and have achieved promising performance in graph representation learning. However, existing GNNs rely heavily on enough labels or well-designed negative samples. To address these issues, we propose a new self-supervised graph representation method: deep graph bootstrapping~(DGB). DGB consists of two neural networks: online and target networks, and the input of them are different augmented views of the initial graph. The online network is trained to predict the target network while the target network is updated with a slow-moving average of the online network, which means the online and target networks can learn from each other. As a result, the proposed DGB can learn graph representation without negative examples in an unsupervised manner. In addition, we summarize three kinds of augmentation methods for graph-structured data and apply them to the DGB. Experiments on the benchmark datasets show the DGB performs better than the current state-of-the-art methods and how the augmentation methods affect the performances.