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Domain adaptation (DA) tries to tackle the scenarios when the test data does not fully follow the same distribution of the training data, and multi-source domain adaptation (MSDA) is very attractive for real world applications. By learning from large-scale unlabeled samples, self-supervised learning has now become a new trend in deep learning. It is worth noting that both self-supervised learning and multi-source domain adaptation share a similar goal: they both aim to leverage unlabeled data to learn more expressive representations. Unfortunately, traditional multi-task self-supervised learning faces two challenges: (1) the pretext task may not strongly relate to the downstream task, thus it could be difficult to learn useful knowledge being shared from the pretext task to the target task; (2) when the same feature extractor is shared between the pretext task and the downstream one and only different prediction heads are used, it is ineffective to enable inter-task information exchange and knowledge sharing. To address these issues, we propose a novel \textbf{S}elf-\textbf{S}upervised \textbf{G}raph Neural Network (SSG), where a graph neural network is used as the bridge to enable more effective inter-task information exchange and knowledge sharing. More expressive representation is learned by adopting a mask token strategy to mask some domain information. Our extensive experiments have demonstrated that our proposed SSG method has achieved state-of-the-art results over four multi-source domain adaptation datasets, which have shown the effectiveness of our proposed SSG method from different aspects.