提出双重重编程框架，解决目标图中存在未知类别时的无监督图域适应问题。

Unsupervised Graph Domain Adaptation has become a promising paradigm for transferring knowledge from a fully labeled source graph to an unlabeled target graph. Existing graph domain adaptation models primarily focus on the closed-set setting, where the source and target domains share the same label spaces. However, this assumption might not be practical in the real-world scenarios, as the target domain might include classes that are not present in the source domain. In this paper, we investigate the problem of unsupervised open-set graph domain adaptation, where the goal is to not only correctly classify target nodes into the known classes, but also recognize previously unseen node types into the unknown class. Towards this end, we propose a novel framework called GraphRTA, which conducts reprogramming on both the graph and model sides. Specifically, we reprogram the graph by modifying target graph structure and node features, which facilitates better separation of known and unknown classes. Meanwhile, we also perform model reprogramming by pruning domain-specific parameters to reduce bias towards the source graph while preserving parameters that capture transferable patterns across graphs. Additionally, we extend the classifier with an extra dimension for the unknown class, thus eliminating the need of manually specified threshold in open-set recognition. Comprehensive experiments on several public datasets demonstrate that our proposed model can achieve satisfied performance compared with recent state-of-the-art baselines. Our source codes and datasets are publicly available at https://github.com/cszhangzhen/GraphRTA.