Preoperative prediction of lymph node (LN) metastasis based on computed tomography (CT) scans is an important task in gastric cancer, but few machine learning-based techniques have been proposed. While multi-center datasets increase sample size and representation ability, they suffer from inter-center heterogeneity. To tackle the above issue, we propose a novel multi-source domain adaptation framework for this diagnosis task, which not only considers domain-invariant and domain-specific features, but also achieves the imbalanced knowledge transfer and class-aware feature alignment across domains. First, we develop a 3D improved feature pyramidal network (i.e., 3D IFPN) to extract common multi-level features from the high-resolution 3D CT images, where a feature dynamic transfer (FDT) module can promote the network's ability to recognize the small target (i.e., LN). Then, we design an unsupervised domain selective graph convolutional network (i.e., UDS-GCN), which mainly includes three types of components: domain-specific feature extractor, domain selector and class-aware GCN classifier. Specifically, multiple domain-specific feature extractors are employed for learning domain-specific features from the common multi-level features generated by the 3D IFPN. A domain selector via the optimal transport (OT) theory is designed for controlling the amount of knowledge transferred from source domains to the target domain. A class-aware GCN classifier is developed to explicitly enhance/weaken the intra-class/inter-class similarity of all sample pairs across domains. To optimize UDS-GCN, the domain selector and the class-aware GCN classifier provide reliable target pseudo-labels to each other in the iterative process by collaborative learning. The extensive experiments are conducted on an in-house CT image dataset collected from four medical centers to demonstrate the efficacy of our proposed method. Experimental results verify that the proposed method boosts LN metastasis diagnosis performance and outperforms state-of-the-art methods. Our code is publically available at https://github.com/infinite-tao/LN _ MSDA .(c) 2022 Elsevier B.V. All rights reserved.