Accurate vascular segmentation is essential for coronary visualization and the diagnosis of coronary heart disease. This task involves the extraction of sparse tree-like vascular branches from the volumetric space. However, existing methods have faced significant challenges due to discontinuous vascular segmentation and missing endpoints. To address this issue, a 3D vision graph neural network framework, named ViG3D-UNet, was introduced. This method integrates 3D graph representation and aggregation within a U-shaped architecture to facilitate continuous vascular segmentation. The ViG3D module captures volumetric vascular connectivity and topology, while the convolutional module extracts fine vascular details. These two branches are combined through channel attention to form the encoder feature. Subsequently, a paperclip-shaped offset decoder minimizes redundant computations in the sparse feature space and restores the feature map size to match the original input dimensions. To evaluate the effectiveness of the proposed approach for continuous vascular segmentation, evaluations were performed on two public datasets, ASOCA and ImageCAS. The segmentation results show that the ViG3D-UNet surpassed competing methods in maintaining vascular segmentation connectivity while achieving high segmentation accuracy. Our code will be available soon.