Anatomical labeling of head and neck vessels is a vital step for cerebrovascular disease diagnosis. However, it remains challenging to automatically and accurately label vessels in computed tomography angiography (CTA) since head and neck vessels are tortuous, branched, and often spatially close to nearby vasculature. To address these challenges, we propose a novel topology-aware graph network (TaG-Net) for vessel labeling. It combines the advantages of volumetric image segmentation in the voxel space and centerline labeling in the line space, wherein the voxel space provides detailed local appearance information, and line space offers high-level anatomical and topological information of vessels through the vascular graph constructed from centerlines. First, we extract centerlines from the initial vessel segmentation and construct a vascular graph from them. Then, we conduct vascular graph labeling using TaG-Net, in which techniques of topology-preserving sampling, topology-aware feature grouping, and multi-scale vascular graph are designed. After that, the labeled vascular graph is utilized to improve volumetric segmentation via vessel completion. Finally, the head and neck vessels of 18 segments are labeled by assigning centerline labels to the refined segmentation. We have conducted experiments on CTA images of 401 subjects, and experimental results show superior vessel segmentation and labeling of our method compared to other state-of-the-art methods.