In medical image analysis, blood vessel segmentation is of considerable clinical value for diagnosis and surgery. The predicaments of complex vascular structures obstruct the development of the field. Despite many algorithms have emerged to get off the tight corners, they rely excessively on careful annotations for tubular vessel extraction. A practical solution is to excavate the feature information distribution from unlabeled data. This work proposes a novel semi-supervised vessel segmentation framework, named EXP-Net, to navigate through finite annotations. Based on the training mechanism of the Mean Teacher model, we innovatively engage an expert network in EXP-Net to enhance knowledge distillation. The expert network comprises knowledge and connectivity enhancement modules, which are respectively in charge of modeling feature relationships from global and detailed perspectives. In particular, the knowledge enhancement module leverages the vision transformer to highlight the long-range dependencies among multi-level token components; the connectivity enhancement module maximizes the properties of topology and geometry by skeletonizing the vessel in a non-parametric manner. The key components are dedicated to the conditions of weak vessel connectivity and poor pixel contrast. Extensive evaluations show that our EXP-Net achieves state-of-the-art performance on subcutaneous vessel, retinal vessel, and coronary artery segmentations.