The segmentation of arteries in invasive coronary angiography is necessary to build quantitative models and eventually improve the diagnosis of cardiovascular diseases. Standard segmentation algorithms suffer due to the lack of fully annotated datasets and tend to return disconnected vessels. Thus, we explore a semi-supervised segmentation framework to address these issues. Specifically, we use a student model and a teacher model as the main framework with Nested U-Nets (UNet++) as their backbones. The student model learns by minimizing a segmentation loss between the output and the ground truth, and a consistency loss guided by the uncertainty information. Additionally, a special loss function based on elastic interaction is used to improve the connectivity of arterial branches. We demonstrate the effectiveness of our proposed techniques over 42 labeled and 60 unlabeled samples and find relative improvement of 5.59% for Dice score and 69.99% for Betti number compared to a U-Net.