Summary: 2D/3D registration is in general a challenging task due to its ill-posed nature. It becomes even more difficult when deformation between the 3D volume and 2D images needs to be recovered. This paper presents an automatic, accurate and efficient deformable 2D/3D registration method that is formulated on a 3D graph and applied for abdominal aortic aneurysm (AAA) interventions. The proposed method takes the 3D graph generated from a segmentation of the CT volume and the 2D distance map calculated from the 2D X-ray image as the input. The similarity measure consists of a difference measure, a length preservation term and a smoothness regularization term, all of which are defined and efficiently calculated on the graph. A hierarchical registration scheme is further designed specific to the anatomy of abdominal aorta and typical deformations observed during AAA cases. The method was validated using both phantom and clinical datasets, and achieved an average error of $< 1 \,\text{mm}$ within $0.1 \,\text{s}$. The proposed method is of general form and has the potential to be applied for a wide range of applications requiring efficient 2D/3D registration of vascular structures.