Surgical rehearsal plays a significant role for surgical procedures because surgery is generally dependent on the patient's anatomy. A surgical rehearsal system, which is a kind of computer simulator, enables to rehearse surgical procedures. Surgical rehearsal description language (SRDL) is a core part of a surgical rehearsal system. Existing techniques have been focused on achieving realistic simulation in surgical procedures; however, it is more critical to enable the surgeons to grasp the vascular anatomic topology intuitively. We propose a graph-based vessel representation as an abstract and cognitive vessel descriptor. Moreover, we demonstrated the scheme by developing an OpenGL-based surgical description language viewer for gastrectomy.