A method for constructing a vascular connector configured to bypass an occluded vessel which comprises a primary graft stem and a venous outflow stem. In general, the primary graft stem accepts a blood flow from an occluded vessel to bypass the occlusion. The venous outflow stem may extend from a wall of the primary graft stem and divert a portion of the blood flow to a native vein or other vessel of the vascular system. This configuration is beneficial in ensuring adequate blood flow at the vascular connector to inhibit the formation of clots and to extend the patency of the vascular connector.