Traditional complementary metal-oxide-semiconductor (CMOS) technology has reached nanoscale and its physical limits are determined by atomic theory and quantum mechanics, which results in a series of problems such as deteriorated device reliability, large circuit interconnection delay, and huge static power dissipation. In the past decades, with the discovery of giant magnetoresistance effect and tunnel magnetoresistance effect, spintronics has become a research hotspot in this field. Specially, spin transfer torque effect has been experimentally verified that the magnetization of a ferromagnet layer can be manipulated using spin polarized current rather than an external magnetic field. Spintronics is a new type of electronics which utilizes spin rather than charge as state variable for electrical information processing and storage. As an example, all spin logic (ASL) devices, which stores information by using the magnetization direction of the nanomagnet and communication by using spin current, is generally thought to be a good post-CMOS candidate. Compared with the typical metal material, the graphene material has a large conductivity, long spin relaxation time, and weak spin-orbit interaction. Therefore, the dissipation of spin current in the graphene material is weaker than the counterpart in typical metal when the injected current is identical. In this paper, the switching characteristics of all spin logic device comprised of graphene interconnects are analyzed by using the coupled spin transport and magneto-dynamics model. The results show that comparing with ASL device comprised of copper interconnects, the magnetic moment reversal time of ASL with graphene interconnection is short and the spin current flows into the output magnet is large under the condition of same applied voltage and device size. Meanwhile, the switching delay and the energy dissipation are lower when the interconnects are shorter and narrower. When the critical switching current which is required for the magnetization reversal is applied, the reliable working length of graphene interconnection is significantly longer than that of copper interconnection. So the graphene is the more ideal interconnect material than metal material. Moreover, the switching delay and power dissipation could be further reduced by properly selecting the interconnection dimension. These results mentioned above provide guidelines for the optimization and applications of ASL devices.