The increasing demand for higher data rates for local area services caused traffic congestion at the base station (BS). One way to overcome this is a Device to Device (D2D) communication system. Device to Device allows nearby User Equipment (UE) to communicate using a direct link with each other without going through the BS. However, D2D communication caused interference to the traditional celullar user, because usually they use same frequency spectrum. A good radio resources allocation algorithm is a must to overcome this problem. This research proposes graph based allocation algorithm, to allocates the resources for D2D user and Cellular user. Graph algorithm is an algorithm which allocated the resource depending on the edge level of each user. The simulation parameters that being used to analyze the graph algorithm’s performance are sumrate, efficiency spectral, power efficiency and fairness, and graph algorithm is compared with a traditional greedy algorithm. Based on the result, graph algorithmm can inprove the fairness among the user in the system by 3.7%. Meanwhile, the sumrate, spectral efficiency, and power efficiency of the system is decreased by 4.24%, 4.52%, and 4.57% respectively compared with traditional greedy algorithm.
