Abstract-In a device-to-device (D2D) communication underlaying cellular network, user equipment are required to operate cooperatively and unselfishly to transmit data as relays. However, most users more or less behave in a selfish way, which makes user selfishness a key factor that affects the performance of the whole communication system. We focus on the impact of user selfishness on D2D communications. By separating the user selfishness into two types in accordance with two D2D transmission modes, which are connected D2D transmission and opportunistic D2D transmission, we propose a time-varying graph model that characterizes the impacts of both individual and social selfishness on the D2D communications. Simulation results obtained under the realistic networking settings indicate that the interaction between connected and opportunistic selfishness worsens the impairment caused by individual selfishness. Additionally, when concerning social selfishness, inside-community selfishness can be ignored in some occasions, while otherwise its role is heavily influenced by community numbers.