Device-to-Device (D2D) communication has received increasing attention and been studied extensively thanks to its advantages in improving spectral efficiency and energy efficiency of cellular networks. This paper proposes a novel relay selection algorithm for multi-hop fullduplex D2D communications underlaying cellular networks. By selecting the relay of each hop in a reverse manner, the proposed algorithm reduces the heavy signaling overhead that traditional relay selection algorithms introduce. In addition, the social domain information of mobile terminals is taken into consideration and its influence on the performance of D2D communications studied, which is found significant enough not to be overlooked. Moreover, simulations show that the proposed algorithm, in absence of social relationship information, improves data throughput by around 70% and 7% and energy efficiency by 64% and 6%, compared with two benchmark algorithms, when D2D distance is 260 meters. In a more practical implementation considering social relationship information, although the proposed algorithm naturally achieves less throughput, it substantially increases the energy efficiency than the benchmarks.