This work focuses on delay-tolerant networks in a social network environment. The nonexistence of end-to-end path between the source and the destination poses great challenges to the successful message transmission in delay-tolerant networks. In this article, we attempt to find a socially connected path above the intermittently connected physical topology. To this end, we study a weighted community graph model, which turns the original network into a network composed of communities and then describes the interaction delays between these communities. By performing a Dijkstra algorithm on this community graph, the expected minimum transmission delay to a destination community can be computed. To improve the performance on delivery delay, we propose a social routing called weighted community graph-based social routing that makes use of interaction delays between communities and social ties among nodes, which consists of two routing phases. In inter-community routing phase, messages are forwarded to its destination communities based on the computed minimum delays, and then in intra-community routing phase, each copy is forwarded within a destination community based on the social ties between nodes until meeting the final destination. Extensive simulations are conducted and the results show that weighted community graph-based social routing can improve routing performance, especially the performance on delivery delay and overhead ratio.