Social awareness and social ties are becoming increasingly fashionable with emerging mobile and handheld devices. Social trust degree describing the strength of the social ties has drawn lots of research interests in many fields including secure cooperative communications. Such trust degree reflects the users' willingness for cooperation, which impacts the selection of the cooperative users in the practical networks. In this paper, we propose a cooperative relay and jamming selection scheme to secure communication based on the social trust degree under a stochastic geometry framework. We aim to analyze the involved secrecy outage probability (SOP) of the system's performance. To achieve this target, we propose a double Gamma ratio (DGR) approach through Gamma approximation. Based on this, the SOP is tractably obtained in closed form. The simulation results verify our theoretical findings, and validate that the social trust degree has dramatic influences on the network's secrecy performance.