Due to the popularity of social networks and human-carried/human-affiliated devices with sensing abilities, like smartphones and smart wearable devices, a novel application was necessitated recently to organize group activities by learning historical data gathered from smart devices and choosing invitees carefully based on their personal interests. We proposed a private and efficient social activity invitation framework. Our main contributions are (1) defining a novel friendship to reduce the communication/update cost within the social network and enhance the privacy guarantee at the same time; () designing a strong privacy-preserving algorithm for graph publication, which addresses an open concern proposed recently; () presenting an efficient invitee-selection algorithm, which outperforms the existing ones. Our simulation results show that the proposed framework has good performance. In our framework, the server is assumed to be untrustworthy but can nonetheless help users organize group activities intelligently and efficiently. Moreover, the new definition of the friendship allows the social network to be described by a directed graph. To the best of our knowledge, it is the first work to publish a directed graph in a differentially private manner with an untrustworthy server.