Small cell base stations (SBSs) endowed with cloud-like computing capabilities are considered as a key enabler of edge computing (EC), which provides ultra-low latency and location-awareness for a variety of emerging mobile applications and the Internet of Things. However, due to the limited computation resources of an individual SBS, providing computation services of high quality to its users faces significant challenges when it is overloaded with an excessive amount of computation workload. In this paper, we propose collaborative edge computing among SBSs by forming SBS coalitions to share computation resources with each other, thereby accommodating more computation workload in the edge system and reducing reliance on the remote cloud. A novel SBS coalition formation algorithm is developed based on the coalitional game theory to cope with various new challenges in small-cell-based edge systems, including the co-provisioning of radio access and computing services, cooperation incentives, and potential security risks. To address these challenges, the proposed method (1) allows collaboration at both the user-SBS association stage and the SBS peer offloading stage by exploiting the ultra dense deployment of SBSs, (2) develops a payment-based incentive mechanism that implements proportionally fair utility division to form stable SBS coalitions, and (3) builds a social trust network for managing security risks among SBSs due to collaboration. Systematic simulations in practical scenarios are carried out to evaluate the efficacy and performance of the proposed method, which shows that tremendous edge computing performance improvement can be achieved.