The paper considers physical layer security (PLS) of an untrusted unmanned aerial vehicle (UAV) network, where a multitude of UAVs communicate in full-duplex (FD) mode. A source-based jamming (SBJ) scheme is exploited for secure communication without utilizing any external jammers. Firstly, the optimal power allocation between the confidential signal and the jamming signal is derived to maximize the secrecy rate of each link between the source and the destination. Then, the best UAV selection scheme is proposed to maximize the overall secrecy rate of the network. The corresponding secrecy outage probability (SOP) and the average secrecy rate (ASR) of the network are analyzed based on the proposed UAV selection and the optimal power allocation schemes. Asymptotic results are also obtained to derive the achievable diversity order. Results are validated through numerical evaluations while providing useful network design insights such as locations and altitudes of the UAVs.Index Terms-Full-duplex, optimal power allocation, physical layer security, source jamming, unmanned aerial vehicle (UAV).