In this correspondence, we study the physical layer security in a stochastic unmanned aerial vehicles (UAVs) network from a network-wide perspective, where the locations of UAVs are modeled as a Mat$\acute{\text{e}}$rn hard-core point process (MHCPP) to characterize the minimum safety distance between UAVs, and the locations of users and eavesdroppers are modeled as a Poisson cluster process and a Poisson point process, respectively. UAVs adopt zero-forcing precoding to serve multiple ground users and emit artificial noise to combat eavesdropping. We derive the approximations for the coverage probability and secrecy probability of a typical user, with which we derive the secrecy throughput of the whole network. Numerical results show the analytical results can well approximate the simulation results. Impacts of parameters on the secrecy performance are shown.