In this paper, we aim to design a deep reinforcement learning (DRL) based control solution to navigating a swarm of unmanned aerial vehicles (UAVs) to fly around an unexplored target area under partial observation, which serves as Mobile Base Stations (MBSs) providing optimal communication coverage for the ground mobile users. To handle the information loss caused by the partial observability, we introduce a novel network architecture named Deep Recurrent Graph Network (DRGN), which could obtain extra spatial information through graph-convolution based inter-UAV communication, and utilize historical features with a recurrent unit. Based on DRGN and maximum-entropy learning, we propose a stochastic DRL policy named Soft Deep Recurrent Graph Network (SDRGN). In SDRGN, a heuristic reward function is elaborated, which is based on the local information of each UAV instead of the global information; thus, SDRGN reduces the training cost and enables distributed online learning. We conducted extensive experiments to design the structure of DRGN and examine the performance of SDRGN. The simulation results show that the proposed model outperforms four state-of-the-art DRL-based approaches and three heuristic baselines, and demonstrate the scalability, transferability, robustness, and interpretability of SDRGN. We release our code at https://github.com/yerfor/Soft-DRGN