A stable formation communication network can improve the task efficiency of a unmanned aerial vehicle (UAV) cluster. Aiming at the topology construction of the UAV formation communication network, combined with the optimal rigid graph theory, we design a three-dimensional UAV formation communication network generation algorithm based on the optimal rigid graph. We construct a new link weight function by introducing node residual energy and communication path loss to reduce the overall energy consumption of formation. Aiming at the problem that the communication link of the UAV is interrupted when the formation network is moving, a UAV communication beam tracking and holding method based on a multiple-input multiple-output (MIMO) structure and position prediction is designed. Simulation results show that the network topology constructed by the UAV formation communication network generation algorithm has a good average node degree, and effectively improves the network connectivity and communication fault tolerance. Compared with the tracking and holding algorithm based on the received signal strength, the beam tracking and holding algorithm significantly reduces the number of link interruptions, and the communication success holding rate can be basically maintained at about 90%.