A stable formation communication network can improve the ability for UAV clusters to perform tasks. Therefore， it is necessary to design an information interaction topology that maintains the formation and minimizes communication costs. This research is aimed at optimizing the topology of a UAV formation network by integrating the benefits of ultraviolet optical communication. Thus an optimally rigid formation generation algorithm for UAVs based on ultraviolet communication is proposed. In analyzing the ultraviolet communication link model between UAVs， an ultraviolet hemispherical LED array is used to assist the UAVs in finding their neighbor nodes. This is achieved by first generating an optimal rigid subgraph and then forming a optimal rigid formation graph through the link deletion. Simulation results show that when compared to other algorithms， the proposed algorithm constructs a topology with both an appropriate average node degree and a small communication radius. The proposed algorithm improves the fault tolerance performance of the network， reduces communication complexity and decreases energy consumption of the formation network.