At the initial stage of unmanned aerial vehicle formation assembly and networking in air, it is necessary to quickly discover neighbours. According to ultraviolet (UV) characteristics near direct vision communication, this study designs a spherical UV LED communication node model. The longitude at each latitude is changed to reasonably distributed UV LED based on the division of longitude and latitude. In addition, a handshake interaction information frame with random probability is designed to solve the problems of channel conflict and neighbour discovery efficiency in the neighbour discovery process. Random probability is introduced to reduce channel conflict generation, and a token-derived random avoidance neighbour discovery algorithm is proposed. Clock synchronisation information is realised through token dynamic derivation and fusion, reducing channel conflict and improving neighbour detection efficiency. The simulation results show that the spherical UV LED communication node model with a reasonable distribution of nodes can appropriately complete the full coverage of the three-dimensional space. Moreover, the neighbour discovery efficiency is significantly improved using the neighbour discovery algorithm compared with the traditional single token neighbour discovery algorithm. Compared with the multi-token random back off algorithm, the developed better reduces the channel conflict, reduces energy consumption, and achieves a good balance of the signal path conflict and neighbour discovery efficiency.