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In this paper, we study the cluster head detection problem of a two-level unmanned aerial vehicle (UAV) swarm network (USNET) with multiple UAV clusters, where the inherent follow strategy (IFS) of low-level follower UAVs (FUAVs) with respect to high-level cluster head UAVs (HUAVs) is unknown. We first propose a graph attention self-supervised learning algorithm (GASSL) to detect the HUAVs of a single UAV cluster, where the GASSL can fit the IFS at the same time. Then, to detect the HUAVs in the USNET with multiple UAV clusters, we develop a multi-cluster graph attention self-supervised learning algorithm (MC-GASSL) based on the GASSL. The MC-GASSL clusters the USNET with a gated recurrent unit (GRU)-based metric learning scheme and finds the HUAVs in each cluster with GASSL. Numerical results show that the GASSL can detect the HUAVs in single UAV clusters obeying various kinds of IFSs with over 98% average accuracy. The simulation results also show that the clustering purity of the USNET with MC-GASSL exceeds that with traditional clustering algorithms by at least 10% average. Furthermore, the MC-GASSL can efficiently detect all the HUAVs in USNETs with various IFSs and cluster numbers with low detection redundancies.