Alzheimer's disease is characterized by alterations of the brain's structural and functional connectivity during its progressive degenerative processes. Existing auxiliary diagnostic methods have accomplished the classification task, but few of them can accurately evaluate the changing characteristics of brain connectivity. In this work, a prior guided adversarial representation learning and hypergraph perceptual network (PGARL-HPN) is proposed to predict abnormal brain connections using triple-modality medical images. Concretely, a prior distribution from the anatomical knowledge is estimated to guide multimodal representation learning using an adversarial strategy. Also, the pairwise collaborative discriminator structure is further utilized to narrow the difference of representation distribution. Moreover, the hypergraph perceptual network is developed to effectively fuse the learned representations while establishing high-order relations within and between multimodal images. Experimental results demonstrate that the proposed model outperforms other related methods in analyzing and predicting Alzheimer's disease progression. More importantly, the identified abnormal connections are partly consistent with the previous neuroscience discoveries. The proposed model can evaluate characteristics of abnormal brain connections at different stages of Alzheimer's disease, which is helpful for cognitive disease study and early treatment.