Brain functional hypernetwork is widely used for the classification of brain diseases. However, in most of the studies, the classification accuracy is mainly increased by improving the construction of resting-state hypernetwork model, and common node topological attributes, such as clustering coefficients, are mainly used to quantify the brain functional hypernetwork. The effective information contained in the topological attributes of the hypernetwork is ignored. It is shown that the higher-order patterns embodied in the hyperedges can better characterize the overall structure of the brain network, and the interactions among the hyperedges can reflect the spatial transfer of information among the hyperedges, which can help to better understand the neural mechanisms of brain diseases. Considering the problem, multiple sets of hyperedge attributes were proposed and combined with existing node attributes to comprehensively characterize the topological information of the brain functional hypernetwork. However, the topological information is more expensive to compute due to the hyperedge property of the hypernetwork, and the high redundancy between multiple topological attributes may exist. Therefore, the existing null model was further optimized to adapt to the brain functional hypernetwork, and the dependencies among topological attributes were evaluated based on the optimized null model. Finally the topological attributes with less dependency were fused to participate in the construction of the classification model. The results show that the dependencies among topological attributes are different, and the topological attributes containing hyperedge has less dependency with the rest of topological attributes. In addition, the classification performance of fusing multiple topological attribute features with less dependency is better than the traditional method, reaching 89.39%. This indicates that not only node topological attributes but also hyperedge information need to be considered when extracting the topological information of brain functional hypernetwork. Meanwhile, on the basis of multiple topological attributes characterizing the topological information of brain functional hypernetwork, the topological attributes with less dependency, i. e. , lower redundancy, can be selected to improve the ability to characterize the differences between groups, and the performance of classifying brain diseases can ultimately be improved.