<p>Alzheimer's disease (AD) classification based on brain functional networks has become a research hotspot in neuroimaging, showing significant clinical application potential. However, challenges remain in brain functional network sparsification, multimodal fusion, and interpretability. A sparsity reconstruction method based on Euler characteristics for brain functional networks is proposed, with classification performed by integrating the sparsified network structure, age, sex, and network features, and key brain regions are identified through gradient backpropagation. Specifically, a threshold sparsity method based on the Euler feature fitting curve is first adopted, and stable points in the network structure are identified by analyzing the trend changes of the Euler fitting feature curve. Then, a hypergraph convolutional neural network with a weighted fusion layer is constructed to integrate age, sex features, and the topological features of the sparsified brain functional network for accurate classification of different disease stages. Finally, gradient backpropagation-based localization is used to identify disease-related key brain regions. Experimental results demonstrate that the Euler characteristic-based sparsification method can objectively simplify and preserve critical information in brain functional networks, achieving an accuracy of 90.22% in the AD versus normal control classification task. Moreover, the identified key regions, the identified key regions, including the hippocampus and precuneus, show strong consistency with known clinical neuropathological findings, improving the interpretability of classification results.</p>