As a complex neural network system, the brain regions and genes collaborate to effectively store and transmit information. We abstract the collaboration correlations as the brain region gene community network (BG-CN) and present a new deep learning approach, such as the community graph convolutional neural network (Com-GCN), for investigating the transmission of information within and between communities. The results can be used for diagnosing and extracting causal factors for Alzheimer's disease (AD). First, an affinity aggregation model for BG-CN is developed to describe intercommunity and intracommunity information transmission. Second, we design the Com-GCN architecture with intercommunity convolution and intracommunity convolution operations based on the affinity aggregation model. Through sufficient experimental validation on the AD neuroimaging initiative (ADNI) dataset, the design of Com-GCN matches the physiological mechanism better and improves the interpretability and classification performance. Furthermore, Com-GCN can identify lesioned brain regions and disease-causing genes, which may assist precision medicine and drug design in AD and serve as a valuable reference for other neurological disorders.