Cancer is one of the leading causes of death for patients, and microarray technology offers new ways to diagnose and treat cancer. However, limited by the difficulty of sample acquisition, its genetic dimension is much higher than the sample dimension. Such data are also called high-dimensional small sample data or microarray data. Feature selection can effectively select effective features from the high-dimensional feature space of microarray data as biomarkers for further analysis. However, there are many interdependencies among genes, such as regulatory networks and pathways, and it is difficult for existing methods to fully utilize this information to guide the feature selection and ranking process and build efficient classification models. Therefore, this paper proposes a feature selection algorithm and classification model based on graph neural networks to solve the above problems. In the proposed method, a multidimensional graph is used to represent the complex interactions between genes, link prediction techniques are used to enrich the existing graph structure relationships, and a multidimensional node evaluator and a supernode discovery algorithm based on spectral clustering are used to achieve the initial filter of nodes. Subsequently, we used a hierarchical graph pooling technique based on downsampling to further screen nodes to achieve feature selection and build classification models. The results on nine publicly available microarray datasets show that the proposed method outperforms both classical feature selection methods and advanced feature selection methods in different evaluation metrics, demonstrating the effectiveness and advancement of the proposed method.