A graph neural network (GNN) is a powerful architecture for semi-supervised learning (SSL). However, the data-driven mode of GNNs raises some challenging problems. In particular, these models suffer from the limitations of incomplete attribute learning, insufficient structure capture, and the inability to distinguish between node attribute and graph structure, especially on label-scarce or attribute-missing data. In this article, we propose a novel framework, called graph coneighbor neural network (GCoNN), for node classification. It is composed of two modules: GCoNN and GCoNN . GCoNN is trained to establish the fundamental prototype for attribute learning on labeled data, while GCoNN $_{\mathring{\Gamma}}$ learns neighbor dependence on transductive data through pseudolabels generated by GCoNN . Next, GCoNN is retrained to improve integration of node attribute and neighbor structure through feedback from GCoNN $_{\mathring{\Gamma}}$ . GCoNN tends to convergence iteratively using such an approach. From a theoretical perspective, we analyze this iteration process from a generalized expectation–maximization (GEM) framework perspective which optimizes an evidence lower bound (ELBO) by amortized variational inference. Empirical evidence demonstrates that the state-of-the-art performance of the proposed approach outperforms other methods. We also apply GCoNN to brain functional networks, the results of which reveal response features across the brain which are physiologically plausible with respect to known language and visual functions.