对比图神经网络全图与小批量训练，揭示批大小和扇出大小的影响。

Full-graph and mini-batch Graph Neural Network (GNN) training approaches have distinct system design demands, making it crucial to choose the appropriate approach to develop. A core challenge in comparing these two GNN training approaches lies in characterizing their model performance (i.e., convergence and generalization) and computational efficiency. While a batch size has been an effective lens in analyzing such behaviors in deep neural networks (DNNs), GNNs extend this lens by introducing a fan-out size, as full-graph training can be viewed as mini-batch training with the largest possible batch size and fan-out size. However, the impact of the batch and fan-out size for GNNs remains insufficiently explored. To this end, this paper systematically compares full-graph vs. mini-batch training of GNNs through empirical and theoretical analyses from the view points of the batch size and fan-out size. Our key contributions include: 1) We provide a novel generalization analysis using the Wasserstein distance to study the impact of the graph structure, especially the fan-out size. 2) We uncover the non-isotropic effects of the batch size and the fan-out size in GNN convergence and generalization, providing practical guidance for tuning these hyperparameters under resource constraints. Finally, full-graph training does not always yield better model performance or computational efficiency than well-tuned smaller mini-batch settings. The implementation can be found in the github link: https://github.com/LIUMENGFAN-gif/GNN_fullgraph_minibatch_training.