  This work provides a theoretical framework for assessing the generalization
error of graph neural networks in the over-parameterized regime, where the
number of parameters surpasses the quantity of data points. We explore two
widely utilized types of graph neural networks: graph convolutional neural
networks and message passing graph neural networks. Prior to this study,
existing bounds on the generalization error in the over-parametrized regime
were uninformative, limiting our understanding of over-parameterized network
performance. Our novel approach involves deriving upper bounds within the
mean-field regime for evaluating the generalization error of these graph neural
networks. We establish upper bounds with a convergence rate of $O(1/n)$, where
$n$ is the number of graph samples. These upper bounds offer a theoretical
assurance of the networks' performance on unseen data in the challenging
over-parameterized regime and overall contribute to our understanding of their
performance.
