  In this paper, we derive generalization bounds for the two primary classes of
graph neural networks (GNNs), namely graph convolutional networks (GCNs) and
message passing GNNs (MPGNNs), via a PAC-Bayesian approach. Our result reveals
that the maximum node degree and spectral norm of the weights govern the
generalization bounds of both models. We also show that our bound for GCNs is a
natural generalization of the results developed in arXiv:1707.09564v2 [cs.LG]
for fully-connected and convolutional neural networks. For message passing
GNNs, our PAC-Bayes bound improves over the Rademacher complexity based bound
in arXiv:2002.06157v1 [cs.LG], showing a tighter dependency on the maximum node
degree and the maximum hidden dimension. The key ingredients of our proofs are
a perturbation analysis of GNNs and the generalization of PAC-Bayes analysis to
non-homogeneous GNNs. We perform an empirical study on several real-world graph
datasets and verify that our PAC-Bayes bound is tighter than others.
