Title: Adversarial Weight Perturbation Improves Generalization in Graph Neural Networks. Abstract: There is growing theoretical and empirical evidence that flatter local minima tend to improve generalization. An efficient and effective technique for finding such minima is Adversarial Weight Perturbation (AWP). The main idea is to minimize the loss w.r.t. a bounded worst-case perturbation of the model parameters by (approximately) solving an associated min-max problem. Intuitively, we favor local minima with a small loss in a neighborhood around them. The benefits of AWP, and more generally the connections between flatness and generalization, have been extensively studied for i.i.d. data such as images. In this paper we initiate the first study of this phenomenon for graph data. Along the way, we identify a vanishing-gradient issue with all existing formulations of AWP and we propose Weighted Truncated AWP (WT-AWP) to alleviate this issue. We show that regularizing graph neural networks with WT-AWP consistently improves both natural and robust generalization across many different graph learning tasks and models.