Vertex classification—the problem of identifying the class labels of nodes in a graph—has applicability in a wide variety of domains. Examples include classifying subject areas of papers in citation net-works or roles of machines in a computer network. Recent work has demonstrated that vertex classification using graph convolutional networks is susceptible to targeted poisoning attacks, in which both graph structure and node attributes can be changed in anattempt to misclassify a target node. This vulnerability decreases users’ confidence in the learning method and can prevent adoption in high-stakes contexts. This paper presents the first work aimed at leveraging network characteristics to improve robustness of these methods. Our focus is on using network features to choose the training set, rather than selecting the training set at random. Our alternative methods of selecting training data are (1) to select the highest-degree nodes in each class and (2) to iteratively select the node with the most neighbors minimally connected to the training set. In the datasets on which the original attack was demonstrated, we show that changing the training set can make the network much harder to attack. To maintain a given probability of attack success, the adversary must use far more perturbations; often a factor of 2–4 over the random training baseline. This increase in robustness is often as substantial as tripling the amount of randomly selected training data. Even in cases where success is relatively easy for the attacker, we show that classification performance degrades much more gradually using the proposed methods, with weaker incorrect predictions for the attacked nodes. Finally, we investigate the potential tradeoff between robustness and performance in various datasets.