What is the worth of a node? We answer this question using an emerging set of data valuation techniques, where the value of a data point is measured via its marginal contribution when added to the (training) dataset. Data valuation has been primarily studied in the i.i.d. setting, giving rise to methods like influence functions, leave-one-out estimation, data Shapley, and data Banzhaf. We conduct a comprehensive study of data valuation approaches applied to graph-structured models such as graph neural networks in a semi-supervised transductive setting. Since all nodes (labeled and unlabeled) influence both training and inference we construct various scenarios to understand the diverse mechanisms by which nodes can impact learning. We show that the resulting node values can be used to identify (positively and negatively) influential nodes, quantify model brittleness, detect poisoned data, and accurately predict counterfactuals.