Network security analysis based on attack graphs has been applied extensively in recent years. The ranking of nodes in an attack graph is an important step towards analyzing network security. This paper proposes an alternative attack graph ranking scheme based on a recent approach to machine learning in a structured graph domain, namely, Graph
Neural Networks (GNNs). Evidence is presented in this paper that the GNN is suitable for the task of ranking attack graphs by learning a ranking function from examples and generalizes the function to unseen possibly noisy data, thus showing that the GNN provides an effective alternative ranking method for attack graphs.