This paper addresses the following basic question: given two layouts of the same graph, which one is more aesthetically pleasing? We propose a neural network-based discriminator model trained on a labeled dataset that decides which of two layouts has a higher aesthetic quality. The feature vectors used as inputs to the model are based on known graph drawing quality metrics, classical statistics, information-theoretical quantities, and two-point statistics inspired by methods of condensed matter physics. The large corpus of layout pairs used for training and testing is constructed using force-directed drawing algorithms and the layouts that naturally stem from the process of graph generation. It is further extended using data augmentation techniques. Our model demonstrates a mean prediction accuracy of 97.58%, outperforming discriminators based on stress and on the linear combination of popular quality metrics by a margin of 2 to 3%. The present paper extends our contribution to the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018) and is based on a significantly larger dataset.