The performance of machine learning methods is strongly dependent on the data representation (features) to which they are applied. For drawings in particular, we cannot rely on texture, color or shading information; there is little information present in a drawing beyond the spatial relationships and topology. A topological graph is an intuitive and powerful data structure and data representation framework that can capture the topological relations and spatial arrangement among entities present in images. In this paper, we use topological features automatically extracted from graph representations of images for image classification. Our approach is simple, intuitive, and generic. We compare our method against a traditional feature descriptor, histogram of oriented gradients (HOG) on the MNIST data set. The results demonstrate the effectiveness of our graph approach, especially when applied to small sets of training data. In addition, our method is very fast to train, and also much less sensitive to hyperparameters, requiring little hyperparameter fine tuning.