Very recent advances in machine learning have expanded deep learning methods to spatially-irregular data domains. Deep learning on graphs in particular has received greater study, providing benefits in numerous fields. In this paper we present a graph-based convolutional autoencoder and assess the contribution of four components towards encoding quality. A graph-based convolution-operator is used to learn localised filtering operations for graph-wise encoding. An evaluation of the proposed method is provided on a topologically-irregular version of MNIST that violates the assumption made by conventional convolutional autoencoder methods of the structure of its input-data.