This paper presents an effective dissimilarity measure for geometric graphs representing shapes. The dissimilarity measure is a distance that combines a sparsification of the geometric graph based on the maximum diversity problem and a new node embedding that captures the topological neighborhood of nodes. The sparsification step aims to correct the misdistribution of nodes on the geometric graph induced by the noise of image handling. Computational experiments on two popular datasets indicate that our approach retains the form of the shapes while decreasing the number of processed nodes which yields interesting results both on accuracy and time processing 1 .