  The emergence of geometric deep learning as a novel framework to deal with
graph-based representations has faded away traditional approaches in favor of
completely new methodologies. In this paper, we propose a new framework able to
combine the advances on deep metric learning with traditional approximations of
the graph edit distance. Hence, we propose an efficient graph distance based on
the novel field of geometric deep learning. Our method employs a message
passing neural network to capture the graph structure, and thus, leveraging
this information for its use on a distance computation. The performance of the
proposed graph distance is validated on two different scenarios. On the one
hand, in a graph retrieval of handwritten words~\ie~keyword spotting, showing
its superior performance when compared with (approximate) graph edit distance
benchmarks. On the other hand, demonstrating competitive results for graph
similarity learning when compared with the current state-of-the-art on a recent
benchmark dataset.
