Before revision:  We first embed and coarsen the large graphs to "abstracted smaller graphs " with denser local topology , similar to molecular groups in biological concept. Then we aggregate both the internal features in "abstracted smaller graphs " and external features across "abstracted smaller graph pair", leading to feature vectors for each graph, with which we calculate the final similarity score.
After revision:  We first embed and coarsen the large graphs to "abstracted smaller graphs " with denser local topology and then matching mechanism is deployed on the coarsened graphs for the final similarity score.