This paper proposes a new approach for graph compression by optimal transport. It adds a sparsity constraint to the resulting Linear Program and relaxes it to the projection into a simplex. The final problem can be solved by a customized mirror prox method. Empirical studies on are also shown. All reviewers agreed that this is a nicely written paper that studies an original problem with a principled approach. This problem is likely to have applications to the broad ML community and therefore the AC recommends acceptance.