This paper presents a novel method that combines multi-graph matching with clustering. The method introduces several interesting components to achieve this goal, namely back-propagating through the Sinkhorn algorithm and solving the multi-graph problem with a first-order Taylor expansion of Koopmans-Beckmann’s QAP. As noted by reviewers, the paper needs some rewriting to better discuss previous work and clarify some of the claims, however, the contributions of this work are sufficiently important to recommend acceptance.