The Mapper graph, seen as a metric measure space, converges to the Reeb graph at rate n^-nu/(d+alpha) in expected Gromov-Wasserstein distance.
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Gromov-Wasserstein Bound between Reeb and Mapper Graphs
The Mapper graph, seen as a metric measure space, converges to the Reeb graph at rate n^-nu/(d+alpha) in expected Gromov-Wasserstein distance.