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Strong Equivalence of the Interleaving and Functional Distortion Metrics for Reeb Graphs Bauer, Ulrich Munch, Elizabeth Wang, Yusu Reeb graph interleaving distance functional distortion distance The Reeb graph is a construction that studies a topological space through the lens of a real valued function. It has been commonly used in applications, however its use on real data means that it is desirable and increasingly necessary to have methods for comparison of Reeb graphs. Recently, several metrics on the set of Reeb graphs have been proposed. In this paper, we focus on two: the functional distortion distance and the interleaving distance. The former is based on the Gromov-Hausdorff distance, while the latter utilizes the equivalence between Reeb graphs and a particular class of cosheaves. However, both are defined by constructing a near-isomorphism between the two graphs of study. In this paper, we show that the two metrics are strongly equivalent on the space of Reeb graphs. Our result also implies the bottleneck stability for persistence diagrams in terms of the Reeb graph interleaving distance. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ulrich Bauer and Elizabeth Munch and Yusu Wang 2015 Is Part Of LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SOCG.2015.461 urn:nbn:de:0030-drops-51467 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.461 eng https://creativecommons.org/licenses/by/3.0/legalcode