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Although graph-based similarity calculation approaches, such as the graph edit distance, have been proposed for calculating molecular similarity, these approaches are nondeterministic polynomial (NP)-hard and thus computationally infeasible for routine use, unlike fingerprint-based methods. To address this limitation, we developed GESim, an ultrafast graph-based method for calculating molecular similarity on the basis of von Neumann graph entropy. GESim enables molecular similarity calculations by considering entire molecular graphs, and evaluations using two benchmarks for molecular similarity suggest that GESim has the ability to differentiate between highly similar molecules, even in cases where other methods fail to effectively distinguish their similarity. 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