GESim: Ultrafast Graph-Based Molecular Similarity Calculation via von Neumann Graph Entropy

Representing molecules as graphs is a natural approach for capturing their structural information, with atoms depicted as nodes and bonds as edges. 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 characteristics intermediate between those of atom-pair fingerprints and extended-connectivity fingerprints. GESim is provided as an open-source package on GitHub at https://github.com/LazyShion/GESim.