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Hydrogen-bond (HB) patterns correspond to topologically distinct isomers of water clusters, and can be expressed by digraphs. The HB pattern is used to divide the configuration space of water cluster at a finite temperature. The populations of the HB patterns are transformed into the relative Helmholtz energies. The method is based on the combination of molecular simulation with graph theory. At a finite temperature it can be observed that other isomers than local minimum structures on thedoi:10.1515/pac-2018-0721 fatcat:dbmqopkvzbfgnpgje3c2qqkd2y