The group theory-based graph automorphism search algorithm implemented in the nauty package efficiently determines the total size of the permutation group and its generators without requiring the explicit generation of all possible permutations. Moreover, the information on orbits -the equivalence classes of the graph's vertices under the action of the automorphisms -can be obtained without additional computations. Different orbits represent atoms with distinct global neighborhood chemical compositions. Compared to the number that can be expected for a given system, a large number of different orbits reveals that the dataset is insufficiently repre-sentative or that a transition state is present, requiring careful construction of the dataset to capture its behavior accurately.