We have developed a graph-based method for identifying permutational symmetries, applicable to both periodic and non-periodic chemical systems. Our approach systematically uncovers symmetries across the entire configurational space by analyzing atomic positions from a dataset of configurations. It outputs the size and generators of atomic permutation sets, along with a classification of atoms into chemi-cally distinct environments (orbits). Notably, this information is determined prior to explicitly computing permutations. Our method has been successfully integrated with the kernelbased sGDML framework and the equivariant MPNN MACE model.