The presence of local symmetry perturbations in the final graph representation reduces the number of permutational symmetries while inflating the number of orbits. Focusing on local neighborhood chemical compositions-rather than relying exclusively on global orbits-can be more advantageous. The extent of these environments is determined by the number of nearest neighbors considered, a choice guided by the range of relevant interactions in the system. In the subsequent section, we will showcase a graphene system with a pyridinic-N defect to illustrate this scenario.