There is a need for theory on how to group atoms in a molecule to define a coarse-grained (CG) mapping. This article investigates the importance of preserving symmetry of the underlying molecular graph of a given molecule when choosing a CG mapping. 26 CG models of seven alkanes with three different CG techniques were examined. We unexpectedly find preserving symmetry has no consistent effect on CG model accuracy regardless of CG method or comparison metric.