An algorithm is presented that quickly detects local and global symmetries of single molecules and complexes. Based upon the Morgan Naming Algorithm, the algorithm involves traversing the molecule from a starting atom and building up a molecule name based upon the names of the atoms encountered along the traversal. Additional molecule names are generated from other starting atoms, and name-name matches are identified as corresponding to symmetry operations. A number of enhancements relative to prior methods yield increased efficiency and extended functionality. In particular, the present method detects not only global symmetries but also local symmetries associated with bond rotations as well as symmetries that are only apparent when alternate resonance forms are considered. Importantly, the present method works not only for single molecules but also for multimolecular complexes. As a consequence, it is well, and perhaps uniquely, suited to applications in supramolecular and host-guest chemistry. Applications include filtering out redundant conformations during conformational searching and free energy calculations; accelerating ligand-receptor docking calculations by reducing the sampling ranges of rotatable bonds linked to locally symmetric groups, such as phenyls; and automating the calculation of symmetry numbers for thermochemical applications.