In chemical structure elucidation, symmetric structures sometimes need careful handling. In the course of the development of a system for NMR-based structure elucidation, we have developed a method for processing chemical structures with high symmetry by applying an efficient algorithm for graph inference. In the present letter, we describe the outline of the algorithm by taking bibenzyl as an example. The method has been implemented to CAST/CNMR, a system for NMR-based structure/chemical shift prediction.