Chemistry Department, Burdwan University, Burdwan-713 104 Manuscript received 8 February 1990, revised 9 July 1991, accepted 3 September 1991 Polyhedra, atom clusters (S4, S8, P4), ligands of complexes with similar vertex atoms are some fertile fields besides many others where topology can play a useful role. Usual graphical reduction technique for writing topological matrices '!f the resulting subgraphs stops at a stage when symmetry is lost during the decomposition process. The process can, however, be continued with a proxy system of enforced symmetry until the stages of 1-vertex and 2-vertex graphs are obtained for an easy evaluation of eigenvalues which are either identical with or very close to the real ones. Even in the face of the availability of PC's, capable of handling large matrices, the purpose of the present paper lies not only in Its practical utility but also in its exhibition that the principle of graphical reduction holds greater potentiality than what has so far been exploited. Secondly, the method can serve as an extremely useful tool even for fairly big molecules or polyhedra.