A modification of the adjacency matrix power method described recently for the perception of symmetry in graphs is introduced, which expands the limits of the method far beyond the realm of chemically interesting graphs. The procedure finds the automorphism partition even for intricate graphs without performing a tree search. The calculation effort increases with the problem size polynomially for all tested cases, including strongly regular graphs, two-level regular graphs, and graphs corresponding to balanced incomplete block designs (BIBD). An equally powerful computer program for testing isomorphism of graphs based on the adjacency matrix power method is introduced.