Abstract: With the construction of adjacency matrices that can effectively describe an arbitrary topological graph,the eigenvectors of the same eigenvalue of the two matrices are calculated respectively and the possible isomorphic correspondences are established on the basis of their maximum impertinent groups.After all the eigenvalues have been considered,isomorphism will be determined and correspondence of vertices in isomorphic graphs can be ultimately identified. With the scale and symmetry of graphs increasing,this method enjoys advantages in efficiency compared with some proposed methods.It has been experimentally verified to be efficient and effective in most cases.