  The graph isomorphism problem is a main problem which has numerous
applications in different fields. Thus, finding an efficient and easy to
implement method to discriminate non-isomorphic graphs is valuable. In this
paper, a new method is introduced which is very simple and easy to implement,
but very efficient in discriminating non-isomorphic graphs, in practice. This
method does not need any heuristic attempt and based on the eigenvalues of a
new matrix representation for graphs. It, almost always, separates
non-isomorphic $n$-vertex graphs in time $O(n^3)$ and in worst cases such as
strongly regular graphs, in time $O(n^4)$. Here, we show that this method,
successfully, characterizes the isomorphism classes of studied instances of
strongly regular graphs (up to 64 vertices). Strongly regular graphs are
believed to be hard cases of the graph isomorphism problem.
