A graph isomorphism algorithm using pseudoinverses

For a graph of m nodes and n edges, an algorithm for testing the isomorphism of graphs is given. The complexity of the algorithm is a maximum of O(mn(2)) in almost all cases, with a considerable reduction if sparsity is exploited. If isomorphism is present, the pseudoinverses of the Laplace matrices of the graphs will be row and column permutations of each other. Advantage can be taken of certain features of the incidence matrices or of properties of the graphs to reduce computation time.