For the i th row of a matrix, the cycle transpositions are calculated based on the ς (𝑖,𝑗) partitions and . These cycle transpositions are used in the automorphisms λ (𝑖-1) λ (𝑖) search. All these cycles are multiplied in DFS manner with all the former automorphisms of τ the graph. This updated list of permutations are used in the canonical test of the matrix. For a graph with p nodes, its list of automorphisms until the i th row is: