Sample graph with its adjacency matrix. A sample graph is shown in (a). As there are 4 vertices in this graph, there are 4! permutations on its vertices to indicate its different adjacency matrices and so different strings according to NAUTY description. The adjacency matrix in (b) reflects (1, 2, 3, 4) ordering of vertices. Among all different permutations (2, 1, 3, 4) ordering, creates the largest string which its related adjacency matrix is shown in (c) and this is the one known as canonical labeling.