The calling sequence PermuteVertices('G','sigma') returns a new graph H with Vertices(H) = sigma.  The list of neighbors data structure is reordered according to sigma so that the adjacency matrix of H will be different in general.  Attribute information, including vertex position information is also permuted according to sigma so that DrawGraph(H) will look identical to DrawGraph(G).

The calling sequence IsomorphicCopy('G','sigma') returns a new graph H where the list of neighbors data structure is reordered according to sigma but the vertex labels of H are the same as G. It also discards all attributes from G so that if H is drawn, it will not be obvious that H is isomorphic to G.

The calling sequence PermuteVertices('G') chooses a random permutation sigma of the vertices of G then returns H = PermuteVertices(G,sigma). Hence Vertices(H) is the permutation used.

The calling sequence IsomorphicCopy('G') chooses a random permutation sigma of the vertices of G and returns IsomorphicCopy('G','sigma').