Labeling vertices of a graph effectively

savecancel

To get what you want, it's best to relabel the vertices of each copy of the cliques and then add edges to the result. This way, you know exactly what's going on.

def Sier(n, k):
    g = graphs.CompleteGraph(n)
    h = Graph()
    for i in range(1, k + 1):
        perm = {u: (i, u) for u in g}
        gg = g.relabel(perm=perm, inplace=False)
        h.add_edges(gg.edges())
    return h

You get

sage: h = Sier(3, 4)
sage: h.vertices()
[(1, 0),
 (1, 1),
 (1, 2),
 (2, 0),
 (2, 1),
 (2, 2),
 (3, 0),
 (3, 1),
 (3, 2),
 (4, 0),
 (4, 1),
 (4, 2)]

You can have a look at the relabel method:

sage: k.relabel?