Any elegant way to construct the complete $k$-partite graph in Python?

[Paul Miller]

I was wondering if there were any neat tools (like for instance, 
something from itertools) that would help me write the following function 
more elegantly.  The return value should, of course, be the complete $k$-
partite graph $K_{n_1, n_2, \dots, n_k}$:

def completeGraph (*ns):
    '''
    Returns the complete graph $K_{n_1, n_2, \dots, n_k}$ when passed
    the sequence \code {n_1, n_2, \dots, n_k}.
    '''
    if len (ns) == 1:
	return completeGraph ( * ([1] * ns[0]) )
    n = sum (ns)
    vertices = range (n)
    partition_indices = [sum (ns[:i]) for i in range (len (ns))] 
    partite_sets = [vertices[partition_indices[i]:partition_indices[i+1]] 
\
		    for i in range (len (partition_indices) - 1)]
    partite_sets.append (vertices[partition_indices [-1]:] )

    edges = []
    for i in range (len (partite_sets)):
	for j in range (i + 1, len (partite_sets)):
	    edges.extend ([ (u, v) for u in partite_sets [i] for v in \
			   partite_sets [j] ])

    return graph.Graph (vertices = vertices, edges = edges)

Many thanks!