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

[geremy condra]

On Mon, Nov 23, 2009 at 7:05 PM, Paul Miller
<paul.w.miller.please.dont.spam.me at wmich.edu> wrote:
> 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!

Graphine does this with the following:

from base import Graph

def K(n):
	"""Generates a completely connected undirected graph of size n.

	The verticies are numbered [0, n).

	The edges are named after the verticies they connect such that
	an edge connected verticies 1 and 2 is named (1,2).
	"""
	# create the graph
	k = Graph()
	# generate all the nodes
	for i in range(n):
		k.add_node(i)
	# generate all the edges
	for i in range(n):
		for j in range(i+1, n):
			k.add_edge(i, j, (i,j), is_directed=False)
	# return the graph
	return k


Disclaimer: I'm the author of graphine.

Geremy Condra