Any elegant way to construct the complete $k$-partite graph in Python?
geremy condra
debatem1 at gmail.com
Tue Nov 24 03:03:38 CET 2009
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
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