Any elegant way to construct the complete \$k\$-partite graph inPython?

Discussion in 'Python' started by Paul Miller, Nov 24, 2009.

1. Paul MillerGuest

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_indicesartition_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 for v in \
partite_sets [j] ])

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

Many thanks!

Paul Miller, Nov 24, 2009

2. geremy condraGuest

On Mon, Nov 23, 2009 at 7:05 PM, Paul Miller
<> 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_indicesartition_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 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):
# generate all the edges
for i in range(n):
for j in range(i+1, n):
# return the graph
return k

Disclaimer: I'm the author of graphine.

Geremy Condra

geremy condra, Nov 24, 2009

3. geremy condraGuest

On Mon, Nov 23, 2009 at 9:03 PM, geremy condra <> wrote:
> On Mon, Nov 23, 2009 at 7:05 PM, Paul Miller
> <> 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_indicesartition_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 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):
>        # generate all the edges
>        for i in range(n):
>                for j in range(i+1, n):
>        # return the graph
>        return k
>
>
> Disclaimer: I'm the author of graphine.
>
> Geremy Condra
>

Sorry, misread- to generate a k-partite graph, you'll need a bit
more legwork. Give me a bit and I'll add it to graphine.

Geremy Condra

geremy condra, Nov 24, 2009
4. geremy condraGuest

On Mon, Nov 23, 2009 at 9:10 PM, geremy condra <> wrote:
> On Mon, Nov 23, 2009 at 9:03 PM, geremy condra <> wrote:
>> On Mon, Nov 23, 2009 at 7:05 PM, Paul Miller
>> <> 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_indicesartition_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 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):
>>        # generate all the edges
>>        for i in range(n):
>>                for j in range(i+1, n):
>>        # return the graph
>>        return k
>>
>>
>> Disclaimer: I'm the author of graphine.
>>
>> Geremy Condra
>>

Alright, how does this look:

def k_partite(*partition_sizes):
g = Graph()
for pos, num_nodes in enumerate(partition_sizes):
for i in range(num_nodes):
for node1 in g.nodes:
for node2 in g.nodes:
if node1.partition != node2.partition:
return g

Geremy Condra

geremy condra, Nov 24, 2009
5. Richard ThomasGuest

On Nov 24, 2:45 am, geremy condra <> wrote:
> On Mon, Nov 23, 2009 at 9:10 PM, geremy condra <> wrote:
> > On Mon, Nov 23, 2009 at 9:03 PM, geremy condra <> wrote:
> >> On Mon, Nov 23, 2009 at 7:05 PM, Paul Miller
> >> <> 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_indicesartition_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 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):
> >>        # 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

>
> Alright, how does this look:
>
> def k_partite(*partition_sizes):
>         g = Graph()
>         for pos, num_nodes in enumerate(partition_sizes):
>                 for i in range(num_nodes):
>         for node1 in g.nodes:
>                 for node2 in g.nodes:
>                         if node1.partition != node2.partition:
>         return g
>
> Geremy Condra

Not sure exactly how you're representing graphs, this seems like the
simplest way of listing the edges.

def complete_partite(*sizes):
total = sum(sizes)
nodes, edges = range(total), []
for group in xrange(len(sizes)):
low = sum(sizes[:group-1])
high = sum(sizes[:group])
edges.extend((i, j) for i in xrange(low, high)
for j in xrange(high, total))
return nodes, edges

Chard

Richard Thomas, Nov 24, 2009
6. Paul MillerGuest

On Mon, 23 Nov 2009 19:57:05 -0800, Richard Thomas wrote:

> Not sure exactly how you're representing graphs, this seems like the
> simplest way of listing the edges.
>
> def complete_partite(*sizes):
> total = sum(sizes)
> nodes, edges = range(total), []
> for group in xrange(len(sizes)):
> low = sum(sizes[:group-1])
> high = sum(sizes[:group])
> edges.extend((i, j) for i in xrange(low, high)
> for j in xrange(high, total))
> return nodes, edges

Thanks! I think this is what I was looking for (unless the collective
wisdom of c.l.py can come up with something *even more* elegant).

Paul Miller, Nov 24, 2009
7. Malte HelmertGuest

Paul Miller wrote:
> On Mon, 23 Nov 2009 19:57:05 -0800, Richard Thomas wrote:
>
>> Not sure exactly how you're representing graphs, this seems like the
>> simplest way of listing the edges.
>>
>> def complete_partite(*sizes):
>> total = sum(sizes)
>> nodes, edges = range(total), []
>> for group in xrange(len(sizes)):
>> low = sum(sizes[:group-1])
>> high = sum(sizes[:group])

I think this has a conceptual off-by-one error. Add

print group, low, high

to see what I mean (especially the first iteration). It still works, but
I think this would be clearer:

low = sum(sizes[:group])
high = sum(sizes[:group + 1])

or to avoid doing essentially the same summation twice:

low = sum(sizes[:group])
high = low + sizes[group]

>> edges.extend((i, j) for i in xrange(low, high)
>> for j in xrange(high, total))
>> return nodes, edges

Here's a variant that uses a running total instead of recomputing the
sum in every iteration, thus getting rid of xrange(len(...)).

def complete_partite(*sizes):
total = sum(sizes)
nodes, edges = range(total), []
curr_total = 0
for size in sizes:
edges.extend((i, j) for i in xrange(curr_total, curr_total+size)
for j in xrange(curr_total+size, total))
curr_total += size
return nodes, edges

Finally, here is a variant that is a bit shorter because it produces the
edges in a different way and hence gets rid of the need for knowing the
total up front and uses total as running total instead. It has the
drawback of not generating the edges in ascending order though, so I
think the previous one is nicer:

def complete_partite(*sizes):
total, edges = 0, []
for size in sizes:
edges.extend((i, j) for i in xrange(total)
for j in xrange(total, total + size))
total += size
return range(total), edges

Finally, here's a variation on the same theme:

def complete_partite(*sizes):
nodes, edges = [], []
for size in sizes:
partition = xrange(len(nodes), len(nodes) + size)
edges.extend((i, j) for i in nodes for j in partition)
nodes.extend(partition)
return nodes, edges

Malte

Malte Helmert, Nov 24, 2009