def complete_multipartite_graph(*subset_sizes):
"""Returns the complete multipartite graph with the specified subset sizes.
Parameters
----------
subset_sizes : tuple of integers or tuple of node iterables
The arguments can either all be integer number of nodes or they
can all be iterables of nodes. If integers, they represent the
number of vertices in each subset of the multipartite graph.
If iterables, each is used to create the nodes for that subset.
The length of subset_sizes is the number of subsets.
Returns
-------
G : NetworkX Graph
Returns the complete multipartite graph with the specified subsets.
For each node, the node attribute 'subset' is an integer
indicating which subset contains the node.
Examples
--------
Creating a complete tripartite graph, with subsets of one, two, and three
vertices, respectively.
>>> import networkx as nx
>>> G = nx.complete_multipartite_graph(1, 2, 3)
>>> [G.node[u]['subset'] for u in G]
[0, 1, 1, 2, 2, 2]
>>> list(G.edges(0))
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)]
>>> list(G.edges(2))
[(2, 0), (2, 3), (2, 4), (2, 5)]
>>> list(G.edges(4))
[(4, 0), (4, 1), (4, 2)]
>>> G = nx.complete_multipartite_graph('a', 'bc', 'def')
>>> [G.node[u]['subset'] for u in sorted(G)]
[0, 1, 1, 2, 2, 2]
Notes
-----
This function generalizes several other graph generator functions.
- If no subset sizes are given, this returns the null graph.
- If a single subset size `n` is given, this returns the empty graph on
`n` nodes.
- If two subset sizes `m` and `n` are given, this returns the complete
bipartite graph on `m + n` nodes.
- If subset sizes `1` and `n` are given, this returns the star graph on
`n + 1` nodes.
See also
--------
complete_bipartite_graph
"""
# The complete multipartite graph is an undirected simple graph.
G = Graph()
G.name = 'complete_multiparite_graph{}'.format(subset_sizes)
if len(subset_sizes) == 0:
return G
# set up subsets of nodes
try:
extents = pairwise(accumulate((0, ) + subset_sizes))
subsets = [range(start, end) for start, end in extents]
except TypeError:
subsets = subset_sizes
# add nodes with subset attribute
# while checking that ints are not mixed with iterables
try:
for (i, subset) in enumerate(subsets):
G.add_nodes_from(subset, subset=i)
except TypeError:
raise NetworkXError("Arguments must be all ints or all iterables")
# Across subsets, all vertices should be adjacent.
# We can use itertools.combinations() because undirected.
for subset1, subset2 in itertools.combinations(subsets, 2):
G.add_edges_from(itertools.product(subset1, subset2))
return G
def empty_graph(n=0, create_using=None):
"""Return the empty graph with n nodes and zero edges.
Parameters
==========
n : int or iterable container of nodes (default = 0)
If n is an integer, nodes are from `range(n)`.
If n is a container of nodes, those nodes appear in the graph.
create_using : Graph, optional (default Graph())
If provided this graph is cleared of nodes and edges and filled
with the new graph. Usually used to set the type of the graph.
For example:
>>> G = nx.empty_graph(10)
>>> G.number_of_nodes()
10
>>> G.number_of_edges()
0
>>> G = nx.empty_graph("ABC")
>>> G.number_of_nodes()
3
>>> sorted(G)
['A', 'B', 'C']
Notes
=====
The variable create_using should point to a "graph"-like object that
will be cleared (nodes and edges will be removed) and refitted as
an empty "graph" with nodes specified in n. This capability
is useful for specifying the class-nature of the resulting empty
"graph" (i.e. Graph, DiGraph, MyWeirdGraphClass, etc.).
The variable create_using has two main uses:
Firstly, the variable create_using can be used to create an
empty digraph, multigraph, etc. For example,
>>> n = 10
>>> G = nx.empty_graph(n, create_using=nx.DiGraph())
will create an empty digraph on n nodes.
Secondly, one can pass an existing graph (digraph, multigraph,
etc.) via create_using. For example, if G is an existing graph
(resp. digraph, multigraph, etc.), then empty_graph(n, create_using=G)
will empty G (i.e. delete all nodes and edges using G.clear())
and then add n nodes and zero edges, and return the modified graph.
See also create_empty_copy(G).
"""
if create_using is None:
# default empty graph is a simple graph
G = Graph()
else:
G = create_using
G.clear()
n_name, nodes = n
G.name = "empty_graph(%s)" % (n_name, )
G.add_nodes_from(nodes)
return G
