Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# Source code for networkx.algorithms.bipartite.basic

# -*- coding: utf-8 -*-
"""
==========================
Bipartite Graph Algorithms
==========================
"""
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
import networkx as nx
__author__ = """\n""".join(['Jordi Torrents <jtorrents@milnou.net>',
'Aric Hagberg <aric.hagberg@gmail.com>'])
__all__ = ['is_bipartite',
'is_bipartite_node_set',
'color',
'sets',
'density',
'degrees']

[docs]def color(G):
"""Returns a two-coloring of the graph.

Raises an exception if the graph is not bipartite.

Parameters
----------
G : NetworkX graph

Returns
-------
color : dictionary
A dictionary keyed by node with a 1 or 0 as data for each node color.

Raises
------
exc:NetworkXError if the graph is not two-colorable.

Examples
--------
>>> from networkx.algorithms import bipartite
>>> G = nx.path_graph(4)
>>> c = bipartite.color(G)
>>> print(c)
{0: 1, 1: 0, 2: 1, 3: 0}

You can use this to set a node attribute indicating the biparite set:

>>> nx.set_node_attributes(G, c, 'bipartite')
>>> print(G.nodes[0]['bipartite'])
1
>>> print(G.nodes[1]['bipartite'])
0
"""
if G.is_directed():
import itertools

def neighbors(v):
return itertools.chain.from_iterable([G.predecessors(v),
G.successors(v)])
else:
neighbors = G.neighbors

color = {}
for n in G:  # handle disconnected graphs
if n in color or len(G[n]) == 0:  # skip isolates
continue
queue = [n]
color[n] = 1  # nodes seen with color (1 or 0)
while queue:
v = queue.pop()
c = 1 - color[v]  # opposite color of node v
for w in neighbors(v):
if w in color:
if color[w] == color[v]:
raise nx.NetworkXError("Graph is not bipartite.")
else:
color[w] = c
queue.append(w)
# color isolates with 0
color.update(dict.fromkeys(nx.isolates(G), 0))
return color

[docs]def is_bipartite(G):
""" Returns True if graph G is bipartite, False if not.

Parameters
----------
G : NetworkX graph

Examples
--------
>>> from networkx.algorithms import bipartite
>>> G = nx.path_graph(4)
>>> print(bipartite.is_bipartite(G))
True

--------
color, is_bipartite_node_set
"""
try:
color(G)
return True
except nx.NetworkXError:
return False

[docs]def is_bipartite_node_set(G, nodes):
"""Returns True if nodes and G/nodes are a bipartition of G.

Parameters
----------
G : NetworkX graph

nodes: list or container
Check if nodes are a one of a bipartite set.

Examples
--------
>>> from networkx.algorithms import bipartite
>>> G = nx.path_graph(4)
>>> X = set([1,3])
>>> bipartite.is_bipartite_node_set(G,X)
True

Notes
-----
For connected graphs the bipartite sets are unique.  This function handles
disconnected graphs.
"""
S = set(nodes)
for CC in nx.connected_component_subgraphs(G):
X, Y = sets(CC)
if not ((X.issubset(S) and Y.isdisjoint(S)) or
(Y.issubset(S) and X.isdisjoint(S))):
return False
return True

[docs]def sets(G, top_nodes=None):
"""Returns bipartite node sets of graph G.

Raises an exception if the graph is not bipartite or if the input
graph is disconnected and thus more than one valid solution exists.
See :mod:bipartite documentation <networkx.algorithms.bipartite>
for further details on how bipartite graphs are handled in NetworkX.

Parameters
----------
G : NetworkX graph

top_nodes : container

Container with all nodes in one bipartite node set. If not supplied
it will be computed. But if more than one solution exists an exception
will be raised.

Returns
-------
(X,Y) : two-tuple of sets
One set of nodes for each part of the bipartite graph.

Raises
------
AmbiguousSolution : Exception

Raised if the input bipartite graph is disconnected and no container
with all nodes in one bipartite set is provided. When determining
the nodes in each bipartite set more than one valid solution is
possible if the input graph is disconnected.

NetworkXError: Exception

Raised if the input graph is not bipartite.

Examples
--------
>>> from networkx.algorithms import bipartite
>>> G = nx.path_graph(4)
>>> X, Y = bipartite.sets(G)
>>> list(X)
[0, 2]
>>> list(Y)
[1, 3]

--------
color

"""
if G.is_directed():
is_connected = nx.is_weakly_connected
else:
is_connected = nx.is_connected
if top_nodes is not None:
X = set(top_nodes)
Y = set(G) - X
else:
if not is_connected(G):
msg = 'Disconnected graph: Ambiguous solution for bipartite sets.'
raise nx.AmbiguousSolution(msg)
c = color(G)
X = {n for n, is_top in c.items() if is_top}
Y = {n for n, is_top in c.items() if not is_top}
return (X, Y)

[docs]def density(B, nodes):
"""Returns density of bipartite graph B.

Parameters
----------
G : NetworkX graph

nodes: list or container
Nodes in one node set of the bipartite graph.

Returns
-------
d : float
The bipartite density

Examples
--------
>>> from networkx.algorithms import bipartite
>>> G = nx.complete_bipartite_graph(3,2)
>>> X=set([0,1,2])
>>> bipartite.density(G,X)
1.0
>>> Y=set([3,4])
>>> bipartite.density(G,Y)
1.0

Notes
-----
The container of nodes passed as argument must contain all nodes
in one of the two bipartite node sets to avoid ambiguity in the
case of disconnected graphs.
See :mod:bipartite documentation <networkx.algorithms.bipartite>
for further details on how bipartite graphs are handled in NetworkX.

--------
color
"""
n = len(B)
m = nx.number_of_edges(B)
nb = len(nodes)
nt = n - nb
if m == 0:  # includes cases n==0 and n==1
d = 0.0
else:
if B.is_directed():
d = m / (2.0 * float(nb * nt))
else:
d = m / float(nb * nt)
return d

[docs]def degrees(B, nodes, weight=None):
"""Returns the degrees of the two node sets in the bipartite graph B.

Parameters
----------
G : NetworkX graph

nodes: list or container
Nodes in one node set of the bipartite graph.

weight : string or None, optional (default=None)
The edge attribute that holds the numerical value used as a weight.
If None, then each edge has weight 1.
The degree is the sum of the edge weights adjacent to the node.

Returns
-------
(degX,degY) : tuple of dictionaries
The degrees of the two bipartite sets as dictionaries keyed by node.

Examples
--------
>>> from networkx.algorithms import bipartite
>>> G = nx.complete_bipartite_graph(3,2)
>>> Y=set([3,4])
>>> degX,degY=bipartite.degrees(G,Y)
>>> dict(degX)
{0: 2, 1: 2, 2: 2}

Notes
-----
The container of nodes passed as argument must contain all nodes
in one of the two bipartite node sets to avoid ambiguity in the
case of disconnected graphs.
See :mod:bipartite documentation <networkx.algorithms.bipartite>
for further details on how bipartite graphs are handled in NetworkX.