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
from itertools import count
__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',

weight='weight', dtype=None):
r"""Return the biadjacency matrix of the bipartite graph G.

Let G = (U, V, E) be a bipartite graph with node sets
U = u_{1},...,u_{r} and V = v_{1},...,v_{s}. The biadjacency
matrix  is the r x s matrix B in which b_{i,j} = 1
if, and only if, (u_i, v_j) \in E. If the parameter weight is
not None and matches the name of an edge attribute, its value is

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

row_order : list of nodes
The rows of the matrix are ordered according to the list of nodes.

column_order : list, optional
The columns of the matrix are ordered according to the list of nodes.
If column_order is None, then the ordering of columns is arbitrary.

weight : string or None, optional (default='weight')
The edge data key used to provide each value in the matrix.
If None, then each edge has weight 1.

dtype : NumPy data type, optional
A valid single NumPy data type used to initialize the array.
This must be a simple type such as int or numpy.float64 and
not a compound data type (see to_numpy_recarray)
If None, then the NumPy default is used.

Returns
-------
B : numpy matrix
Biadjacency matrix representation of the bipartite graph G.

Notes
-----
No attempt is made to check that the input graph is bipartite.

For directed bipartite graphs only successors are considered as neighbors.
To obtain an adjacency matrix with ones (or weight values) for both
predecessors and successors you have to generate two biadjacency matrices
where the rows of one of them are the columns of the other, and then add
one to the transpose of the other.

--------
to_numpy_matrix

References
----------
"""
try:
import numpy as np
except ImportError:
'http://scipy.org/')
if column_order is None:
column_order = list(set(G) - set(row_order))
row = dict(zip(row_order,count()))
col = dict(zip(column_order,count()))
M = np.zeros((len(row),len(col)), dtype=dtype)
for u in row_order:
for v, d in G[u].items():
M[row[u],col[v]] = d.get(weight, 1)
return np.asmatrix(M)

[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
------
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, 'bipartite', c)
>>> print(G.node['bipartite'])
1
>>> print(G.node['bipartite'])
0
"""
if G.is_directed():
import itertools
def neighbors(v):
return itertools.chain.from_iterable([G.predecessors_iter(v),
G.successors_iter(v)])
else:
neighbors=G.neighbors_iter

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):
"""Returns bipartite node sets of graph G.

Raises an exception if the graph is not bipartite.

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

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

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
"""
c = color(G)
X = set(n for n in c if c[n]) # c[n] == 1
Y = set(n for n in c if not c[n]) # c[n] == 0
return (X, Y)

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

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

nodes: list or container
Nodes in one 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

--------
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):
"""Return the degrees of the two node sets in the bipartite graph B.

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

nodes: list or container
Nodes in one 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)
>>> degX
{0: 2, 1: 2, 2: 2}

--------
color, density
"""
bottom=set(nodes)
top=set(B)-bottom
return (B.degree(top,weight),B.degree(bottom,weight))

# fixture for nose tests
def setup_module(module):
from nose import SkipTest
try:
import numpy
except:
raise SkipTest("NumPy not available")