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.assortativity.mixing

#-*- coding: utf-8 -*-
"""
Mixing matrices for node attributes and degree.
"""
import networkx as nx
from networkx.utils import dict_to_numpy_array
from networkx.algorithms.assortativity.pairs import node_degree_xy, \
node_attribute_xy
__author__ = ' '.join(['Aric Hagberg <aric.hagberg@gmail.com>'])
__all__ = ['attribute_mixing_matrix',
'attribute_mixing_dict',
'degree_mixing_matrix',
'degree_mixing_dict',
'numeric_mixing_matrix',
'mixing_dict']

[docs]def attribute_mixing_dict(G, attribute, nodes=None, normalized=False):
"""Returns dictionary representation of mixing matrix for attribute.

Parameters
----------
G : graph
NetworkX graph object.

attribute : string
Node attribute key.

nodes: list or iterable (optional)
Unse nodes in container to build the dict. The default is all nodes.

normalized : bool (default=False)
Return counts if False or probabilities if True.

Examples
--------
>>> G=nx.Graph()
>>> d=nx.attribute_mixing_dict(G,'color')
>>> print(d['red']['blue'])
1
>>> print(d['blue']['red']) # d symmetric for undirected graphs
1

Returns
-------
d : dictionary
Counts or joint probability of occurrence of attribute pairs.
"""
xy_iter = node_attribute_xy(G, attribute, nodes)
return mixing_dict(xy_iter, normalized=normalized)

[docs]def attribute_mixing_matrix(G, attribute, nodes=None, mapping=None,
normalized=True):
"""Returns mixing matrix for attribute.

Parameters
----------
G : graph
NetworkX graph object.

attribute : string
Node attribute key.

nodes: list or iterable (optional)
Use only nodes in container to build the matrix. The default is
all nodes.

mapping : dictionary, optional
Mapping from node attribute to integer index in matrix.
If not specified, an arbitrary ordering will be used.

normalized : bool (default=True)
Return counts if False or probabilities if True.

Returns
-------
m: numpy array
Counts or joint probability of occurrence of attribute pairs.
"""
d = attribute_mixing_dict(G, attribute, nodes)
a = dict_to_numpy_array(d, mapping=mapping)
if normalized:
a = a / a.sum()
return a

[docs]def degree_mixing_dict(G, x='out', y='in', weight=None,
nodes=None, normalized=False):
"""Returns dictionary representation of mixing matrix for degree.

Parameters
----------
G : graph
NetworkX graph object.

x: string ('in','out')
The degree type for source node (directed graphs only).

y: string ('in','out')
The degree type for target node (directed graphs only).

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.

normalized : bool (default=False)
Return counts if False or probabilities if True.

Returns
-------
d: dictionary
Counts or joint probability of occurrence of degree pairs.
"""
xy_iter = node_degree_xy(G, x=x, y=y, nodes=nodes, weight=weight)
return mixing_dict(xy_iter, normalized=normalized)

[docs]def degree_mixing_matrix(G, x='out', y='in', weight=None,
nodes=None, normalized=True):
"""Returns mixing matrix for attribute.

Parameters
----------
G : graph
NetworkX graph object.

x: string ('in','out')
The degree type for source node (directed graphs only).

y: string ('in','out')
The degree type for target node (directed graphs only).

nodes: list or iterable (optional)
Build the matrix using only nodes in container.
The default is all nodes.

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.

normalized : bool (default=True)
Return counts if False or probabilities if True.

Returns
-------
m: numpy array
Counts, or joint probability, of occurrence of node degree.
"""
d = degree_mixing_dict(G, x=x, y=y, nodes=nodes, weight=weight)
s = set(d.keys())
for k, v in d.items():
s.update(v.keys())
m = max(s)
mapping = {x: x for x in range(m + 1)}
a = dict_to_numpy_array(d, mapping=mapping)
if normalized:
a = a / a.sum()
return a

[docs]def numeric_mixing_matrix(G, attribute, nodes=None, normalized=True):
"""Returns numeric mixing matrix for attribute.

The attribute must be an integer.

Parameters
----------
G : graph
NetworkX graph object.

attribute : string
Node attribute key.  The corresponding attribute must be an integer.

nodes: list or iterable (optional)
Build the matrix only with nodes in container. The default is all nodes.

normalized : bool (default=True)
Return counts if False or probabilities if True.

Returns
-------
m: numpy array
Counts, or joint, probability of occurrence of node attribute pairs.
"""
d = attribute_mixing_dict(G, attribute, nodes)
s = set(d.keys())
for k, v in d.items():
s.update(v.keys())
m = max(s)
mapping = {x: x for x in range(m + 1)}
a = dict_to_numpy_array(d, mapping=mapping)
if normalized:
a = a / a.sum()
return a

[docs]def mixing_dict(xy, normalized=False):
"""Returns a dictionary representation of mixing matrix.

Parameters
----------
xy : list or container of two-tuples
Pairs of (x,y) items.

attribute : string
Node attribute key

normalized : bool (default=False)
Return counts if False or probabilities if True.

Returns
-------
d: dictionary
Counts or Joint probability of occurrence of values in xy.
"""
d = {}
psum = 0.0
for x, y in xy:
if x not in d:
d[x] = {}
if y not in d:
d[y] = {}
v = d[x].get(y, 0)
d[x][y] = v + 1
psum += 1

if normalized:
for k, jdict in d.items():
for j in jdict:
jdict[j] /= psum
return d

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