/usr/lib/python3/dist-packages/networkx/algorithms/assortativity/correlation.py is in python3-networkx 1.11-1ubuntu2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 | #-*- coding: utf-8 -*-
"""Node assortativity coefficients and correlation measures.
"""
import networkx as nx
from networkx.algorithms.assortativity.mixing import degree_mixing_matrix, \
attribute_mixing_matrix, numeric_mixing_matrix
from networkx.algorithms.assortativity.pairs import node_degree_xy, \
node_attribute_xy
__author__ = ' '.join(['Aric Hagberg <aric.hagberg@gmail.com>',
'Oleguer Sagarra <oleguer.sagarra@gmail.com>'])
__all__ = ['degree_pearson_correlation_coefficient',
'degree_assortativity_coefficient',
'attribute_assortativity_coefficient',
'numeric_assortativity_coefficient']
def degree_assortativity_coefficient(G, x='out', y='in', weight=None,
nodes=None):
"""Compute degree assortativity of graph.
Assortativity measures the similarity of connections
in the graph with respect to the node degree.
Parameters
----------
G : NetworkX graph
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.
nodes: list or iterable (optional)
Compute degree assortativity only for nodes in container.
The default is all nodes.
Returns
-------
r : float
Assortativity of graph by degree.
Examples
--------
>>> G=nx.path_graph(4)
>>> r=nx.degree_assortativity_coefficient(G)
>>> print("%3.1f"%r)
-0.5
See Also
--------
attribute_assortativity_coefficient
numeric_assortativity_coefficient
neighbor_connectivity
degree_mixing_dict
degree_mixing_matrix
Notes
-----
This computes Eq. (21) in Ref. [1]_ , where e is the joint
probability distribution (mixing matrix) of the degrees. If G is
directed than the matrix e is the joint probability of the
user-specified degree type for the source and target.
References
----------
.. [1] M. E. J. Newman, Mixing patterns in networks,
Physical Review E, 67 026126, 2003
.. [2] Foster, J.G., Foster, D.V., Grassberger, P. & Paczuski, M.
Edge direction and the structure of networks, PNAS 107, 10815-20 (2010).
"""
M = degree_mixing_matrix(G, x=x, y=y, nodes=nodes, weight=weight)
return numeric_ac(M)
def degree_pearson_correlation_coefficient(G, x='out', y='in',
weight=None, nodes=None):
"""Compute degree assortativity of graph.
Assortativity measures the similarity of connections
in the graph with respect to the node degree.
This is the same as degree_assortativity_coefficient but uses the
potentially faster scipy.stats.pearsonr function.
Parameters
----------
G : NetworkX graph
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.
nodes: list or iterable (optional)
Compute pearson correlation of degrees only for specified nodes.
The default is all nodes.
Returns
-------
r : float
Assortativity of graph by degree.
Examples
--------
>>> G=nx.path_graph(4)
>>> r=nx.degree_pearson_correlation_coefficient(G)
>>> print("%3.1f"%r)
-0.5
Notes
-----
This calls scipy.stats.pearsonr.
References
----------
.. [1] M. E. J. Newman, Mixing patterns in networks
Physical Review E, 67 026126, 2003
.. [2] Foster, J.G., Foster, D.V., Grassberger, P. & Paczuski, M.
Edge direction and the structure of networks, PNAS 107, 10815-20 (2010).
"""
try:
import scipy.stats as stats
except ImportError:
raise ImportError(
"Assortativity requires SciPy: http://scipy.org/ ")
xy=node_degree_xy(G, x=x, y=y, nodes=nodes, weight=weight)
x,y=zip(*xy)
return stats.pearsonr(x,y)[0]
def attribute_assortativity_coefficient(G,attribute,nodes=None):
"""Compute assortativity for node attributes.
Assortativity measures the similarity of connections
in the graph with respect to the given attribute.
Parameters
----------
G : NetworkX graph
attribute : string
Node attribute key
nodes: list or iterable (optional)
Compute attribute assortativity for nodes in container.
The default is all nodes.
Returns
-------
r: float
Assortativity of graph for given attribute
Examples
--------
>>> G=nx.Graph()
>>> G.add_nodes_from([0,1],color='red')
>>> G.add_nodes_from([2,3],color='blue')
>>> G.add_edges_from([(0,1),(2,3)])
>>> print(nx.attribute_assortativity_coefficient(G,'color'))
1.0
Notes
-----
This computes Eq. (2) in Ref. [1]_ , trace(M)-sum(M))/(1-sum(M),
where M is the joint probability distribution (mixing matrix)
of the specified attribute.
References
----------
.. [1] M. E. J. Newman, Mixing patterns in networks,
Physical Review E, 67 026126, 2003
"""
M = attribute_mixing_matrix(G,attribute,nodes)
return attribute_ac(M)
def numeric_assortativity_coefficient(G, attribute, nodes=None):
"""Compute assortativity for numerical node attributes.
Assortativity measures the similarity of connections
in the graph with respect to the given numeric attribute.
Parameters
----------
G : NetworkX graph
attribute : string
Node attribute key
nodes: list or iterable (optional)
Compute numeric assortativity only for attributes of nodes in
container. The default is all nodes.
Returns
-------
r: float
Assortativity of graph for given attribute
Examples
--------
>>> G=nx.Graph()
>>> G.add_nodes_from([0,1],size=2)
>>> G.add_nodes_from([2,3],size=3)
>>> G.add_edges_from([(0,1),(2,3)])
>>> print(nx.numeric_assortativity_coefficient(G,'size'))
1.0
Notes
-----
This computes Eq. (21) in Ref. [1]_ , for the mixing matrix of
of the specified attribute.
References
----------
.. [1] M. E. J. Newman, Mixing patterns in networks
Physical Review E, 67 026126, 2003
"""
a = numeric_mixing_matrix(G,attribute,nodes)
return numeric_ac(a)
def attribute_ac(M):
"""Compute assortativity for attribute matrix M.
Parameters
----------
M : numpy array or matrix
Attribute mixing matrix.
Notes
-----
This computes Eq. (2) in Ref. [1]_ , (trace(e)-sum(e))/(1-sum(e)),
where e is the joint probability distribution (mixing matrix)
of the specified attribute.
References
----------
.. [1] M. E. J. Newman, Mixing patterns in networks,
Physical Review E, 67 026126, 2003
"""
try:
import numpy
except ImportError:
raise ImportError(
"attribute_assortativity requires NumPy: http://scipy.org/ ")
if M.sum() != 1.0:
M=M/float(M.sum())
M=numpy.asmatrix(M)
s=(M*M).sum()
t=M.trace()
r=(t-s)/(1-s)
return float(r)
def numeric_ac(M):
# M is a numpy matrix or array
# numeric assortativity coefficient, pearsonr
try:
import numpy
except ImportError:
raise ImportError('numeric_assortativity requires ',
'NumPy: http://scipy.org/')
if M.sum() != 1.0:
M=M/float(M.sum())
nx,ny=M.shape # nx=ny
x=numpy.arange(nx)
y=numpy.arange(ny)
a=M.sum(axis=0)
b=M.sum(axis=1)
vara=(a*x**2).sum()-((a*x).sum())**2
varb=(b*x**2).sum()-((b*x).sum())**2
xy=numpy.outer(x,y)
ab=numpy.outer(a,b)
return (xy*(M-ab)).sum()/numpy.sqrt(vara*varb)
# 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")
|