from nose import SkipTest
import networkx as nx
from networkx.generators.degree_seq import havel_hakimi_graph
class TestModularity(object):
numpy = 1 # nosetests attribute, use nosetests -a 'not numpy' to skip test
@classmethod
def setupClass(cls):
global numpy
global scipy
global assert_equal
global assert_almost_equal
try:
import numpy
import scipy
from numpy.testing import assert_equal, assert_almost_equal
except ImportError:
raise SkipTest('SciPy not available.')
def setUp(self):
deg = [3, 2, 2, 1, 0]
self.G = havel_hakimi_graph(deg)
# Graph used as an example in Sec. 4.1 of Langville and Meyer,
# "Google's PageRank and Beyond". (Used for test_directed_laplacian)
self.DG = nx.DiGraph()
self.DG.add_edges_from(((1, 2), (1, 3), (3, 1), (3, 2), (3, 5), (4, 5), (4, 6),
(5, 4), (5, 6), (6, 4)))
def test_modularity(self):
"Modularity matrix"
B = numpy.matrix([[-1.125, 0.25, 0.25, 0.625, 0.],
[0.25, -0.5, 0.5, -0.25, 0.],
[0.25, 0.5, -0.5, -0.25, 0.],
[0.625, -0.25, -0.25, -0.125, 0.],
[0., 0., 0., 0., 0.]])
permutation = [4, 0, 1, 2, 3]
assert_equal(nx.modularity_matrix(self.G), B)
assert_equal(nx.modularity_matrix(self.G, nodelist=permutation),
B[numpy.ix_(permutation, permutation)])
def test_modularity_weight(self):
"Modularity matrix with weights"
B = numpy.matrix([[-1.125, 0.25, 0.25, 0.625, 0.],
[0.25, -0.5, 0.5, -0.25, 0.],
[0.25, 0.5, -0.5, -0.25, 0.],
[0.625, -0.25, -0.25, -0.125, 0.],
[0., 0., 0., 0., 0.]])
G_weighted = self.G.copy()
for n1, n2 in G_weighted.edges():
G_weighted.edges[n1, n2]["weight"] = 0.5
# The following test would fail in networkx 1.1
assert_equal(nx.modularity_matrix(G_weighted), B)
# The following test that the modularity matrix get rescaled accordingly
assert_equal(nx.modularity_matrix(G_weighted, weight="weight"), 0.5 * B)
def test_directed_modularity(self):
"Directed Modularity matrix"
B = numpy.matrix([[-0.2, 0.6, 0.8, -0.4, -0.4, -0.4],
[0., 0., 0., 0., 0., 0.],
[0.7, 0.4, -0.3, -0.6, 0.4, -0.6],
[-0.2, -0.4, -0.2, -0.4, 0.6, 0.6],
[-0.2, -0.4, -0.2, 0.6, -0.4, 0.6],
[-0.1, -0.2, -0.1, 0.8, -0.2, -0.2]])
node_permutation = [5, 1, 2, 3, 4, 6]
idx_permutation = [4, 0, 1, 2, 3, 5]
mm = nx.directed_modularity_matrix(self.DG, nodelist=sorted(self.DG))
assert_equal(mm, B)
assert_equal(nx.directed_modularity_matrix(self.DG,
nodelist=node_permutation),
B[numpy.ix_(idx_permutation, idx_permutation)])
