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import pytest
np = pytest.importorskip("numpy")
pytest.importorskip("scipy")
import networkx as nx
from networkx.generators.degree_seq import havel_hakimi_graph
class TestModularity:
@classmethod
def setup_class(cls):
deg = [3, 2, 2, 1, 0]
cls.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)
cls.DG = nx.DiGraph()
cls.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"
# fmt: off
B = np.array([[-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.]])
# fmt: on
permutation = [4, 0, 1, 2, 3]
np.testing.assert_equal(nx.modularity_matrix(self.G), B)
np.testing.assert_equal(
nx.modularity_matrix(self.G, nodelist=permutation),
B[np.ix_(permutation, permutation)],
)
def test_modularity_weight(self):
"Modularity matrix with weights"
# fmt: off
B = np.array([[-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.]])
# fmt: on
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
np.testing.assert_equal(nx.modularity_matrix(G_weighted), B)
# The following test that the modularity matrix get rescaled accordingly
np.testing.assert_equal(
nx.modularity_matrix(G_weighted, weight="weight"), 0.5 * B
)
def test_directed_modularity(self):
"Directed Modularity matrix"
# fmt: off
B = np.array([[-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]])
# fmt: on
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))
np.testing.assert_equal(mm, B)
np.testing.assert_equal(
nx.directed_modularity_matrix(self.DG, nodelist=node_permutation),
B[np.ix_(idx_permutation, idx_permutation)],
)
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