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
|
import random
import networkx as nx
import pytest
np = pytest.importorskip("numpy")
pytest.importorskip("scipy")
from networkx.algorithms.link_analysis.pagerank_alg import _pagerank_python
# Example from
# A. Langville and C. Meyer, "A survey of eigenvector methods of web
# information retrieval." http://citeseer.ist.psu.edu/713792.html
class TestPageRank:
@classmethod
def setup_class(cls):
G = nx.DiGraph()
edges = [
(1, 2),
(1, 3),
# 2 is a dangling node
(3, 1),
(3, 2),
(3, 5),
(4, 5),
(4, 6),
(5, 4),
(5, 6),
(6, 4),
]
G.add_edges_from(edges)
cls.G = G
cls.G.pagerank = dict(
zip(
sorted(G),
[
0.03721197,
0.05395735,
0.04150565,
0.37508082,
0.20599833,
0.28624589,
],
)
)
cls.dangling_node_index = 1
cls.dangling_edges = {1: 2, 2: 3, 3: 0, 4: 0, 5: 0, 6: 0}
cls.G.dangling_pagerank = dict(
zip(
sorted(G),
[0.10844518, 0.18618601, 0.0710892, 0.2683668, 0.15919783, 0.20671497],
)
)
@pytest.mark.parametrize("alg", (nx.pagerank, _pagerank_python))
def test_pagerank(self, alg):
G = self.G
p = alg(G, alpha=0.9, tol=1.0e-08)
for n in G:
assert p[n] == pytest.approx(G.pagerank[n], abs=1e-4)
nstart = {n: random.random() for n in G}
p = alg(G, alpha=0.9, tol=1.0e-08, nstart=nstart)
for n in G:
assert p[n] == pytest.approx(G.pagerank[n], abs=1e-4)
@pytest.mark.parametrize("alg", (nx.pagerank, _pagerank_python))
def test_pagerank_max_iter(self, alg):
with pytest.raises(nx.PowerIterationFailedConvergence):
alg(self.G, max_iter=0)
def test_numpy_pagerank(self):
G = self.G
p = nx.pagerank_numpy(G, alpha=0.9)
for n in G:
assert p[n] == pytest.approx(G.pagerank[n], abs=1e-4)
def test_google_matrix(self):
G = self.G
M = nx.google_matrix(G, alpha=0.9, nodelist=sorted(G))
e, ev = np.linalg.eig(M.T)
p = np.array(ev[:, 0] / ev[:, 0].sum())[:, 0]
for (a, b) in zip(p, self.G.pagerank.values()):
assert a == pytest.approx(b, abs=1e-7)
@pytest.mark.parametrize("alg", (nx.pagerank, _pagerank_python, nx.pagerank_numpy))
def test_personalization(self, alg):
G = nx.complete_graph(4)
personalize = {0: 1, 1: 1, 2: 4, 3: 4}
answer = {
0: 0.23246732615667579,
1: 0.23246732615667579,
2: 0.267532673843324,
3: 0.2675326738433241,
}
p = alg(G, alpha=0.85, personalization=personalize)
for n in G:
assert p[n] == pytest.approx(answer[n], abs=1e-4)
@pytest.mark.parametrize("alg", (nx.pagerank, _pagerank_python, nx.google_matrix))
def test_zero_personalization_vector(self, alg):
G = nx.complete_graph(4)
personalize = {0: 0, 1: 0, 2: 0, 3: 0}
pytest.raises(ZeroDivisionError, alg, G, personalization=personalize)
@pytest.mark.parametrize("alg", (nx.pagerank, _pagerank_python))
def test_one_nonzero_personalization_value(self, alg):
G = nx.complete_graph(4)
personalize = {0: 0, 1: 0, 2: 0, 3: 1}
answer = {
0: 0.22077931820379187,
1: 0.22077931820379187,
2: 0.22077931820379187,
3: 0.3376620453886241,
}
p = alg(G, alpha=0.85, personalization=personalize)
for n in G:
assert p[n] == pytest.approx(answer[n], abs=1e-4)
@pytest.mark.parametrize("alg", (nx.pagerank, _pagerank_python))
def test_incomplete_personalization(self, alg):
G = nx.complete_graph(4)
personalize = {3: 1}
answer = {
0: 0.22077931820379187,
1: 0.22077931820379187,
2: 0.22077931820379187,
3: 0.3376620453886241,
}
p = alg(G, alpha=0.85, personalization=personalize)
for n in G:
assert p[n] == pytest.approx(answer[n], abs=1e-4)
def test_dangling_matrix(self):
"""
Tests that the google_matrix doesn't change except for the dangling
nodes.
"""
G = self.G
dangling = self.dangling_edges
dangling_sum = float(sum(dangling.values()))
M1 = nx.google_matrix(G, personalization=dangling)
M2 = nx.google_matrix(G, personalization=dangling, dangling=dangling)
for i in range(len(G)):
for j in range(len(G)):
if i == self.dangling_node_index and (j + 1) in dangling:
assert M2[i, j] == pytest.approx(
dangling[j + 1] / dangling_sum, abs=1e-4
)
else:
assert M2[i, j] == pytest.approx(M1[i, j], abs=1e-4)
@pytest.mark.parametrize("alg", (nx.pagerank, _pagerank_python, nx.pagerank_numpy))
def test_dangling_pagerank(self, alg):
pr = alg(self.G, dangling=self.dangling_edges)
for n in self.G:
assert pr[n] == pytest.approx(self.G.dangling_pagerank[n], abs=1e-4)
def test_empty(self):
G = nx.Graph()
assert nx.pagerank(G) == {}
assert _pagerank_python(G) == {}
assert nx.pagerank_numpy(G) == {}
assert nx.google_matrix(G).shape == (0, 0)
@pytest.mark.parametrize("alg", (nx.pagerank, _pagerank_python))
def test_multigraph(self, alg):
G = nx.MultiGraph()
G.add_edges_from([(1, 2), (1, 2), (1, 2), (2, 3), (2, 3), ("3", 3), ("3", 3)])
answer = {
1: 0.21066048614468322,
2: 0.3395308825985378,
3: 0.28933951385531687,
"3": 0.16046911740146227,
}
p = alg(G)
for n in G:
assert p[n] == pytest.approx(answer[n], abs=1e-4)
class TestPageRankScipy(TestPageRank):
def test_scipy_pagerank(self):
G = self.G
p = nx.pagerank_scipy(G, alpha=0.9, tol=1.0e-08)
for n in G:
assert p[n] == pytest.approx(G.pagerank[n], abs=1e-4)
personalize = {n: random.random() for n in G}
p = nx.pagerank_scipy(G, alpha=0.9, tol=1.0e-08, personalization=personalize)
nstart = {n: random.random() for n in G}
p = nx.pagerank_scipy(G, alpha=0.9, tol=1.0e-08, nstart=nstart)
for n in G:
assert p[n] == pytest.approx(G.pagerank[n], abs=1e-4)
def test_scipy_pagerank_max_iter(self):
with pytest.raises(nx.PowerIterationFailedConvergence):
nx.pagerank_scipy(self.G, max_iter=0)
def test_dangling_scipy_pagerank(self):
pr = nx.pagerank_scipy(self.G, dangling=self.dangling_edges)
for n in self.G:
assert pr[n] == pytest.approx(self.G.dangling_pagerank[n], abs=1e-4)
def test_empty_scipy(self):
G = nx.Graph()
assert nx.pagerank_scipy(G) == {}
@pytest.mark.parametrize(
"pagerank_alg",
(nx.pagerank_numpy, nx.pagerank_scipy),
)
def test_deprecation_warnings(pagerank_alg):
"""Make sure deprecation warnings are raised.
To be removed when deprecations expire.
"""
G = nx.DiGraph(nx.path_graph(4))
with pytest.warns(DeprecationWarning):
pr = pagerank_alg(G, alpha=0.9)
|
