annotate env/lib/python3.9/site-packages/networkx/algorithms/tests/test_link_prediction.py @ 0:4f3585e2f14b draft default tip

"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
author shellac
date Mon, 22 Mar 2021 18:12:50 +0000
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1 import math
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2
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3 from functools import partial
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4 import pytest
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5
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6 import networkx as nx
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7
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8
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9 def _test_func(G, ebunch, expected, predict_func, **kwargs):
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10 result = predict_func(G, ebunch, **kwargs)
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11 exp_dict = {tuple(sorted([u, v])): score for u, v, score in expected}
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12 res_dict = {tuple(sorted([u, v])): score for u, v, score in result}
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13
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14 assert len(exp_dict) == len(res_dict)
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15 for p in exp_dict:
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16 assert nx.testing.almost_equal(exp_dict[p], res_dict[p])
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17
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18
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19 class TestResourceAllocationIndex:
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20 @classmethod
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21 def setup_class(cls):
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22 cls.func = staticmethod(nx.resource_allocation_index)
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23 cls.test = partial(_test_func, predict_func=cls.func)
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24
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25 def test_K5(self):
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26 G = nx.complete_graph(5)
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27 self.test(G, [(0, 1)], [(0, 1, 0.75)])
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28
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29 def test_P3(self):
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30 G = nx.path_graph(3)
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31 self.test(G, [(0, 2)], [(0, 2, 0.5)])
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32
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33 def test_S4(self):
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34 G = nx.star_graph(4)
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35 self.test(G, [(1, 2)], [(1, 2, 0.25)])
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36
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37 def test_notimplemented(self):
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38 assert pytest.raises(
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39 nx.NetworkXNotImplemented, self.func, nx.DiGraph([(0, 1), (1, 2)]), [(0, 2)]
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40 )
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41 assert pytest.raises(
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42 nx.NetworkXNotImplemented,
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43 self.func,
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44 nx.MultiGraph([(0, 1), (1, 2)]),
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45 [(0, 2)],
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46 )
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47 assert pytest.raises(
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48 nx.NetworkXNotImplemented,
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49 self.func,
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50 nx.MultiDiGraph([(0, 1), (1, 2)]),
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51 [(0, 2)],
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52 )
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53
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54 def test_no_common_neighbor(self):
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55 G = nx.Graph()
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56 G.add_nodes_from([0, 1])
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57 self.test(G, [(0, 1)], [(0, 1, 0)])
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58
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59 def test_equal_nodes(self):
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60 G = nx.complete_graph(4)
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61 self.test(G, [(0, 0)], [(0, 0, 1)])
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62
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63 def test_all_nonexistent_edges(self):
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64 G = nx.Graph()
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65 G.add_edges_from([(0, 1), (0, 2), (2, 3)])
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66 self.test(G, None, [(0, 3, 0.5), (1, 2, 0.5), (1, 3, 0)])
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67
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68
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69 class TestJaccardCoefficient:
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70 @classmethod
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71 def setup_class(cls):
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72 cls.func = staticmethod(nx.jaccard_coefficient)
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73 cls.test = partial(_test_func, predict_func=cls.func)
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74
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75 def test_K5(self):
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76 G = nx.complete_graph(5)
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77 self.test(G, [(0, 1)], [(0, 1, 0.6)])
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78
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79 def test_P4(self):
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80 G = nx.path_graph(4)
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81 self.test(G, [(0, 2)], [(0, 2, 0.5)])
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82
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83 def test_notimplemented(self):
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84 assert pytest.raises(
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85 nx.NetworkXNotImplemented, self.func, nx.DiGraph([(0, 1), (1, 2)]), [(0, 2)]
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86 )
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87 assert pytest.raises(
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88 nx.NetworkXNotImplemented,
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89 self.func,
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90 nx.MultiGraph([(0, 1), (1, 2)]),
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91 [(0, 2)],
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92 )
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93 assert pytest.raises(
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94 nx.NetworkXNotImplemented,
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95 self.func,
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96 nx.MultiDiGraph([(0, 1), (1, 2)]),
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97 [(0, 2)],
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98 )
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99
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100 def test_no_common_neighbor(self):
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101 G = nx.Graph()
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102 G.add_edges_from([(0, 1), (2, 3)])
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103 self.test(G, [(0, 2)], [(0, 2, 0)])
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104
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105 def test_isolated_nodes(self):
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106 G = nx.Graph()
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107 G.add_nodes_from([0, 1])
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108 self.test(G, [(0, 1)], [(0, 1, 0)])
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109
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110 def test_all_nonexistent_edges(self):
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111 G = nx.Graph()
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112 G.add_edges_from([(0, 1), (0, 2), (2, 3)])
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113 self.test(G, None, [(0, 3, 0.5), (1, 2, 0.5), (1, 3, 0)])
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114
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115
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116 class TestAdamicAdarIndex:
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117 @classmethod
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118 def setup_class(cls):
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119 cls.func = staticmethod(nx.adamic_adar_index)
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120 cls.test = partial(_test_func, predict_func=cls.func)
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121
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122 def test_K5(self):
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123 G = nx.complete_graph(5)
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124 self.test(G, [(0, 1)], [(0, 1, 3 / math.log(4))])
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125
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126 def test_P3(self):
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127 G = nx.path_graph(3)
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128 self.test(G, [(0, 2)], [(0, 2, 1 / math.log(2))])
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129
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130 def test_S4(self):
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131 G = nx.star_graph(4)
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132 self.test(G, [(1, 2)], [(1, 2, 1 / math.log(4))])
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133
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134 def test_notimplemented(self):
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135 assert pytest.raises(
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136 nx.NetworkXNotImplemented, self.func, nx.DiGraph([(0, 1), (1, 2)]), [(0, 2)]
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137 )
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138 assert pytest.raises(
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139 nx.NetworkXNotImplemented,
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140 self.func,
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141 nx.MultiGraph([(0, 1), (1, 2)]),
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142 [(0, 2)],
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143 )
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144 assert pytest.raises(
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145 nx.NetworkXNotImplemented,
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146 self.func,
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147 nx.MultiDiGraph([(0, 1), (1, 2)]),
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148 [(0, 2)],
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149 )
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150
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151 def test_no_common_neighbor(self):
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152 G = nx.Graph()
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153 G.add_nodes_from([0, 1])
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154 self.test(G, [(0, 1)], [(0, 1, 0)])
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155
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156 def test_equal_nodes(self):
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157 G = nx.complete_graph(4)
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158 self.test(G, [(0, 0)], [(0, 0, 3 / math.log(3))])
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159
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160 def test_all_nonexistent_edges(self):
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161 G = nx.Graph()
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162 G.add_edges_from([(0, 1), (0, 2), (2, 3)])
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163 self.test(
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164 G, None, [(0, 3, 1 / math.log(2)), (1, 2, 1 / math.log(2)), (1, 3, 0)]
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165 )
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166
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167
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168 class TestPreferentialAttachment:
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169 @classmethod
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170 def setup_class(cls):
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171 cls.func = staticmethod(nx.preferential_attachment)
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172 cls.test = partial(_test_func, predict_func=cls.func)
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173
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174 def test_K5(self):
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175 G = nx.complete_graph(5)
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176 self.test(G, [(0, 1)], [(0, 1, 16)])
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177
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178 def test_P3(self):
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179 G = nx.path_graph(3)
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180 self.test(G, [(0, 1)], [(0, 1, 2)])
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181
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182 def test_S4(self):
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183 G = nx.star_graph(4)
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184 self.test(G, [(0, 2)], [(0, 2, 4)])
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185
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186 def test_notimplemented(self):
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187 assert pytest.raises(
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188 nx.NetworkXNotImplemented, self.func, nx.DiGraph([(0, 1), (1, 2)]), [(0, 2)]
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189 )
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190 assert pytest.raises(
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191 nx.NetworkXNotImplemented,
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192 self.func,
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193 nx.MultiGraph([(0, 1), (1, 2)]),
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194 [(0, 2)],
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195 )
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196 assert pytest.raises(
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197 nx.NetworkXNotImplemented,
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198 self.func,
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199 nx.MultiDiGraph([(0, 1), (1, 2)]),
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200 [(0, 2)],
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201 )
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202
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203 def test_zero_degrees(self):
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204 G = nx.Graph()
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205 G.add_nodes_from([0, 1])
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206 self.test(G, [(0, 1)], [(0, 1, 0)])
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207
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208 def test_all_nonexistent_edges(self):
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209 G = nx.Graph()
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210 G.add_edges_from([(0, 1), (0, 2), (2, 3)])
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211 self.test(G, None, [(0, 3, 2), (1, 2, 2), (1, 3, 1)])
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212
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213
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214 class TestCNSoundarajanHopcroft:
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215 @classmethod
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216 def setup_class(cls):
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217 cls.func = staticmethod(nx.cn_soundarajan_hopcroft)
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218 cls.test = partial(_test_func, predict_func=cls.func, community="community")
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219
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220 def test_K5(self):
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221 G = nx.complete_graph(5)
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222 G.nodes[0]["community"] = 0
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223 G.nodes[1]["community"] = 0
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224 G.nodes[2]["community"] = 0
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225 G.nodes[3]["community"] = 0
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226 G.nodes[4]["community"] = 1
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227 self.test(G, [(0, 1)], [(0, 1, 5)])
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228
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229 def test_P3(self):
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230 G = nx.path_graph(3)
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231 G.nodes[0]["community"] = 0
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232 G.nodes[1]["community"] = 1
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233 G.nodes[2]["community"] = 0
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234 self.test(G, [(0, 2)], [(0, 2, 1)])
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235
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236 def test_S4(self):
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237 G = nx.star_graph(4)
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238 G.nodes[0]["community"] = 1
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239 G.nodes[1]["community"] = 1
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240 G.nodes[2]["community"] = 1
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241 G.nodes[3]["community"] = 0
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242 G.nodes[4]["community"] = 0
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243 self.test(G, [(1, 2)], [(1, 2, 2)])
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244
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245 def test_notimplemented(self):
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246 G = nx.DiGraph([(0, 1), (1, 2)])
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247 G.add_nodes_from([0, 1, 2], community=0)
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248 assert pytest.raises(nx.NetworkXNotImplemented, self.func, G, [(0, 2)])
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249 G = nx.MultiGraph([(0, 1), (1, 2)])
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250 G.add_nodes_from([0, 1, 2], community=0)
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251 assert pytest.raises(nx.NetworkXNotImplemented, self.func, G, [(0, 2)])
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252 G = nx.MultiDiGraph([(0, 1), (1, 2)])
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253 G.add_nodes_from([0, 1, 2], community=0)
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254 assert pytest.raises(nx.NetworkXNotImplemented, self.func, G, [(0, 2)])
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255
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256 def test_no_common_neighbor(self):
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257 G = nx.Graph()
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258 G.add_nodes_from([0, 1])
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259 G.nodes[0]["community"] = 0
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260 G.nodes[1]["community"] = 0
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261 self.test(G, [(0, 1)], [(0, 1, 0)])
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262
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263 def test_equal_nodes(self):
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264 G = nx.complete_graph(3)
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265 G.nodes[0]["community"] = 0
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266 G.nodes[1]["community"] = 0
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267 G.nodes[2]["community"] = 0
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268 self.test(G, [(0, 0)], [(0, 0, 4)])
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269
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270 def test_different_community(self):
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271 G = nx.Graph()
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272 G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)])
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273 G.nodes[0]["community"] = 0
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274 G.nodes[1]["community"] = 0
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275 G.nodes[2]["community"] = 0
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276 G.nodes[3]["community"] = 1
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277 self.test(G, [(0, 3)], [(0, 3, 2)])
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278
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279 def test_no_community_information(self):
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280 G = nx.complete_graph(5)
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281 assert pytest.raises(nx.NetworkXAlgorithmError, list, self.func(G, [(0, 1)]))
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282
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283 def test_insufficient_community_information(self):
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284 G = nx.Graph()
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285 G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)])
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286 G.nodes[0]["community"] = 0
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287 G.nodes[1]["community"] = 0
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288 G.nodes[3]["community"] = 0
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289 assert pytest.raises(nx.NetworkXAlgorithmError, list, self.func(G, [(0, 3)]))
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290
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291 def test_sufficient_community_information(self):
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292 G = nx.Graph()
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293 G.add_edges_from([(0, 1), (1, 2), (1, 3), (2, 4), (3, 4), (4, 5)])
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294 G.nodes[1]["community"] = 0
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295 G.nodes[2]["community"] = 0
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296 G.nodes[3]["community"] = 0
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297 G.nodes[4]["community"] = 0
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298 self.test(G, [(1, 4)], [(1, 4, 4)])
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299
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300 def test_custom_community_attribute_name(self):
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301 G = nx.Graph()
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302 G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)])
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303 G.nodes[0]["cmty"] = 0
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304 G.nodes[1]["cmty"] = 0
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305 G.nodes[2]["cmty"] = 0
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306 G.nodes[3]["cmty"] = 1
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307 self.test(G, [(0, 3)], [(0, 3, 2)], community="cmty")
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308
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309 def test_all_nonexistent_edges(self):
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310 G = nx.Graph()
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311 G.add_edges_from([(0, 1), (0, 2), (2, 3)])
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312 G.nodes[0]["community"] = 0
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313 G.nodes[1]["community"] = 1
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314 G.nodes[2]["community"] = 0
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315 G.nodes[3]["community"] = 0
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316 self.test(G, None, [(0, 3, 2), (1, 2, 1), (1, 3, 0)])
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317
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318
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319 class TestRAIndexSoundarajanHopcroft:
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320 @classmethod
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321 def setup_class(cls):
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322 cls.func = staticmethod(nx.ra_index_soundarajan_hopcroft)
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323 cls.test = partial(_test_func, predict_func=cls.func, community="community")
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324
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325 def test_K5(self):
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326 G = nx.complete_graph(5)
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327 G.nodes[0]["community"] = 0
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328 G.nodes[1]["community"] = 0
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329 G.nodes[2]["community"] = 0
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330 G.nodes[3]["community"] = 0
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331 G.nodes[4]["community"] = 1
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332 self.test(G, [(0, 1)], [(0, 1, 0.5)])
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333
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334 def test_P3(self):
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335 G = nx.path_graph(3)
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336 G.nodes[0]["community"] = 0
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337 G.nodes[1]["community"] = 1
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338 G.nodes[2]["community"] = 0
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339 self.test(G, [(0, 2)], [(0, 2, 0)])
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340
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341 def test_S4(self):
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342 G = nx.star_graph(4)
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343 G.nodes[0]["community"] = 1
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344 G.nodes[1]["community"] = 1
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345 G.nodes[2]["community"] = 1
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346 G.nodes[3]["community"] = 0
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347 G.nodes[4]["community"] = 0
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348 self.test(G, [(1, 2)], [(1, 2, 0.25)])
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349
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350 def test_notimplemented(self):
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351 G = nx.DiGraph([(0, 1), (1, 2)])
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352 G.add_nodes_from([0, 1, 2], community=0)
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353 assert pytest.raises(nx.NetworkXNotImplemented, self.func, G, [(0, 2)])
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354 G = nx.MultiGraph([(0, 1), (1, 2)])
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355 G.add_nodes_from([0, 1, 2], community=0)
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356 assert pytest.raises(nx.NetworkXNotImplemented, self.func, G, [(0, 2)])
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357 G = nx.MultiDiGraph([(0, 1), (1, 2)])
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358 G.add_nodes_from([0, 1, 2], community=0)
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359 assert pytest.raises(nx.NetworkXNotImplemented, self.func, G, [(0, 2)])
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360
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361 def test_no_common_neighbor(self):
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362 G = nx.Graph()
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363 G.add_nodes_from([0, 1])
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364 G.nodes[0]["community"] = 0
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365 G.nodes[1]["community"] = 0
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366 self.test(G, [(0, 1)], [(0, 1, 0)])
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367
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368 def test_equal_nodes(self):
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369 G = nx.complete_graph(3)
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370 G.nodes[0]["community"] = 0
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371 G.nodes[1]["community"] = 0
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372 G.nodes[2]["community"] = 0
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373 self.test(G, [(0, 0)], [(0, 0, 1)])
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374
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375 def test_different_community(self):
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376 G = nx.Graph()
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377 G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)])
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378 G.nodes[0]["community"] = 0
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379 G.nodes[1]["community"] = 0
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380 G.nodes[2]["community"] = 0
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381 G.nodes[3]["community"] = 1
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382 self.test(G, [(0, 3)], [(0, 3, 0)])
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383
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384 def test_no_community_information(self):
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385 G = nx.complete_graph(5)
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386 assert pytest.raises(nx.NetworkXAlgorithmError, list, self.func(G, [(0, 1)]))
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387
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388 def test_insufficient_community_information(self):
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389 G = nx.Graph()
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390 G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)])
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391 G.nodes[0]["community"] = 0
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392 G.nodes[1]["community"] = 0
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393 G.nodes[3]["community"] = 0
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394 assert pytest.raises(nx.NetworkXAlgorithmError, list, self.func(G, [(0, 3)]))
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395
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396 def test_sufficient_community_information(self):
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397 G = nx.Graph()
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398 G.add_edges_from([(0, 1), (1, 2), (1, 3), (2, 4), (3, 4), (4, 5)])
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399 G.nodes[1]["community"] = 0
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400 G.nodes[2]["community"] = 0
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401 G.nodes[3]["community"] = 0
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402 G.nodes[4]["community"] = 0
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403 self.test(G, [(1, 4)], [(1, 4, 1)])
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404
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405 def test_custom_community_attribute_name(self):
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406 G = nx.Graph()
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407 G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)])
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408 G.nodes[0]["cmty"] = 0
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409 G.nodes[1]["cmty"] = 0
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410 G.nodes[2]["cmty"] = 0
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411 G.nodes[3]["cmty"] = 1
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412 self.test(G, [(0, 3)], [(0, 3, 0)], community="cmty")
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413
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414 def test_all_nonexistent_edges(self):
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415 G = nx.Graph()
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416 G.add_edges_from([(0, 1), (0, 2), (2, 3)])
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417 G.nodes[0]["community"] = 0
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418 G.nodes[1]["community"] = 1
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419 G.nodes[2]["community"] = 0
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420 G.nodes[3]["community"] = 0
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421 self.test(G, None, [(0, 3, 0.5), (1, 2, 0), (1, 3, 0)])
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422
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423
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424 class TestWithinInterCluster:
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425 @classmethod
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426 def setup_class(cls):
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427 cls.delta = 0.001
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428 cls.func = staticmethod(nx.within_inter_cluster)
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429 cls.test = partial(
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430 _test_func, predict_func=cls.func, delta=cls.delta, community="community"
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431 )
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432
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433 def test_K5(self):
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434 G = nx.complete_graph(5)
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435 G.nodes[0]["community"] = 0
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436 G.nodes[1]["community"] = 0
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437 G.nodes[2]["community"] = 0
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438 G.nodes[3]["community"] = 0
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439 G.nodes[4]["community"] = 1
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440 self.test(G, [(0, 1)], [(0, 1, 2 / (1 + self.delta))])
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441
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442 def test_P3(self):
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443 G = nx.path_graph(3)
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444 G.nodes[0]["community"] = 0
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445 G.nodes[1]["community"] = 1
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446 G.nodes[2]["community"] = 0
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447 self.test(G, [(0, 2)], [(0, 2, 0)])
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448
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449 def test_S4(self):
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450 G = nx.star_graph(4)
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451 G.nodes[0]["community"] = 1
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452 G.nodes[1]["community"] = 1
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453 G.nodes[2]["community"] = 1
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454 G.nodes[3]["community"] = 0
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455 G.nodes[4]["community"] = 0
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456 self.test(G, [(1, 2)], [(1, 2, 1 / self.delta)])
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457
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458 def test_notimplemented(self):
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459 G = nx.DiGraph([(0, 1), (1, 2)])
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460 G.add_nodes_from([0, 1, 2], community=0)
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461 assert pytest.raises(nx.NetworkXNotImplemented, self.func, G, [(0, 2)])
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462 G = nx.MultiGraph([(0, 1), (1, 2)])
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463 G.add_nodes_from([0, 1, 2], community=0)
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464 assert pytest.raises(nx.NetworkXNotImplemented, self.func, G, [(0, 2)])
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465 G = nx.MultiDiGraph([(0, 1), (1, 2)])
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466 G.add_nodes_from([0, 1, 2], community=0)
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467 assert pytest.raises(nx.NetworkXNotImplemented, self.func, G, [(0, 2)])
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468
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469 def test_no_common_neighbor(self):
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470 G = nx.Graph()
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471 G.add_nodes_from([0, 1])
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472 G.nodes[0]["community"] = 0
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473 G.nodes[1]["community"] = 0
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474 self.test(G, [(0, 1)], [(0, 1, 0)])
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475
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476 def test_equal_nodes(self):
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477 G = nx.complete_graph(3)
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478 G.nodes[0]["community"] = 0
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479 G.nodes[1]["community"] = 0
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480 G.nodes[2]["community"] = 0
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481 self.test(G, [(0, 0)], [(0, 0, 2 / self.delta)])
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482
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483 def test_different_community(self):
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484 G = nx.Graph()
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485 G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)])
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parents:
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486 G.nodes[0]["community"] = 0
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shellac
parents:
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487 G.nodes[1]["community"] = 0
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shellac
parents:
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488 G.nodes[2]["community"] = 0
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shellac
parents:
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489 G.nodes[3]["community"] = 1
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parents:
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490 self.test(G, [(0, 3)], [(0, 3, 0)])
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parents:
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491
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parents:
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492 def test_no_inter_cluster_common_neighbor(self):
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493 G = nx.complete_graph(4)
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parents:
diff changeset
494 G.nodes[0]["community"] = 0
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shellac
parents:
diff changeset
495 G.nodes[1]["community"] = 0
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shellac
parents:
diff changeset
496 G.nodes[2]["community"] = 0
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shellac
parents:
diff changeset
497 G.nodes[3]["community"] = 0
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shellac
parents:
diff changeset
498 self.test(G, [(0, 3)], [(0, 3, 2 / self.delta)])
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parents:
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499
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parents:
diff changeset
500 def test_no_community_information(self):
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parents:
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501 G = nx.complete_graph(5)
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parents:
diff changeset
502 assert pytest.raises(nx.NetworkXAlgorithmError, list, self.func(G, [(0, 1)]))
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parents:
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503
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parents:
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504 def test_insufficient_community_information(self):
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parents:
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505 G = nx.Graph()
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parents:
diff changeset
506 G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)])
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shellac
parents:
diff changeset
507 G.nodes[0]["community"] = 0
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shellac
parents:
diff changeset
508 G.nodes[1]["community"] = 0
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shellac
parents:
diff changeset
509 G.nodes[3]["community"] = 0
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shellac
parents:
diff changeset
510 assert pytest.raises(nx.NetworkXAlgorithmError, list, self.func(G, [(0, 3)]))
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parents:
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511
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parents:
diff changeset
512 def test_sufficient_community_information(self):
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parents:
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513 G = nx.Graph()
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shellac
parents:
diff changeset
514 G.add_edges_from([(0, 1), (1, 2), (1, 3), (2, 4), (3, 4), (4, 5)])
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shellac
parents:
diff changeset
515 G.nodes[1]["community"] = 0
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shellac
parents:
diff changeset
516 G.nodes[2]["community"] = 0
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shellac
parents:
diff changeset
517 G.nodes[3]["community"] = 0
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shellac
parents:
diff changeset
518 G.nodes[4]["community"] = 0
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shellac
parents:
diff changeset
519 self.test(G, [(1, 4)], [(1, 4, 2 / self.delta)])
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parents:
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520
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parents:
diff changeset
521 def test_invalid_delta(self):
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parents:
diff changeset
522 G = nx.complete_graph(3)
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shellac
parents:
diff changeset
523 G.add_nodes_from([0, 1, 2], community=0)
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shellac
parents:
diff changeset
524 assert pytest.raises(nx.NetworkXAlgorithmError, self.func, G, [(0, 1)], 0)
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shellac
parents:
diff changeset
525 assert pytest.raises(nx.NetworkXAlgorithmError, self.func, G, [(0, 1)], -0.5)
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parents:
diff changeset
526
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parents:
diff changeset
527 def test_custom_community_attribute_name(self):
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shellac
parents:
diff changeset
528 G = nx.complete_graph(4)
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shellac
parents:
diff changeset
529 G.nodes[0]["cmty"] = 0
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shellac
parents:
diff changeset
530 G.nodes[1]["cmty"] = 0
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shellac
parents:
diff changeset
531 G.nodes[2]["cmty"] = 0
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shellac
parents:
diff changeset
532 G.nodes[3]["cmty"] = 0
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shellac
parents:
diff changeset
533 self.test(G, [(0, 3)], [(0, 3, 2 / self.delta)], community="cmty")
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parents:
diff changeset
534
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parents:
diff changeset
535 def test_all_nonexistent_edges(self):
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parents:
diff changeset
536 G = nx.Graph()
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shellac
parents:
diff changeset
537 G.add_edges_from([(0, 1), (0, 2), (2, 3)])
4f3585e2f14b "planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff changeset
538 G.nodes[0]["community"] = 0
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shellac
parents:
diff changeset
539 G.nodes[1]["community"] = 1
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shellac
parents:
diff changeset
540 G.nodes[2]["community"] = 0
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shellac
parents:
diff changeset
541 G.nodes[3]["community"] = 0
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shellac
parents:
diff changeset
542 self.test(G, None, [(0, 3, 1 / self.delta), (1, 2, 0), (1, 3, 0)])