annotate env/lib/python3.9/site-packages/networkx/algorithms/connectivity/tests/test_edge_kcomponents.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 networkx as nx
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2 import itertools as it
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3 import pytest
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4 from networkx.utils import pairwise
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5 from networkx.algorithms.connectivity import bridge_components, EdgeComponentAuxGraph
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6 from networkx.algorithms.connectivity.edge_kcomponents import general_k_edge_subgraphs
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7
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8
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9 # ----------------
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10 # Helper functions
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11 # ----------------
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12
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13
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14 def fset(list_of_sets):
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15 """ allows == to be used for list of sets """
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16 return set(map(frozenset, list_of_sets))
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17
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18
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19 def _assert_subgraph_edge_connectivity(G, ccs_subgraph, k):
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20 """
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21 tests properties of k-edge-connected subgraphs
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22
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23 the actual edge connectivity should be no less than k unless the cc is a
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24 single node.
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25 """
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26 for cc in ccs_subgraph:
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27 C = G.subgraph(cc)
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28 if len(cc) > 1:
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29 connectivity = nx.edge_connectivity(C)
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30 assert connectivity >= k
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31
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32
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33 def _memo_connectivity(G, u, v, memo):
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34 edge = (u, v)
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35 if edge in memo:
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36 return memo[edge]
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37 if not G.is_directed():
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38 redge = (v, u)
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39 if redge in memo:
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40 return memo[redge]
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41 memo[edge] = nx.edge_connectivity(G, *edge)
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42 return memo[edge]
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43
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44
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45 def _all_pairs_connectivity(G, cc, k, memo):
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46 # Brute force check
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47 for u, v in it.combinations(cc, 2):
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48 # Use a memoization dict to save on computation
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49 connectivity = _memo_connectivity(G, u, v, memo)
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50 if G.is_directed():
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51 connectivity = min(connectivity, _memo_connectivity(G, v, u, memo))
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52 assert connectivity >= k
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53
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54
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55 def _assert_local_cc_edge_connectivity(G, ccs_local, k, memo):
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56 """
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57 tests properties of k-edge-connected components
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58
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59 the local edge connectivity between each pair of nodes in the the original
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60 graph should be no less than k unless the cc is a single node.
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61 """
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62 for cc in ccs_local:
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63 if len(cc) > 1:
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64 # Strategy for testing a bit faster: If the subgraph has high edge
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65 # connectivity then it must have local connectivity
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66 C = G.subgraph(cc)
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67 connectivity = nx.edge_connectivity(C)
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68 if connectivity < k:
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69 # Otherwise do the brute force (with memoization) check
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70 _all_pairs_connectivity(G, cc, k, memo)
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71
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72
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73 # Helper function
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74 def _check_edge_connectivity(G):
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75 """
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76 Helper - generates all k-edge-components using the aux graph. Checks the
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77 both local and subgraph edge connectivity of each cc. Also checks that
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78 alternate methods of computing the k-edge-ccs generate the same result.
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79 """
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80 # Construct the auxiliary graph that can be used to make each k-cc or k-sub
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81 aux_graph = EdgeComponentAuxGraph.construct(G)
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82
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83 # memoize the local connectivity in this graph
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84 memo = {}
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85
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86 for k in it.count(1):
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87 # Test "local" k-edge-components and k-edge-subgraphs
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88 ccs_local = fset(aux_graph.k_edge_components(k))
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89 ccs_subgraph = fset(aux_graph.k_edge_subgraphs(k))
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90
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91 # Check connectivity properties that should be garuenteed by the
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92 # algorithms.
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93 _assert_local_cc_edge_connectivity(G, ccs_local, k, memo)
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94 _assert_subgraph_edge_connectivity(G, ccs_subgraph, k)
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95
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96 if k == 1 or k == 2 and not G.is_directed():
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97 assert (
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98 ccs_local == ccs_subgraph
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99 ), "Subgraphs and components should be the same when k == 1 or (k == 2 and not G.directed())"
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100
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101 if G.is_directed():
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102 # Test special case methods are the same as the aux graph
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103 if k == 1:
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104 alt_sccs = fset(nx.strongly_connected_components(G))
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105 assert alt_sccs == ccs_local, "k=1 failed alt"
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106 assert alt_sccs == ccs_subgraph, "k=1 failed alt"
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107 else:
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108 # Test special case methods are the same as the aux graph
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109 if k == 1:
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110 alt_ccs = fset(nx.connected_components(G))
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111 assert alt_ccs == ccs_local, "k=1 failed alt"
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112 assert alt_ccs == ccs_subgraph, "k=1 failed alt"
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113 elif k == 2:
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114 alt_bridge_ccs = fset(bridge_components(G))
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115 assert alt_bridge_ccs == ccs_local, "k=2 failed alt"
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116 assert alt_bridge_ccs == ccs_subgraph, "k=2 failed alt"
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117 # if new methods for k == 3 or k == 4 are implemented add them here
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118
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119 # Check the general subgraph method works by itself
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120 alt_subgraph_ccs = fset(
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121 [set(C.nodes()) for C in general_k_edge_subgraphs(G, k=k)]
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122 )
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123 assert alt_subgraph_ccs == ccs_subgraph, "alt subgraph method failed"
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124
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125 # Stop once k is larger than all special case methods
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126 # and we cannot break down ccs any further.
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127 if k > 2 and all(len(cc) == 1 for cc in ccs_local):
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128 break
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129
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130
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131 # ----------------
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132 # Misc tests
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133 # ----------------
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134
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135
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136 def test_zero_k_exception():
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137 G = nx.Graph()
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138 # functions that return generators error immediately
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139 pytest.raises(ValueError, nx.k_edge_components, G, k=0)
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140 pytest.raises(ValueError, nx.k_edge_subgraphs, G, k=0)
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141
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142 # actual generators only error when you get the first item
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143 aux_graph = EdgeComponentAuxGraph.construct(G)
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144 pytest.raises(ValueError, list, aux_graph.k_edge_components(k=0))
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145 pytest.raises(ValueError, list, aux_graph.k_edge_subgraphs(k=0))
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146
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147 pytest.raises(ValueError, list, general_k_edge_subgraphs(G, k=0))
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148
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149
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150 def test_empty_input():
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151 G = nx.Graph()
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152 assert [] == list(nx.k_edge_components(G, k=5))
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153 assert [] == list(nx.k_edge_subgraphs(G, k=5))
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154
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155 G = nx.DiGraph()
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156 assert [] == list(nx.k_edge_components(G, k=5))
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157 assert [] == list(nx.k_edge_subgraphs(G, k=5))
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158
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159
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160 def test_not_implemented():
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161 G = nx.MultiGraph()
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162 pytest.raises(nx.NetworkXNotImplemented, EdgeComponentAuxGraph.construct, G)
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163 pytest.raises(nx.NetworkXNotImplemented, nx.k_edge_components, G, k=2)
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164 pytest.raises(nx.NetworkXNotImplemented, nx.k_edge_subgraphs, G, k=2)
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165 pytest.raises(nx.NetworkXNotImplemented, bridge_components, G)
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166 pytest.raises(nx.NetworkXNotImplemented, bridge_components, nx.DiGraph())
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167
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168
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169 def test_general_k_edge_subgraph_quick_return():
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170 # tests quick return optimization
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171 G = nx.Graph()
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172 G.add_node(0)
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173 subgraphs = list(general_k_edge_subgraphs(G, k=1))
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174 assert len(subgraphs) == 1
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175 for subgraph in subgraphs:
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176 assert subgraph.number_of_nodes() == 1
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177
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178 G.add_node(1)
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179 subgraphs = list(general_k_edge_subgraphs(G, k=1))
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180 assert len(subgraphs) == 2
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181 for subgraph in subgraphs:
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182 assert subgraph.number_of_nodes() == 1
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183
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184
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185 # ----------------
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186 # Undirected tests
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187 # ----------------
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188
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189
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190 def test_random_gnp():
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191 # seeds = [1550709854, 1309423156, 4208992358, 2785630813, 1915069929]
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192 seeds = [12, 13]
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193
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194 for seed in seeds:
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195 G = nx.gnp_random_graph(20, 0.2, seed=seed)
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196 _check_edge_connectivity(G)
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197
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198
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199 def test_configuration():
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200 # seeds = [2718183590, 2470619828, 1694705158, 3001036531, 2401251497]
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201 seeds = [14, 15]
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202 for seed in seeds:
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203 deg_seq = nx.random_powerlaw_tree_sequence(20, seed=seed, tries=5000)
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204 G = nx.Graph(nx.configuration_model(deg_seq, seed=seed))
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205 G.remove_edges_from(nx.selfloop_edges(G))
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206 _check_edge_connectivity(G)
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207
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208
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209 def test_shell():
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210 # seeds = [2057382236, 3331169846, 1840105863, 476020778, 2247498425]
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211 seeds = [20]
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212 for seed in seeds:
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213 constructor = [(12, 70, 0.8), (15, 40, 0.6)]
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214 G = nx.random_shell_graph(constructor, seed=seed)
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215 _check_edge_connectivity(G)
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216
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217
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218 def test_karate():
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219 G = nx.karate_club_graph()
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220 _check_edge_connectivity(G)
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221
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222
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223 def test_tarjan_bridge():
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224 # graph from tarjan paper
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225 # RE Tarjan - "A note on finding the bridges of a graph"
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226 # Information Processing Letters, 1974 - Elsevier
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227 # doi:10.1016/0020-0190(74)90003-9.
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228 # define 2-connected components and bridges
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229 ccs = [
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230 (1, 2, 4, 3, 1, 4),
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231 (5, 6, 7, 5),
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232 (8, 9, 10, 8),
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233 (17, 18, 16, 15, 17),
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234 (11, 12, 14, 13, 11, 14),
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235 ]
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236 bridges = [(4, 8), (3, 5), (3, 17)]
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237 G = nx.Graph(it.chain(*(pairwise(path) for path in ccs + bridges)))
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238 _check_edge_connectivity(G)
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239
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240
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241 def test_bridge_cc():
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242 # define 2-connected components and bridges
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243 cc2 = [(1, 2, 4, 3, 1, 4), (8, 9, 10, 8), (11, 12, 13, 11)]
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244 bridges = [(4, 8), (3, 5), (20, 21), (22, 23, 24)]
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245 G = nx.Graph(it.chain(*(pairwise(path) for path in cc2 + bridges)))
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246 bridge_ccs = fset(bridge_components(G))
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247 target_ccs = fset(
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248 [{1, 2, 3, 4}, {5}, {8, 9, 10}, {11, 12, 13}, {20}, {21}, {22}, {23}, {24}]
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249 )
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250 assert bridge_ccs == target_ccs
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251 _check_edge_connectivity(G)
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252
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253
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254 def test_undirected_aux_graph():
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255 # Graph similar to the one in
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256 # http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0136264
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257 a, b, c, d, e, f, g, h, i = "abcdefghi"
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258 paths = [
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259 (a, d, b, f, c),
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260 (a, e, b),
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261 (a, e, b, c, g, b, a),
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262 (c, b),
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263 (f, g, f),
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264 (h, i),
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265 ]
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266 G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
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267 aux_graph = EdgeComponentAuxGraph.construct(G)
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268
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269 components_1 = fset(aux_graph.k_edge_subgraphs(k=1))
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270 target_1 = fset([{a, b, c, d, e, f, g}, {h, i}])
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271 assert target_1 == components_1
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272
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273 # Check that the undirected case for k=1 agrees with CCs
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274 alt_1 = fset(nx.k_edge_subgraphs(G, k=1))
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275 assert alt_1 == components_1
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276
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277 components_2 = fset(aux_graph.k_edge_subgraphs(k=2))
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278 target_2 = fset([{a, b, c, d, e, f, g}, {h}, {i}])
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279 assert target_2 == components_2
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280
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281 # Check that the undirected case for k=2 agrees with bridge components
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282 alt_2 = fset(nx.k_edge_subgraphs(G, k=2))
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283 assert alt_2 == components_2
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284
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285 components_3 = fset(aux_graph.k_edge_subgraphs(k=3))
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286 target_3 = fset([{a}, {b, c, f, g}, {d}, {e}, {h}, {i}])
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287 assert target_3 == components_3
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288
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289 components_4 = fset(aux_graph.k_edge_subgraphs(k=4))
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290 target_4 = fset([{a}, {b}, {c}, {d}, {e}, {f}, {g}, {h}, {i}])
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291 assert target_4 == components_4
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292
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293 _check_edge_connectivity(G)
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294
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295
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296 def test_local_subgraph_difference():
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297 paths = [
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298 (11, 12, 13, 14, 11, 13, 14, 12), # first 4-clique
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299 (21, 22, 23, 24, 21, 23, 24, 22), # second 4-clique
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300 # paths connecting each node of the 4 cliques
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301 (11, 101, 21),
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302 (12, 102, 22),
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303 (13, 103, 23),
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304 (14, 104, 24),
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305 ]
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306 G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
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307 aux_graph = EdgeComponentAuxGraph.construct(G)
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308
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309 # Each clique is returned separately in k-edge-subgraphs
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310 subgraph_ccs = fset(aux_graph.k_edge_subgraphs(3))
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311 subgraph_target = fset(
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312 [{101}, {102}, {103}, {104}, {21, 22, 23, 24}, {11, 12, 13, 14}]
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313 )
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314 assert subgraph_ccs == subgraph_target
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315
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316 # But in k-edge-ccs they are returned together
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317 # because they are locally 3-edge-connected
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318 local_ccs = fset(aux_graph.k_edge_components(3))
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319 local_target = fset([{101}, {102}, {103}, {104}, {11, 12, 13, 14, 21, 22, 23, 24}])
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320 assert local_ccs == local_target
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321
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322
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323 def test_local_subgraph_difference_directed():
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324 dipaths = [(1, 2, 3, 4, 1), (1, 3, 1)]
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325 G = nx.DiGraph(it.chain(*[pairwise(path) for path in dipaths]))
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326
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327 assert fset(nx.k_edge_components(G, k=1)) == fset(nx.k_edge_subgraphs(G, k=1))
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328
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329 # Unlike undirected graphs, when k=2, for directed graphs there is a case
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330 # where the k-edge-ccs are not the same as the k-edge-subgraphs.
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331 # (in directed graphs ccs and subgraphs are the same when k=2)
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332 assert fset(nx.k_edge_components(G, k=2)) != fset(nx.k_edge_subgraphs(G, k=2))
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333
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334 assert fset(nx.k_edge_components(G, k=3)) == fset(nx.k_edge_subgraphs(G, k=3))
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335
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336 _check_edge_connectivity(G)
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337
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338
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339 def test_triangles():
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340 paths = [
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341 (11, 12, 13, 11), # first 3-clique
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342 (21, 22, 23, 21), # second 3-clique
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343 (11, 21), # connected by an edge
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344 ]
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345 G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
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346
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347 # subgraph and ccs are the same in all cases here
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348 assert fset(nx.k_edge_components(G, k=1)) == fset(nx.k_edge_subgraphs(G, k=1))
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349
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350 assert fset(nx.k_edge_components(G, k=2)) == fset(nx.k_edge_subgraphs(G, k=2))
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351
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352 assert fset(nx.k_edge_components(G, k=3)) == fset(nx.k_edge_subgraphs(G, k=3))
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353
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354 _check_edge_connectivity(G)
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355
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356
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357 def test_four_clique():
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358 paths = [
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359 (11, 12, 13, 14, 11, 13, 14, 12), # first 4-clique
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360 (21, 22, 23, 24, 21, 23, 24, 22), # second 4-clique
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361 # paths connecting the 4 cliques such that they are
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362 # 3-connected in G, but not in the subgraph.
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363 # Case where the nodes bridging them do not have degree less than 3.
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364 (100, 13),
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365 (12, 100, 22),
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366 (13, 200, 23),
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parents:
diff changeset
367 (14, 300, 24),
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368 ]
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369 G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
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parents:
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370
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371 # The subgraphs and ccs are different for k=3
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372 local_ccs = fset(nx.k_edge_components(G, k=3))
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parents:
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373 subgraphs = fset(nx.k_edge_subgraphs(G, k=3))
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parents:
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374 assert local_ccs != subgraphs
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parents:
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375
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parents:
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376 # The cliques ares in the same cc
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377 clique1 = frozenset(paths[0])
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parents:
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378 clique2 = frozenset(paths[1])
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parents:
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379 assert clique1.union(clique2).union({100}) in local_ccs
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parents:
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380
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parents:
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381 # but different subgraphs
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parents:
diff changeset
382 assert clique1 in subgraphs
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parents:
diff changeset
383 assert clique2 in subgraphs
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384
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385 assert G.degree(100) == 3
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386
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387 _check_edge_connectivity(G)
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388
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389
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390 def test_five_clique():
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391 # Make a graph that can be disconnected less than 4 edges, but no node has
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392 # degree less than 4.
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393 G = nx.disjoint_union(nx.complete_graph(5), nx.complete_graph(5))
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394 paths = [
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395 # add aux-connections
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diff changeset
396 (1, 100, 6),
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parents:
diff changeset
397 (2, 100, 7),
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parents:
diff changeset
398 (3, 200, 8),
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parents:
diff changeset
399 (4, 200, 100),
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400 ]
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401 G.add_edges_from(it.chain(*[pairwise(path) for path in paths]))
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402 assert min(dict(nx.degree(G)).values()) == 4
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403
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404 # For k=3 they are the same
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405 assert fset(nx.k_edge_components(G, k=3)) == fset(nx.k_edge_subgraphs(G, k=3))
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406
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407 # For k=4 they are the different
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408 # the aux nodes are in the same CC as clique 1 but no the same subgraph
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409 assert fset(nx.k_edge_components(G, k=4)) != fset(nx.k_edge_subgraphs(G, k=4))
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410
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411 # For k=5 they are not the same
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412 assert fset(nx.k_edge_components(G, k=5)) != fset(nx.k_edge_subgraphs(G, k=5))
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413
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414 # For k=6 they are the same
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415 assert fset(nx.k_edge_components(G, k=6)) == fset(nx.k_edge_subgraphs(G, k=6))
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416 _check_edge_connectivity(G)
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417
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418
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419 # ----------------
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420 # Undirected tests
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421 # ----------------
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422
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423
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424 def test_directed_aux_graph():
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425 # Graph similar to the one in
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426 # http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0136264
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diff changeset
427 a, b, c, d, e, f, g, h, i = "abcdefghi"
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428 dipaths = [
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429 (a, d, b, f, c),
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diff changeset
430 (a, e, b),
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diff changeset
431 (a, e, b, c, g, b, a),
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432 (c, b),
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diff changeset
433 (f, g, f),
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diff changeset
434 (h, i),
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parents:
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435 ]
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diff changeset
436 G = nx.DiGraph(it.chain(*[pairwise(path) for path in dipaths]))
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diff changeset
437 aux_graph = EdgeComponentAuxGraph.construct(G)
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diff changeset
438
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439 components_1 = fset(aux_graph.k_edge_subgraphs(k=1))
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parents:
diff changeset
440 target_1 = fset([{a, b, c, d, e, f, g}, {h}, {i}])
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diff changeset
441 assert target_1 == components_1
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442
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diff changeset
443 # Check that the directed case for k=1 agrees with SCCs
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diff changeset
444 alt_1 = fset(nx.strongly_connected_components(G))
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diff changeset
445 assert alt_1 == components_1
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diff changeset
446
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447 components_2 = fset(aux_graph.k_edge_subgraphs(k=2))
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parents:
diff changeset
448 target_2 = fset([{i}, {e}, {d}, {b, c, f, g}, {h}, {a}])
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diff changeset
449 assert target_2 == components_2
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450
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451 components_3 = fset(aux_graph.k_edge_subgraphs(k=3))
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diff changeset
452 target_3 = fset([{a}, {b}, {c}, {d}, {e}, {f}, {g}, {h}, {i}])
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parents:
diff changeset
453 assert target_3 == components_3
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parents:
diff changeset
454
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diff changeset
455
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diff changeset
456 def test_random_gnp_directed():
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parents:
diff changeset
457 # seeds = [3894723670, 500186844, 267231174, 2181982262, 1116750056]
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diff changeset
458 seeds = [21]
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diff changeset
459 for seed in seeds:
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parents:
diff changeset
460 G = nx.gnp_random_graph(20, 0.2, directed=True, seed=seed)
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diff changeset
461 _check_edge_connectivity(G)
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462
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463
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diff changeset
464 def test_configuration_directed():
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parents:
diff changeset
465 # seeds = [671221681, 2403749451, 124433910, 672335939, 1193127215]
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diff changeset
466 seeds = [67]
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467 for seed in seeds:
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diff changeset
468 deg_seq = nx.random_powerlaw_tree_sequence(20, seed=seed, tries=5000)
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parents:
diff changeset
469 G = nx.DiGraph(nx.configuration_model(deg_seq, seed=seed))
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parents:
diff changeset
470 G.remove_edges_from(nx.selfloop_edges(G))
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diff changeset
471 _check_edge_connectivity(G)
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472
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diff changeset
473
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diff changeset
474 def test_shell_directed():
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parents:
diff changeset
475 # seeds = [3134027055, 4079264063, 1350769518, 1405643020, 530038094]
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diff changeset
476 seeds = [31]
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parents:
diff changeset
477 for seed in seeds:
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parents:
diff changeset
478 constructor = [(12, 70, 0.8), (15, 40, 0.6)]
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parents:
diff changeset
479 G = nx.random_shell_graph(constructor, seed=seed).to_directed()
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parents:
diff changeset
480 _check_edge_connectivity(G)
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parents:
diff changeset
481
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parents:
diff changeset
482
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parents:
diff changeset
483 def test_karate_directed():
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diff changeset
484 G = nx.karate_club_graph().to_directed()
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parents:
diff changeset
485 _check_edge_connectivity(G)