Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/hybrid.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """ |
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2 Provides functions for finding and testing for locally `(k, l)`-connected |
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3 graphs. |
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4 |
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5 """ |
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6 import copy |
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7 import networkx as nx |
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8 |
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9 __all__ = ["kl_connected_subgraph", "is_kl_connected"] |
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10 |
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11 |
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12 def kl_connected_subgraph(G, k, l, low_memory=False, same_as_graph=False): |
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13 """Returns the maximum locally `(k, l)`-connected subgraph of `G`. |
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14 |
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15 A graph is locally `(k, l)`-connected if for each edge `(u, v)` in the |
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16 graph there are at least `l` edge-disjoint paths of length at most `k` |
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17 joining `u` to `v`. |
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18 |
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19 Parameters |
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20 ---------- |
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21 G : NetworkX graph |
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22 The graph in which to find a maximum locally `(k, l)`-connected |
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23 subgraph. |
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24 |
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25 k : integer |
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26 The maximum length of paths to consider. A higher number means a looser |
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27 connectivity requirement. |
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28 |
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29 l : integer |
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30 The number of edge-disjoint paths. A higher number means a stricter |
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31 connectivity requirement. |
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32 |
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33 low_memory : bool |
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34 If this is True, this function uses an algorithm that uses slightly |
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35 more time but less memory. |
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36 |
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37 same_as_graph : bool |
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38 If True then return a tuple of the form `(H, is_same)`, |
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39 where `H` is the maximum locally `(k, l)`-connected subgraph and |
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40 `is_same` is a Boolean representing whether `G` is locally `(k, |
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41 l)`-connected (and hence, whether `H` is simply a copy of the input |
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42 graph `G`). |
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43 |
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44 Returns |
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45 ------- |
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46 NetworkX graph or two-tuple |
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47 If `same_as_graph` is True, then this function returns a |
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48 two-tuple as described above. Otherwise, it returns only the maximum |
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49 locally `(k, l)`-connected subgraph. |
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50 |
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51 See also |
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52 -------- |
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53 is_kl_connected |
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54 |
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55 References |
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56 ---------- |
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57 .. [1]: Chung, Fan and Linyuan Lu. "The Small World Phenomenon in Hybrid |
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58 Power Law Graphs." *Complex Networks*. Springer Berlin Heidelberg, |
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59 2004. 89--104. |
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60 |
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61 """ |
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62 H = copy.deepcopy(G) # subgraph we construct by removing from G |
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63 |
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64 graphOK = True |
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65 deleted_some = True # hack to start off the while loop |
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66 while deleted_some: |
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67 deleted_some = False |
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68 # We use `for edge in list(H.edges()):` instead of |
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69 # `for edge in H.edges():` because we edit the graph `H` in |
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70 # the loop. Hence using an iterator will result in |
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71 # `RuntimeError: dictionary changed size during iteration` |
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72 for edge in list(H.edges()): |
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73 (u, v) = edge |
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74 # Get copy of graph needed for this search |
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75 if low_memory: |
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76 verts = {u, v} |
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77 for i in range(k): |
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78 for w in verts.copy(): |
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79 verts.update(G[w]) |
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80 G2 = G.subgraph(verts).copy() |
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81 else: |
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82 G2 = copy.deepcopy(G) |
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83 ### |
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84 path = [u, v] |
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85 cnt = 0 |
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86 accept = 0 |
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87 while path: |
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88 cnt += 1 # Found a path |
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89 if cnt >= l: |
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90 accept = 1 |
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91 break |
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92 # record edges along this graph |
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93 prev = u |
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94 for w in path: |
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95 if prev != w: |
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96 G2.remove_edge(prev, w) |
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97 prev = w |
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98 # path = shortest_path(G2, u, v, k) # ??? should "Cutoff" be k+1? |
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99 try: |
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100 path = nx.shortest_path(G2, u, v) # ??? should "Cutoff" be k+1? |
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101 except nx.NetworkXNoPath: |
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102 path = False |
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103 # No Other Paths |
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104 if accept == 0: |
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105 H.remove_edge(u, v) |
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106 deleted_some = True |
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107 if graphOK: |
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108 graphOK = False |
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109 # We looked through all edges and removed none of them. |
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110 # So, H is the maximal (k,l)-connected subgraph of G |
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111 if same_as_graph: |
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112 return (H, graphOK) |
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113 return H |
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114 |
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115 |
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116 def is_kl_connected(G, k, l, low_memory=False): |
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117 """Returns True if and only if `G` is locally `(k, l)`-connected. |
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118 |
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119 A graph is locally `(k, l)`-connected if for each edge `(u, v)` in the |
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120 graph there are at least `l` edge-disjoint paths of length at most `k` |
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121 joining `u` to `v`. |
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122 |
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123 Parameters |
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124 ---------- |
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125 G : NetworkX graph |
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126 The graph to test for local `(k, l)`-connectedness. |
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127 |
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128 k : integer |
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129 The maximum length of paths to consider. A higher number means a looser |
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130 connectivity requirement. |
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131 |
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132 l : integer |
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133 The number of edge-disjoint paths. A higher number means a stricter |
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134 connectivity requirement. |
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135 |
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136 low_memory : bool |
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137 If this is True, this function uses an algorithm that uses slightly |
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138 more time but less memory. |
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139 |
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140 Returns |
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141 ------- |
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142 bool |
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143 Whether the graph is locally `(k, l)`-connected subgraph. |
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144 |
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145 See also |
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146 -------- |
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147 kl_connected_subgraph |
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148 |
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149 References |
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150 ---------- |
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151 .. [1]: Chung, Fan and Linyuan Lu. "The Small World Phenomenon in Hybrid |
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152 Power Law Graphs." *Complex Networks*. Springer Berlin Heidelberg, |
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153 2004. 89--104. |
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154 |
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155 """ |
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156 graphOK = True |
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157 for edge in G.edges(): |
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158 (u, v) = edge |
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159 # Get copy of graph needed for this search |
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160 if low_memory: |
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161 verts = {u, v} |
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162 for i in range(k): |
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163 [verts.update(G.neighbors(w)) for w in verts.copy()] |
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164 G2 = G.subgraph(verts) |
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165 else: |
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166 G2 = copy.deepcopy(G) |
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167 ### |
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168 path = [u, v] |
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169 cnt = 0 |
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170 accept = 0 |
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171 while path: |
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172 cnt += 1 # Found a path |
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173 if cnt >= l: |
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174 accept = 1 |
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175 break |
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176 # record edges along this graph |
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177 prev = u |
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178 for w in path: |
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179 if w != prev: |
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180 G2.remove_edge(prev, w) |
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181 prev = w |
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182 # path = shortest_path(G2, u, v, k) # ??? should "Cutoff" be k+1? |
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183 try: |
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184 path = nx.shortest_path(G2, u, v) # ??? should "Cutoff" be k+1? |
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185 except nx.NetworkXNoPath: |
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186 path = False |
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187 # No Other Paths |
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188 if accept == 0: |
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189 graphOK = False |
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190 break |
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191 # return status |
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192 return graphOK |