Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/shortest_paths/generic.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 Compute the shortest paths and path lengths between nodes in the graph. |
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3 |
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4 These algorithms work with undirected and directed graphs. |
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5 |
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6 """ |
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7 |
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8 import networkx as nx |
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9 |
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10 __all__ = [ |
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11 "shortest_path", |
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12 "all_shortest_paths", |
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13 "shortest_path_length", |
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14 "average_shortest_path_length", |
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15 "has_path", |
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16 ] |
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17 |
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18 |
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19 def has_path(G, source, target): |
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20 """Returns *True* if *G* has a path from *source* to *target*. |
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21 |
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22 Parameters |
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23 ---------- |
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24 G : NetworkX graph |
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25 |
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26 source : node |
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27 Starting node for path |
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28 |
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29 target : node |
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30 Ending node for path |
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31 """ |
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32 try: |
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33 nx.shortest_path(G, source, target) |
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34 except nx.NetworkXNoPath: |
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35 return False |
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36 return True |
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37 |
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38 |
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39 def shortest_path(G, source=None, target=None, weight=None, method="dijkstra"): |
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40 """Compute shortest paths in the graph. |
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41 |
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42 Parameters |
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43 ---------- |
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44 G : NetworkX graph |
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45 |
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46 source : node, optional |
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47 Starting node for path. If not specified, compute shortest |
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48 paths for each possible starting node. |
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49 |
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50 target : node, optional |
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51 Ending node for path. If not specified, compute shortest |
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52 paths to all possible nodes. |
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53 |
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54 weight : None or string, optional (default = None) |
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55 If None, every edge has weight/distance/cost 1. |
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56 If a string, use this edge attribute as the edge weight. |
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57 Any edge attribute not present defaults to 1. |
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58 |
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59 method : string, optional (default = 'dijkstra') |
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60 The algorithm to use to compute the path. |
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61 Supported options: 'dijkstra', 'bellman-ford'. |
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62 Other inputs produce a ValueError. |
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63 If `weight` is None, unweighted graph methods are used, and this |
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64 suggestion is ignored. |
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65 |
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66 Returns |
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67 ------- |
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68 path: list or dictionary |
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69 All returned paths include both the source and target in the path. |
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70 |
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71 If the source and target are both specified, return a single list |
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72 of nodes in a shortest path from the source to the target. |
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73 |
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74 If only the source is specified, return a dictionary keyed by |
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75 targets with a list of nodes in a shortest path from the source |
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76 to one of the targets. |
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77 |
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78 If only the target is specified, return a dictionary keyed by |
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79 sources with a list of nodes in a shortest path from one of the |
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80 sources to the target. |
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81 |
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82 If neither the source nor target are specified return a dictionary |
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83 of dictionaries with path[source][target]=[list of nodes in path]. |
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84 |
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85 Raises |
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86 ------ |
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87 NodeNotFound |
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88 If `source` is not in `G`. |
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89 |
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90 ValueError |
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91 If `method` is not among the supported options. |
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92 |
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93 Examples |
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94 -------- |
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95 >>> G = nx.path_graph(5) |
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96 >>> print(nx.shortest_path(G, source=0, target=4)) |
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97 [0, 1, 2, 3, 4] |
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98 >>> p = nx.shortest_path(G, source=0) # target not specified |
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99 >>> p[4] |
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100 [0, 1, 2, 3, 4] |
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101 >>> p = nx.shortest_path(G, target=4) # source not specified |
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102 >>> p[0] |
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103 [0, 1, 2, 3, 4] |
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104 >>> p = nx.shortest_path(G) # source, target not specified |
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105 >>> p[0][4] |
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106 [0, 1, 2, 3, 4] |
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107 |
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108 Notes |
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109 ----- |
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110 There may be more than one shortest path between a source and target. |
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111 This returns only one of them. |
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112 |
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113 See Also |
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114 -------- |
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115 all_pairs_shortest_path() |
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116 all_pairs_dijkstra_path() |
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117 all_pairs_bellman_ford_path() |
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118 single_source_shortest_path() |
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119 single_source_dijkstra_path() |
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120 single_source_bellman_ford_path() |
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121 """ |
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122 if method not in ("dijkstra", "bellman-ford"): |
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123 # so we don't need to check in each branch later |
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124 raise ValueError(f"method not supported: {method}") |
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125 method = "unweighted" if weight is None else method |
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126 if source is None: |
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127 if target is None: |
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128 # Find paths between all pairs. |
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129 if method == "unweighted": |
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130 paths = dict(nx.all_pairs_shortest_path(G)) |
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131 elif method == "dijkstra": |
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132 paths = dict(nx.all_pairs_dijkstra_path(G, weight=weight)) |
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133 else: # method == 'bellman-ford': |
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134 paths = dict(nx.all_pairs_bellman_ford_path(G, weight=weight)) |
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135 else: |
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136 # Find paths from all nodes co-accessible to the target. |
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137 if G.is_directed(): |
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138 G = G.reverse(copy=False) |
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139 if method == "unweighted": |
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140 paths = nx.single_source_shortest_path(G, target) |
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141 elif method == "dijkstra": |
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142 paths = nx.single_source_dijkstra_path(G, target, weight=weight) |
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143 else: # method == 'bellman-ford': |
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144 paths = nx.single_source_bellman_ford_path(G, target, weight=weight) |
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145 # Now flip the paths so they go from a source to the target. |
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146 for target in paths: |
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147 paths[target] = list(reversed(paths[target])) |
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148 else: |
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149 if target is None: |
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150 # Find paths to all nodes accessible from the source. |
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151 if method == "unweighted": |
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152 paths = nx.single_source_shortest_path(G, source) |
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153 elif method == "dijkstra": |
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154 paths = nx.single_source_dijkstra_path(G, source, weight=weight) |
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155 else: # method == 'bellman-ford': |
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156 paths = nx.single_source_bellman_ford_path(G, source, weight=weight) |
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157 else: |
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158 # Find shortest source-target path. |
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159 if method == "unweighted": |
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160 paths = nx.bidirectional_shortest_path(G, source, target) |
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161 elif method == "dijkstra": |
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162 paths = nx.dijkstra_path(G, source, target, weight) |
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163 else: # method == 'bellman-ford': |
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164 paths = nx.bellman_ford_path(G, source, target, weight) |
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165 return paths |
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166 |
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167 |
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168 def shortest_path_length(G, source=None, target=None, weight=None, method="dijkstra"): |
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169 """Compute shortest path lengths in the graph. |
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170 |
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171 Parameters |
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172 ---------- |
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173 G : NetworkX graph |
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174 |
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175 source : node, optional |
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176 Starting node for path. |
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177 If not specified, compute shortest path lengths using all nodes as |
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178 source nodes. |
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179 |
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180 target : node, optional |
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181 Ending node for path. |
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182 If not specified, compute shortest path lengths using all nodes as |
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183 target nodes. |
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184 |
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185 weight : None or string, optional (default = None) |
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186 If None, every edge has weight/distance/cost 1. |
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187 If a string, use this edge attribute as the edge weight. |
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188 Any edge attribute not present defaults to 1. |
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189 |
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190 method : string, optional (default = 'dijkstra') |
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191 The algorithm to use to compute the path length. |
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192 Supported options: 'dijkstra', 'bellman-ford'. |
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193 Other inputs produce a ValueError. |
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194 If `weight` is None, unweighted graph methods are used, and this |
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195 suggestion is ignored. |
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196 |
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197 Returns |
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198 ------- |
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199 length: int or iterator |
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200 If the source and target are both specified, return the length of |
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201 the shortest path from the source to the target. |
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202 |
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203 If only the source is specified, return a dict keyed by target |
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204 to the shortest path length from the source to that target. |
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205 |
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206 If only the target is specified, return a dict keyed by source |
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207 to the shortest path length from that source to the target. |
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208 |
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209 If neither the source nor target are specified, return an iterator |
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210 over (source, dictionary) where dictionary is keyed by target to |
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211 shortest path length from source to that target. |
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212 |
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213 Raises |
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214 ------ |
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215 NodeNotFound |
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216 If `source` is not in `G`. |
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217 |
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218 NetworkXNoPath |
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219 If no path exists between source and target. |
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220 |
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221 ValueError |
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222 If `method` is not among the supported options. |
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223 |
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224 Examples |
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225 -------- |
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226 >>> G = nx.path_graph(5) |
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227 >>> nx.shortest_path_length(G, source=0, target=4) |
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228 4 |
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229 >>> p = nx.shortest_path_length(G, source=0) # target not specified |
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230 >>> p[4] |
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231 4 |
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232 >>> p = nx.shortest_path_length(G, target=4) # source not specified |
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233 >>> p[0] |
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234 4 |
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235 >>> p = dict(nx.shortest_path_length(G)) # source,target not specified |
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236 >>> p[0][4] |
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237 4 |
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238 |
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239 Notes |
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240 ----- |
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241 The length of the path is always 1 less than the number of nodes involved |
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242 in the path since the length measures the number of edges followed. |
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243 |
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244 For digraphs this returns the shortest directed path length. To find path |
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245 lengths in the reverse direction use G.reverse(copy=False) first to flip |
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246 the edge orientation. |
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247 |
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248 See Also |
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249 -------- |
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250 all_pairs_shortest_path_length() |
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251 all_pairs_dijkstra_path_length() |
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252 all_pairs_bellman_ford_path_length() |
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253 single_source_shortest_path_length() |
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254 single_source_dijkstra_path_length() |
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255 single_source_bellman_ford_path_length() |
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256 """ |
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257 if method not in ("dijkstra", "bellman-ford"): |
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258 # so we don't need to check in each branch later |
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259 raise ValueError(f"method not supported: {method}") |
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260 method = "unweighted" if weight is None else method |
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261 if source is None: |
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262 if target is None: |
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263 # Find paths between all pairs. |
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264 if method == "unweighted": |
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265 paths = nx.all_pairs_shortest_path_length(G) |
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266 elif method == "dijkstra": |
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267 paths = nx.all_pairs_dijkstra_path_length(G, weight=weight) |
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268 else: # method == 'bellman-ford': |
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269 paths = nx.all_pairs_bellman_ford_path_length(G, weight=weight) |
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270 else: |
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271 # Find paths from all nodes co-accessible to the target. |
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272 if G.is_directed(): |
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273 G = G.reverse(copy=False) |
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274 if method == "unweighted": |
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275 path_length = nx.single_source_shortest_path_length |
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276 paths = path_length(G, target) |
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277 elif method == "dijkstra": |
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278 path_length = nx.single_source_dijkstra_path_length |
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279 paths = path_length(G, target, weight=weight) |
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280 else: # method == 'bellman-ford': |
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281 path_length = nx.single_source_bellman_ford_path_length |
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282 paths = path_length(G, target, weight=weight) |
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283 else: |
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284 if target is None: |
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285 # Find paths to all nodes accessible from the source. |
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286 if method == "unweighted": |
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287 paths = nx.single_source_shortest_path_length(G, source) |
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288 elif method == "dijkstra": |
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289 path_length = nx.single_source_dijkstra_path_length |
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290 paths = path_length(G, source, weight=weight) |
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291 else: # method == 'bellman-ford': |
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292 path_length = nx.single_source_bellman_ford_path_length |
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293 paths = path_length(G, source, weight=weight) |
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294 else: |
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295 # Find shortest source-target path. |
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296 if method == "unweighted": |
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297 p = nx.bidirectional_shortest_path(G, source, target) |
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298 paths = len(p) - 1 |
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299 elif method == "dijkstra": |
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300 paths = nx.dijkstra_path_length(G, source, target, weight) |
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301 else: # method == 'bellman-ford': |
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302 paths = nx.bellman_ford_path_length(G, source, target, weight) |
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303 return paths |
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304 |
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305 |
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306 def average_shortest_path_length(G, weight=None, method=None): |
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307 r"""Returns the average shortest path length. |
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308 |
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309 The average shortest path length is |
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310 |
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311 .. math:: |
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312 |
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313 a =\sum_{s,t \in V} \frac{d(s, t)}{n(n-1)} |
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314 |
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315 where `V` is the set of nodes in `G`, |
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316 `d(s, t)` is the shortest path from `s` to `t`, |
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317 and `n` is the number of nodes in `G`. |
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318 |
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319 Parameters |
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320 ---------- |
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321 G : NetworkX graph |
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322 |
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323 weight : None or string, optional (default = None) |
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324 If None, every edge has weight/distance/cost 1. |
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325 If a string, use this edge attribute as the edge weight. |
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326 Any edge attribute not present defaults to 1. |
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327 |
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328 method : string, optional (default = 'unweighted' or 'djikstra') |
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329 The algorithm to use to compute the path lengths. |
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330 Supported options are 'unweighted', 'dijkstra', 'bellman-ford', |
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331 'floyd-warshall' and 'floyd-warshall-numpy'. |
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332 Other method values produce a ValueError. |
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333 The default method is 'unweighted' if `weight` is None, |
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334 otherwise the default method is 'dijkstra'. |
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335 |
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336 Raises |
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337 ------ |
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338 NetworkXPointlessConcept |
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339 If `G` is the null graph (that is, the graph on zero nodes). |
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340 |
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341 NetworkXError |
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342 If `G` is not connected (or not weakly connected, in the case |
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343 of a directed graph). |
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344 |
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345 ValueError |
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346 If `method` is not among the supported options. |
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347 |
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348 Examples |
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349 -------- |
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350 >>> G = nx.path_graph(5) |
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351 >>> nx.average_shortest_path_length(G) |
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352 2.0 |
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353 |
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354 For disconnected graphs, you can compute the average shortest path |
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355 length for each component |
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356 |
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357 >>> G = nx.Graph([(1, 2), (3, 4)]) |
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358 >>> for C in (G.subgraph(c).copy() for c in nx.connected_components(G)): |
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359 ... print(nx.average_shortest_path_length(C)) |
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360 1.0 |
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361 1.0 |
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362 |
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363 """ |
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364 single_source_methods = ["unweighted", "dijkstra", "bellman-ford"] |
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365 all_pairs_methods = ["floyd-warshall", "floyd-warshall-numpy"] |
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366 supported_methods = single_source_methods + all_pairs_methods |
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367 |
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368 if method is None: |
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369 method = "unweighted" if weight is None else "dijkstra" |
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370 if method not in supported_methods: |
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371 raise ValueError(f"method not supported: {method}") |
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372 |
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373 n = len(G) |
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374 # For the special case of the null graph, raise an exception, since |
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375 # there are no paths in the null graph. |
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376 if n == 0: |
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377 msg = ( |
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378 "the null graph has no paths, thus there is no average" |
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379 "shortest path length" |
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380 ) |
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381 raise nx.NetworkXPointlessConcept(msg) |
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382 # For the special case of the trivial graph, return zero immediately. |
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383 if n == 1: |
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384 return 0 |
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385 # Shortest path length is undefined if the graph is disconnected. |
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386 if G.is_directed() and not nx.is_weakly_connected(G): |
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387 raise nx.NetworkXError("Graph is not weakly connected.") |
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388 if not G.is_directed() and not nx.is_connected(G): |
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389 raise nx.NetworkXError("Graph is not connected.") |
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390 |
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391 # Compute all-pairs shortest paths. |
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392 def path_length(v): |
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393 if method == "unweighted": |
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394 return nx.single_source_shortest_path_length(G, v) |
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395 elif method == "dijkstra": |
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396 return nx.single_source_dijkstra_path_length(G, v, weight=weight) |
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397 elif method == "bellman-ford": |
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398 return nx.single_source_bellman_ford_path_length(G, v, weight=weight) |
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399 |
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400 if method in single_source_methods: |
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401 # Sum the distances for each (ordered) pair of source and target node. |
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402 s = sum(l for u in G for l in path_length(u).values()) |
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403 else: |
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404 if method == "floyd-warshall": |
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405 all_pairs = nx.floyd_warshall(G, weight=weight) |
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406 s = sum([sum(t.values()) for t in all_pairs.values()]) |
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407 elif method == "floyd-warshall-numpy": |
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408 s = nx.floyd_warshall_numpy(G, weight=weight).sum() |
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409 return s / (n * (n - 1)) |
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410 |
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411 |
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412 def all_shortest_paths(G, source, target, weight=None, method="dijkstra"): |
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413 """Compute all shortest simple paths in the graph. |
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414 |
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415 Parameters |
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416 ---------- |
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417 G : NetworkX graph |
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418 |
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419 source : node |
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420 Starting node for path. |
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421 |
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422 target : node |
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423 Ending node for path. |
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424 |
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425 weight : None or string, optional (default = None) |
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426 If None, every edge has weight/distance/cost 1. |
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427 If a string, use this edge attribute as the edge weight. |
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428 Any edge attribute not present defaults to 1. |
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429 |
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430 method : string, optional (default = 'dijkstra') |
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431 The algorithm to use to compute the path lengths. |
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432 Supported options: 'dijkstra', 'bellman-ford'. |
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433 Other inputs produce a ValueError. |
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434 If `weight` is None, unweighted graph methods are used, and this |
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435 suggestion is ignored. |
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436 |
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437 Returns |
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438 ------- |
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439 paths : generator of lists |
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440 A generator of all paths between source and target. |
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441 |
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442 Raises |
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443 ------ |
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444 ValueError |
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445 If `method` is not among the supported options. |
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446 |
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447 NetworkXNoPath |
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448 If `target` cannot be reached from `source`. |
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449 |
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450 Examples |
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451 -------- |
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452 >>> G = nx.Graph() |
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453 >>> nx.add_path(G, [0, 1, 2]) |
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454 >>> nx.add_path(G, [0, 10, 2]) |
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455 >>> print([p for p in nx.all_shortest_paths(G, source=0, target=2)]) |
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456 [[0, 1, 2], [0, 10, 2]] |
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457 |
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458 Notes |
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459 ----- |
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460 There may be many shortest paths between the source and target. If G |
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461 contains zero-weight cycles, this function will not produce all shortest |
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462 paths because doing so would produce infinitely many paths of unbounded |
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463 length -- instead, we only produce the shortest simple paths. |
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464 |
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465 See Also |
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466 -------- |
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467 shortest_path() |
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468 single_source_shortest_path() |
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469 all_pairs_shortest_path() |
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470 """ |
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471 method = "unweighted" if weight is None else method |
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472 if method == "unweighted": |
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473 pred = nx.predecessor(G, source) |
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474 elif method == "dijkstra": |
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475 pred, dist = nx.dijkstra_predecessor_and_distance(G, source, weight=weight) |
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476 elif method == "bellman-ford": |
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477 pred, dist = nx.bellman_ford_predecessor_and_distance(G, source, weight=weight) |
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478 else: |
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479 raise ValueError(f"method not supported: {method}") |
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480 |
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481 return _build_paths_from_predecessors({source}, target, pred) |
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482 |
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483 |
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484 def _build_paths_from_predecessors(sources, target, pred): |
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485 """Compute all simple paths to target, given the predecessors found in |
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486 pred, terminating when any source in sources is found. |
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487 |
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488 Parameters |
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489 ---------- |
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490 sources : set |
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491 Starting nodes for path. |
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492 |
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493 target : node |
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494 Ending node for path. |
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495 |
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496 pred : dict |
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497 A dictionary of predecessor lists, keyed by node |
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498 |
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499 Returns |
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500 ------- |
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501 paths : generator of lists |
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502 A generator of all paths between source and target. |
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503 |
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504 Raises |
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505 ------ |
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506 NetworkXNoPath |
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507 If `target` cannot be reached from `source`. |
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508 |
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509 Notes |
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510 ----- |
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511 There may be many paths between the sources and target. If there are |
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512 cycles among the predecessors, this function will not produce all |
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513 possible paths because doing so would produce infinitely many paths |
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514 of unbounded length -- instead, we only produce simple paths. |
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515 |
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516 See Also |
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517 -------- |
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518 shortest_path() |
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519 single_source_shortest_path() |
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520 all_pairs_shortest_path() |
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521 all_shortest_paths() |
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522 bellman_ford_path() |
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523 """ |
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524 if target not in pred: |
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525 raise nx.NetworkXNoPath( |
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526 f"Target {target} cannot be reached" f"from given sources" |
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527 ) |
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528 |
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529 seen = {target} |
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530 stack = [[target, 0]] |
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531 top = 0 |
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532 while top >= 0: |
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533 node, i = stack[top] |
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534 if node in sources: |
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535 yield [p for p, n in reversed(stack[: top + 1])] |
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536 if len(pred[node]) > i: |
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537 stack[top][1] = i + 1 |
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538 next = pred[node][i] |
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539 if next in seen: |
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540 continue |
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541 else: |
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542 seen.add(next) |
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543 top += 1 |
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544 if top == len(stack): |
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545 stack.append([next, 0]) |
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546 else: |
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547 stack[top][:] = [next, 0] |
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548 else: |
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549 seen.discard(node) |
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550 top -= 1 |