Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/traversal/breadth_first_search.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 """Basic algorithms for breadth-first searching the nodes of a graph.""" |
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2 import networkx as nx |
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3 from collections import deque |
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4 |
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5 __all__ = [ |
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6 "bfs_edges", |
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7 "bfs_tree", |
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8 "bfs_predecessors", |
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9 "bfs_successors", |
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10 "descendants_at_distance", |
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11 ] |
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12 |
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13 |
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14 def generic_bfs_edges(G, source, neighbors=None, depth_limit=None, sort_neighbors=None): |
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15 """Iterate over edges in a breadth-first search. |
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16 |
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17 The breadth-first search begins at `source` and enqueues the |
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18 neighbors of newly visited nodes specified by the `neighbors` |
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19 function. |
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20 |
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21 Parameters |
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22 ---------- |
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23 G : NetworkX graph |
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24 |
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25 source : node |
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26 Starting node for the breadth-first search; this function |
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27 iterates over only those edges in the component reachable from |
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28 this node. |
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29 |
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30 neighbors : function |
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31 A function that takes a newly visited node of the graph as input |
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32 and returns an *iterator* (not just a list) of nodes that are |
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33 neighbors of that node. If not specified, this is just the |
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34 ``G.neighbors`` method, but in general it can be any function |
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35 that returns an iterator over some or all of the neighbors of a |
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36 given node, in any order. |
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37 |
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38 depth_limit : int, optional(default=len(G)) |
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39 Specify the maximum search depth |
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40 |
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41 sort_neighbors : function |
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42 A function that takes the list of neighbors of given node as input, and |
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43 returns an *iterator* over these neighbors but with custom ordering. |
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44 |
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45 Yields |
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46 ------ |
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47 edge |
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48 Edges in the breadth-first search starting from `source`. |
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49 |
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50 Examples |
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51 -------- |
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52 >>> G = nx.path_graph(3) |
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53 >>> print(list(nx.bfs_edges(G, 0))) |
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54 [(0, 1), (1, 2)] |
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55 >>> print(list(nx.bfs_edges(G, source=0, depth_limit=1))) |
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56 [(0, 1)] |
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57 |
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58 Notes |
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59 ----- |
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60 This implementation is from `PADS`_, which was in the public domain |
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61 when it was first accessed in July, 2004. The modifications |
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62 to allow depth limits are based on the Wikipedia article |
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63 "`Depth-limited-search`_". |
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64 |
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65 .. _PADS: http://www.ics.uci.edu/~eppstein/PADS/BFS.py |
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66 .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search |
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67 """ |
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68 if callable(sort_neighbors): |
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69 _neighbors = neighbors |
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70 neighbors = lambda node: iter(sort_neighbors(_neighbors(node))) |
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71 |
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72 visited = {source} |
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73 if depth_limit is None: |
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74 depth_limit = len(G) |
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75 queue = deque([(source, depth_limit, neighbors(source))]) |
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76 while queue: |
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77 parent, depth_now, children = queue[0] |
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78 try: |
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79 child = next(children) |
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80 if child not in visited: |
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81 yield parent, child |
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82 visited.add(child) |
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83 if depth_now > 1: |
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84 queue.append((child, depth_now - 1, neighbors(child))) |
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85 except StopIteration: |
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86 queue.popleft() |
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87 |
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88 |
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89 def bfs_edges(G, source, reverse=False, depth_limit=None, sort_neighbors=None): |
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90 """Iterate over edges in a breadth-first-search starting at source. |
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91 |
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92 Parameters |
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93 ---------- |
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94 G : NetworkX graph |
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95 |
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96 source : node |
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97 Specify starting node for breadth-first search; this function |
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98 iterates over only those edges in the component reachable from |
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99 this node. |
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100 |
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101 reverse : bool, optional |
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102 If True traverse a directed graph in the reverse direction |
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103 |
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104 depth_limit : int, optional(default=len(G)) |
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105 Specify the maximum search depth |
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106 |
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107 sort_neighbors : function |
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108 A function that takes the list of neighbors of given node as input, and |
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109 returns an *iterator* over these neighbors but with custom ordering. |
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110 |
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111 Returns |
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112 ------- |
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113 edges: generator |
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114 A generator of edges in the breadth-first-search. |
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115 |
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116 Examples |
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117 -------- |
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118 To get the edges in a breadth-first search:: |
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119 |
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120 >>> G = nx.path_graph(3) |
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121 >>> list(nx.bfs_edges(G, 0)) |
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122 [(0, 1), (1, 2)] |
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123 >>> list(nx.bfs_edges(G, source=0, depth_limit=1)) |
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124 [(0, 1)] |
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125 |
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126 To get the nodes in a breadth-first search order:: |
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127 |
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128 >>> G = nx.path_graph(3) |
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129 >>> root = 2 |
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130 >>> edges = nx.bfs_edges(G, root) |
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131 >>> nodes = [root] + [v for u, v in edges] |
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132 >>> nodes |
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133 [2, 1, 0] |
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134 |
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135 Notes |
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136 ----- |
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137 The naming of this function is very similar to edge_bfs. The difference |
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138 is that 'edge_bfs' yields edges even if they extend back to an already |
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139 explored node while 'bfs_edges' yields the edges of the tree that results |
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140 from a breadth-first-search (BFS) so no edges are reported if they extend |
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141 to already explored nodes. That means 'edge_bfs' reports all edges while |
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142 'bfs_edges' only reports those traversed by a node-based BFS. Yet another |
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143 description is that 'bfs_edges' reports the edges traversed during BFS |
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144 while 'edge_bfs' reports all edges in the order they are explored. |
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145 |
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146 Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py. |
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147 by D. Eppstein, July 2004. The modifications |
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148 to allow depth limits based on the Wikipedia article |
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149 "`Depth-limited-search`_". |
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150 |
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151 .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search |
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152 |
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153 See Also |
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154 -------- |
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155 bfs_tree |
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156 dfs_edges |
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157 edge_bfs |
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158 |
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159 """ |
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160 if reverse and G.is_directed(): |
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161 successors = G.predecessors |
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162 else: |
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163 successors = G.neighbors |
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164 yield from generic_bfs_edges(G, source, successors, depth_limit, sort_neighbors) |
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165 |
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166 |
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167 def bfs_tree(G, source, reverse=False, depth_limit=None, sort_neighbors=None): |
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168 """Returns an oriented tree constructed from of a breadth-first-search |
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169 starting at source. |
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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 |
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176 Specify starting node for breadth-first search |
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177 |
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178 reverse : bool, optional |
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179 If True traverse a directed graph in the reverse direction |
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180 |
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181 depth_limit : int, optional(default=len(G)) |
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182 Specify the maximum search depth |
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183 |
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184 sort_neighbors : function |
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185 A function that takes the list of neighbors of given node as input, and |
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186 returns an *iterator* over these neighbors but with custom ordering. |
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187 |
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188 Returns |
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189 ------- |
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190 T: NetworkX DiGraph |
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191 An oriented tree |
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192 |
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193 Examples |
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194 -------- |
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195 >>> G = nx.path_graph(3) |
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196 >>> print(list(nx.bfs_tree(G, 1).edges())) |
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197 [(1, 0), (1, 2)] |
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198 >>> H = nx.Graph() |
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199 >>> nx.add_path(H, [0, 1, 2, 3, 4, 5, 6]) |
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200 >>> nx.add_path(H, [2, 7, 8, 9, 10]) |
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201 >>> print(sorted(list(nx.bfs_tree(H, source=3, depth_limit=3).edges()))) |
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202 [(1, 0), (2, 1), (2, 7), (3, 2), (3, 4), (4, 5), (5, 6), (7, 8)] |
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203 |
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204 |
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205 Notes |
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206 ----- |
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207 Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py |
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208 by D. Eppstein, July 2004. The modifications |
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209 to allow depth limits based on the Wikipedia article |
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210 "`Depth-limited-search`_". |
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211 |
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212 .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search |
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213 |
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214 See Also |
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215 -------- |
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216 dfs_tree |
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217 bfs_edges |
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218 edge_bfs |
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219 """ |
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220 T = nx.DiGraph() |
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221 T.add_node(source) |
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222 edges_gen = bfs_edges( |
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223 G, |
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224 source, |
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225 reverse=reverse, |
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226 depth_limit=depth_limit, |
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227 sort_neighbors=sort_neighbors, |
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228 ) |
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229 T.add_edges_from(edges_gen) |
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230 return T |
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231 |
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232 |
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233 def bfs_predecessors(G, source, depth_limit=None, sort_neighbors=None): |
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234 """Returns an iterator of predecessors in breadth-first-search from source. |
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235 |
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236 Parameters |
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237 ---------- |
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238 G : NetworkX graph |
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239 |
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240 source : node |
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241 Specify starting node for breadth-first search |
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242 |
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243 depth_limit : int, optional(default=len(G)) |
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244 Specify the maximum search depth |
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245 |
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246 sort_neighbors : function |
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247 A function that takes the list of neighbors of given node as input, and |
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248 returns an *iterator* over these neighbors but with custom ordering. |
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249 |
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250 Returns |
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251 ------- |
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252 pred: iterator |
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253 (node, predecessors) iterator where predecessors is the list of |
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254 predecessors of the node. |
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255 |
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256 Examples |
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257 -------- |
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258 >>> G = nx.path_graph(3) |
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259 >>> print(dict(nx.bfs_predecessors(G, 0))) |
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260 {1: 0, 2: 1} |
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261 >>> H = nx.Graph() |
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262 >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) |
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263 >>> print(dict(nx.bfs_predecessors(H, 0))) |
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264 {1: 0, 2: 0, 3: 1, 4: 1, 5: 2, 6: 2} |
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265 >>> M = nx.Graph() |
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266 >>> nx.add_path(M, [0, 1, 2, 3, 4, 5, 6]) |
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267 >>> nx.add_path(M, [2, 7, 8, 9, 10]) |
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268 >>> print(sorted(nx.bfs_predecessors(M, source=1, depth_limit=3))) |
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269 [(0, 1), (2, 1), (3, 2), (4, 3), (7, 2), (8, 7)] |
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270 |
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271 |
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272 Notes |
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273 ----- |
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274 Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py |
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275 by D. Eppstein, July 2004. The modifications |
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276 to allow depth limits based on the Wikipedia article |
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277 "`Depth-limited-search`_". |
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278 |
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279 .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search |
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280 |
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281 See Also |
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282 -------- |
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283 bfs_tree |
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284 bfs_edges |
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285 edge_bfs |
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286 """ |
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287 for s, t in bfs_edges( |
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288 G, source, depth_limit=depth_limit, sort_neighbors=sort_neighbors |
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289 ): |
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290 yield (t, s) |
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291 |
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292 |
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293 def bfs_successors(G, source, depth_limit=None, sort_neighbors=None): |
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294 """Returns an iterator of successors in breadth-first-search from source. |
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295 |
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296 Parameters |
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297 ---------- |
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298 G : NetworkX graph |
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299 |
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300 source : node |
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301 Specify starting node for breadth-first search |
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302 |
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303 depth_limit : int, optional(default=len(G)) |
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304 Specify the maximum search depth |
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305 |
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306 sort_neighbors : function |
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307 A function that takes the list of neighbors of given node as input, and |
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308 returns an *iterator* over these neighbors but with custom ordering. |
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309 |
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310 Returns |
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311 ------- |
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312 succ: iterator |
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313 (node, successors) iterator where successors is the list of |
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314 successors of the node. |
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315 |
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316 Examples |
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317 -------- |
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318 >>> G = nx.path_graph(3) |
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319 >>> print(dict(nx.bfs_successors(G, 0))) |
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320 {0: [1], 1: [2]} |
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321 >>> H = nx.Graph() |
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322 >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) |
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323 >>> print(dict(nx.bfs_successors(H, 0))) |
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324 {0: [1, 2], 1: [3, 4], 2: [5, 6]} |
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325 >>> G = nx.Graph() |
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326 >>> nx.add_path(G, [0, 1, 2, 3, 4, 5, 6]) |
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327 >>> nx.add_path(G, [2, 7, 8, 9, 10]) |
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328 >>> print(dict(nx.bfs_successors(G, source=1, depth_limit=3))) |
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329 {1: [0, 2], 2: [3, 7], 3: [4], 7: [8]} |
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330 |
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331 |
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332 Notes |
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333 ----- |
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334 Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py |
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335 by D. Eppstein, July 2004.The modifications |
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336 to allow depth limits based on the Wikipedia article |
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337 "`Depth-limited-search`_". |
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338 |
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339 .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search |
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340 |
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341 See Also |
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342 -------- |
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343 bfs_tree |
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344 bfs_edges |
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345 edge_bfs |
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346 """ |
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347 parent = source |
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348 children = [] |
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349 for p, c in bfs_edges( |
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350 G, source, depth_limit=depth_limit, sort_neighbors=sort_neighbors |
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351 ): |
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352 if p == parent: |
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353 children.append(c) |
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354 continue |
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355 yield (parent, children) |
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356 children = [c] |
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357 parent = p |
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358 yield (parent, children) |
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359 |
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360 |
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361 def descendants_at_distance(G, source, distance): |
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362 """Returns all nodes at a fixed `distance` from `source` in `G`. |
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363 |
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364 Parameters |
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365 ---------- |
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366 G : NetworkX DiGraph |
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367 A directed graph |
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368 source : node in `G` |
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369 distance : the distance of the wanted nodes from `source` |
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370 |
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371 Returns |
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372 ------- |
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373 set() |
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374 The descendants of `source` in `G` at the given `distance` from `source` |
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375 """ |
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376 if not G.has_node(source): |
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377 raise nx.NetworkXError(f"The node {source} is not in the graph.") |
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378 current_distance = 0 |
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379 queue = {source} |
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380 visited = {source} |
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381 |
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382 # this is basically BFS, except that the queue only stores the nodes at |
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383 # current_distance from source at each iteration |
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384 while queue: |
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385 if current_distance == distance: |
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386 return queue |
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387 |
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388 current_distance += 1 |
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389 |
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390 next_vertices = set() |
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391 for vertex in queue: |
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392 for child in G[vertex]: |
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393 if child not in visited: |
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394 visited.add(child) |
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395 next_vertices.add(child) |
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396 |
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397 queue = next_vertices |
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398 |
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399 return set() |