Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/generators/nonisomorphic_trees.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 Implementation of the Wright, Richmond, Odlyzko and McKay (WROM) |
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3 algorithm for the enumeration of all non-isomorphic free trees of a |
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4 given order. Rooted trees are represented by level sequences, i.e., |
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5 lists in which the i-th element specifies the distance of vertex i to |
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6 the root. |
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7 |
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8 """ |
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9 |
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10 __all__ = ["nonisomorphic_trees", "number_of_nonisomorphic_trees"] |
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11 |
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12 import networkx as nx |
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13 |
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14 |
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15 def nonisomorphic_trees(order, create="graph"): |
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16 """Returns a list of nonisomporphic trees |
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17 |
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18 Parameters |
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19 ---------- |
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20 order : int |
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21 order of the desired tree(s) |
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22 |
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23 create : graph or matrix (default="Graph) |
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24 If graph is selected a list of trees will be returned, |
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25 if matrix is selected a list of adjancency matrix will |
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26 be returned |
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27 |
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28 Returns |
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29 ------- |
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30 G : List of NetworkX Graphs |
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31 |
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32 M : List of Adjacency matrices |
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33 |
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34 References |
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35 ---------- |
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36 |
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37 """ |
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38 |
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39 if order < 2: |
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40 raise ValueError |
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41 # start at the path graph rooted at its center |
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42 layout = list(range(order // 2 + 1)) + list(range(1, (order + 1) // 2)) |
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43 |
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44 while layout is not None: |
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45 layout = _next_tree(layout) |
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46 if layout is not None: |
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47 if create == "graph": |
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48 yield _layout_to_graph(layout) |
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49 elif create == "matrix": |
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50 yield _layout_to_matrix(layout) |
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51 layout = _next_rooted_tree(layout) |
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52 |
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53 |
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54 def number_of_nonisomorphic_trees(order): |
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55 """Returns the number of nonisomorphic trees |
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56 |
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57 Parameters |
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58 ---------- |
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59 order : int |
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60 order of the desired tree(s) |
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61 |
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62 Returns |
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63 ------- |
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64 length : Number of nonisomorphic graphs for the given order |
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65 |
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66 References |
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67 ---------- |
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68 |
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69 """ |
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70 return sum(1 for _ in nonisomorphic_trees(order)) |
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71 |
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72 |
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73 def _next_rooted_tree(predecessor, p=None): |
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74 """One iteration of the Beyer-Hedetniemi algorithm.""" |
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75 |
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76 if p is None: |
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77 p = len(predecessor) - 1 |
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78 while predecessor[p] == 1: |
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79 p -= 1 |
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80 if p == 0: |
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81 return None |
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82 |
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83 q = p - 1 |
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84 while predecessor[q] != predecessor[p] - 1: |
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85 q -= 1 |
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86 result = list(predecessor) |
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87 for i in range(p, len(result)): |
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88 result[i] = result[i - p + q] |
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89 return result |
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90 |
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91 |
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92 def _next_tree(candidate): |
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93 """One iteration of the Wright, Richmond, Odlyzko and McKay |
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94 algorithm.""" |
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95 |
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96 # valid representation of a free tree if: |
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97 # there are at least two vertices at layer 1 |
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98 # (this is always the case because we start at the path graph) |
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99 left, rest = _split_tree(candidate) |
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100 |
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101 # and the left subtree of the root |
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102 # is less high than the tree with the left subtree removed |
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103 left_height = max(left) |
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104 rest_height = max(rest) |
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105 valid = rest_height >= left_height |
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106 |
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107 if valid and rest_height == left_height: |
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108 # and, if left and rest are of the same height, |
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109 # if left does not encompass more vertices |
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110 if len(left) > len(rest): |
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111 valid = False |
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112 # and, if they have the same number or vertices, |
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113 # if left does not come after rest lexicographically |
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114 elif len(left) == len(rest) and left > rest: |
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115 valid = False |
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116 |
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117 if valid: |
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118 return candidate |
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119 else: |
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120 # jump to the next valid free tree |
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121 p = len(left) |
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122 new_candidate = _next_rooted_tree(candidate, p) |
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123 if candidate[p] > 2: |
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124 new_left, new_rest = _split_tree(new_candidate) |
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125 new_left_height = max(new_left) |
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126 suffix = range(1, new_left_height + 2) |
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127 new_candidate[-len(suffix) :] = suffix |
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128 return new_candidate |
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129 |
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130 |
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131 def _split_tree(layout): |
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132 """Returns a tuple of two layouts, one containing the left |
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133 subtree of the root vertex, and one containing the original tree |
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134 with the left subtree removed.""" |
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135 |
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136 one_found = False |
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137 m = None |
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138 for i in range(len(layout)): |
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139 if layout[i] == 1: |
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140 if one_found: |
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141 m = i |
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142 break |
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143 else: |
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144 one_found = True |
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145 |
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146 if m is None: |
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147 m = len(layout) |
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148 |
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149 left = [layout[i] - 1 for i in range(1, m)] |
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150 rest = [0] + [layout[i] for i in range(m, len(layout))] |
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151 return (left, rest) |
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152 |
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153 |
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154 def _layout_to_matrix(layout): |
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155 """Create the adjacency matrix for the tree specified by the |
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156 given layout (level sequence).""" |
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157 |
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158 result = [[0] * len(layout) for i in range(len(layout))] |
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159 stack = [] |
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160 for i in range(len(layout)): |
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161 i_level = layout[i] |
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162 if stack: |
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163 j = stack[-1] |
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164 j_level = layout[j] |
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165 while j_level >= i_level: |
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166 stack.pop() |
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167 j = stack[-1] |
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168 j_level = layout[j] |
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169 result[i][j] = result[j][i] = 1 |
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170 stack.append(i) |
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171 return result |
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172 |
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173 |
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174 def _layout_to_graph(layout): |
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175 """Create a NetworkX Graph for the tree specified by the |
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176 given layout(level sequence)""" |
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177 result = [[0] * len(layout) for i in range(len(layout))] |
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178 G = nx.Graph() |
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179 stack = [] |
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180 for i in range(len(layout)): |
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181 i_level = layout[i] |
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182 if stack: |
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183 j = stack[-1] |
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184 j_level = layout[j] |
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185 while j_level >= i_level: |
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186 stack.pop() |
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187 j = stack[-1] |
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188 j_level = layout[j] |
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189 G.add_edge(i, j) |
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190 stack.append(i) |
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191 return G |