Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/triads.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 # See https://github.com/networkx/networkx/pull/1474 |
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2 # Copyright 2011 Reya Group <http://www.reyagroup.com> |
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3 # Copyright 2011 Alex Levenson <alex@isnotinvain.com> |
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4 # Copyright 2011 Diederik van Liere <diederik.vanliere@rotman.utoronto.ca> |
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5 """Functions for analyzing triads of a graph.""" |
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6 |
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7 from itertools import combinations, permutations |
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8 from collections import defaultdict |
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9 from random import sample |
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10 |
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11 import networkx as nx |
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12 from networkx.utils import not_implemented_for |
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13 |
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14 __all__ = [ |
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15 "triadic_census", |
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16 "is_triad", |
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17 "all_triplets", |
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18 "all_triads", |
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19 "triads_by_type", |
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20 "triad_type", |
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21 "random_triad", |
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22 ] |
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23 |
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24 #: The integer codes representing each type of triad. |
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25 #: |
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26 #: Triads that are the same up to symmetry have the same code. |
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27 TRICODES = ( |
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28 1, |
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90 15, |
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91 16, |
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92 ) |
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93 |
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94 #: The names of each type of triad. The order of the elements is |
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95 #: important: it corresponds to the tricodes given in :data:`TRICODES`. |
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96 TRIAD_NAMES = ( |
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97 "003", |
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98 "012", |
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99 "102", |
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100 "021D", |
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101 "021U", |
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102 "021C", |
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103 "111D", |
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104 "111U", |
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105 "030T", |
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106 "030C", |
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107 "201", |
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108 "120D", |
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109 "120U", |
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110 "120C", |
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111 "210", |
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112 "300", |
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113 ) |
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114 |
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115 |
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116 #: A dictionary mapping triad code to triad name. |
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117 TRICODE_TO_NAME = {i: TRIAD_NAMES[code - 1] for i, code in enumerate(TRICODES)} |
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118 |
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119 |
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120 def _tricode(G, v, u, w): |
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121 """Returns the integer code of the given triad. |
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122 |
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123 This is some fancy magic that comes from Batagelj and Mrvar's paper. It |
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124 treats each edge joining a pair of `v`, `u`, and `w` as a bit in |
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125 the binary representation of an integer. |
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126 |
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127 """ |
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128 combos = ((v, u, 1), (u, v, 2), (v, w, 4), (w, v, 8), (u, w, 16), (w, u, 32)) |
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129 return sum(x for u, v, x in combos if v in G[u]) |
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130 |
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131 |
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132 @not_implemented_for("undirected") |
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133 def triadic_census(G): |
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134 """Determines the triadic census of a directed graph. |
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135 |
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136 The triadic census is a count of how many of the 16 possible types of |
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137 triads are present in a directed graph. |
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138 |
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139 Parameters |
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140 ---------- |
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141 G : digraph |
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142 A NetworkX DiGraph |
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143 |
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144 Returns |
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145 ------- |
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146 census : dict |
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147 Dictionary with triad type as keys and number of occurrences as values. |
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148 |
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149 Notes |
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150 ----- |
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151 This algorithm has complexity $O(m)$ where $m$ is the number of edges in |
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152 the graph. |
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153 |
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154 See also |
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155 -------- |
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156 triad_graph |
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157 |
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158 References |
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159 ---------- |
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160 .. [1] Vladimir Batagelj and Andrej Mrvar, A subquadratic triad census |
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161 algorithm for large sparse networks with small maximum degree, |
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162 University of Ljubljana, |
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163 http://vlado.fmf.uni-lj.si/pub/networks/doc/triads/triads.pdf |
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164 |
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165 """ |
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166 # Initialize the count for each triad to be zero. |
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167 census = {name: 0 for name in TRIAD_NAMES} |
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168 n = len(G) |
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169 # m = dict(zip(G, range(n))) |
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170 m = {v: i for i, v in enumerate(G)} |
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171 for v in G: |
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172 vnbrs = set(G.pred[v]) | set(G.succ[v]) |
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173 for u in vnbrs: |
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174 if m[u] <= m[v]: |
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175 continue |
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176 neighbors = (vnbrs | set(G.succ[u]) | set(G.pred[u])) - {u, v} |
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177 # Calculate dyadic triads instead of counting them. |
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178 if v in G[u] and u in G[v]: |
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179 census["102"] += n - len(neighbors) - 2 |
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180 else: |
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181 census["012"] += n - len(neighbors) - 2 |
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182 # Count connected triads. |
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183 for w in neighbors: |
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184 if m[u] < m[w] or ( |
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185 m[v] < m[w] < m[u] and v not in G.pred[w] and v not in G.succ[w] |
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186 ): |
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187 code = _tricode(G, v, u, w) |
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188 census[TRICODE_TO_NAME[code]] += 1 |
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189 # null triads = total number of possible triads - all found triads |
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190 # |
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191 # Use integer division here, since we know this formula guarantees an |
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192 # integral value. |
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193 census["003"] = ((n * (n - 1) * (n - 2)) // 6) - sum(census.values()) |
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194 return census |
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195 |
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196 |
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197 def is_triad(G): |
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198 """Returns True if the graph G is a triad, else False. |
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199 |
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200 Parameters |
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201 ---------- |
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202 G : graph |
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203 A NetworkX Graph |
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204 |
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205 Returns |
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206 ------- |
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207 istriad : boolean |
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208 Whether G is a valid triad |
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209 """ |
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210 if isinstance(G, nx.Graph): |
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211 if G.order() == 3 and nx.is_directed(G): |
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212 if not any((n, n) in G.edges() for n in G.nodes()): |
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213 return True |
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214 return False |
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215 |
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216 |
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217 @not_implemented_for("undirected") |
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218 def all_triplets(G): |
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219 """Returns a generator of all possible sets of 3 nodes in a DiGraph. |
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220 |
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221 Parameters |
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222 ---------- |
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223 G : digraph |
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224 A NetworkX DiGraph |
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225 |
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226 Returns |
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227 ------- |
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228 triplets : generator of 3-tuples |
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229 Generator of tuples of 3 nodes |
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230 """ |
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231 triplets = combinations(G.nodes(), 3) |
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232 return triplets |
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233 |
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234 |
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235 @not_implemented_for("undirected") |
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236 def all_triads(G): |
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237 """A generator of all possible triads in G. |
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238 |
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239 Parameters |
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240 ---------- |
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241 G : digraph |
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242 A NetworkX DiGraph |
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243 |
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244 Returns |
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245 ------- |
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246 all_triads : generator of DiGraphs |
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247 Generator of triads (order-3 DiGraphs) |
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248 """ |
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249 triplets = combinations(G.nodes(), 3) |
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250 for triplet in triplets: |
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251 yield G.subgraph(triplet).copy() |
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252 |
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253 |
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254 @not_implemented_for("undirected") |
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255 def triads_by_type(G): |
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256 """Returns a list of all triads for each triad type in a directed graph. |
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257 |
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258 Parameters |
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259 ---------- |
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260 G : digraph |
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261 A NetworkX DiGraph |
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262 |
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263 Returns |
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264 ------- |
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265 tri_by_type : dict |
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266 Dictionary with triad types as keys and lists of triads as values. |
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267 """ |
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268 # num_triads = o * (o - 1) * (o - 2) // 6 |
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269 # if num_triads > TRIAD_LIMIT: print(WARNING) |
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270 all_tri = all_triads(G) |
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271 tri_by_type = defaultdict(list) |
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272 for triad in all_tri: |
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273 name = triad_type(triad) |
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274 tri_by_type[name].append(triad) |
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275 return tri_by_type |
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276 |
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277 |
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278 @not_implemented_for("undirected") |
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279 def triad_type(G): |
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280 """Returns the sociological triad type for a triad. |
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281 |
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282 Parameters |
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283 ---------- |
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284 G : digraph |
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285 A NetworkX DiGraph with 3 nodes |
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286 |
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287 Returns |
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288 ------- |
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289 triad_type : str |
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290 A string identifying the triad type |
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291 |
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292 Notes |
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293 ----- |
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294 There can be 6 unique edges in a triad (order-3 DiGraph) (so 2^^6=64 unique |
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295 triads given 3 nodes). These 64 triads each display exactly 1 of 16 |
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296 topologies of triads (topologies can be permuted). These topologies are |
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297 identified by the following notation: |
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298 |
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299 {m}{a}{n}{type} (for example: 111D, 210, 102) |
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300 |
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301 Here: |
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302 |
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303 {m} = number of mutual ties (takes 0, 1, 2, 3); a mutual tie is (0,1) |
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304 AND (1,0) |
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305 {a} = number of assymmetric ties (takes 0, 1, 2, 3); an assymmetric tie |
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306 is (0,1) BUT NOT (1,0) or vice versa |
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307 {n} = number of null ties (takes 0, 1, 2, 3); a null tie is NEITHER |
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308 (0,1) NOR (1,0) |
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309 {type} = a letter (takes U, D, C, T) corresponding to up, down, cyclical |
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310 and transitive. This is only used for topologies that can have |
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311 more than one form (eg: 021D and 021U). |
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312 |
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313 References |
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314 ---------- |
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315 .. [1] Snijders, T. (2012). "Transitivity and triads." University of |
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316 Oxford. |
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317 http://www.stats.ox.ac.uk/snijders/Trans_Triads_ha.pdf |
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318 """ |
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319 if not is_triad(G): |
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320 raise nx.NetworkXAlgorithmError("G is not a triad (order-3 DiGraph)") |
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321 num_edges = len(G.edges()) |
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322 if num_edges == 0: |
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323 return "003" |
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324 elif num_edges == 1: |
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325 return "012" |
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326 elif num_edges == 2: |
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327 e1, e2 = G.edges() |
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328 if set(e1) == set(e2): |
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329 return "102" |
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330 elif e1[0] == e2[0]: |
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331 return "021D" |
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332 elif e1[1] == e2[1]: |
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333 return "021U" |
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334 elif e1[1] == e2[0] or e2[1] == e1[0]: |
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335 return "021C" |
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336 elif num_edges == 3: |
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337 for (e1, e2, e3) in permutations(G.edges(), 3): |
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338 if set(e1) == set(e2): |
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339 if e3[0] in e1: |
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340 return "111U" |
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341 # e3[1] in e1: |
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342 return "111D" |
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343 elif set(e1).symmetric_difference(set(e2)) == set(e3): |
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344 if {e1[0], e2[0], e3[0]} == {e1[0], e2[0], e3[0]} == set(G.nodes()): |
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345 return "030C" |
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346 # e3 == (e1[0], e2[1]) and e2 == (e1[1], e3[1]): |
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347 return "030T" |
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348 elif num_edges == 4: |
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349 for (e1, e2, e3, e4) in permutations(G.edges(), 4): |
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350 if set(e1) == set(e2): |
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351 # identify pair of symmetric edges (which necessarily exists) |
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352 if set(e3) == set(e4): |
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353 return "201" |
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354 if {e3[0]} == {e4[0]} == set(e3).intersection(set(e4)): |
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355 return "120D" |
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356 if {e3[1]} == {e4[1]} == set(e3).intersection(set(e4)): |
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357 return "120U" |
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358 if e3[1] == e4[0]: |
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359 return "120C" |
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360 elif num_edges == 5: |
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361 return "210" |
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362 elif num_edges == 6: |
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363 return "300" |
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364 |
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365 |
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366 @not_implemented_for("undirected") |
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367 def random_triad(G): |
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368 """Returns a random triad from a directed graph. |
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369 |
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370 Parameters |
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371 ---------- |
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372 G : digraph |
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373 A NetworkX DiGraph |
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374 |
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375 Returns |
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376 ------- |
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377 G2 : subgraph |
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378 A randomly selected triad (order-3 NetworkX DiGraph) |
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379 """ |
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380 nodes = sample(G.nodes(), 3) |
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381 G2 = G.subgraph(nodes) |
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382 return G2 |
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383 |
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384 |
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385 """ |
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386 @not_implemented_for('undirected') |
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387 def triadic_closures(G): |
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388 '''Returns a list of order-3 subgraphs of G that are triadic closures. |
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389 |
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390 Parameters |
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391 ---------- |
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392 G : digraph |
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393 A NetworkX DiGraph |
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394 |
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395 Returns |
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396 ------- |
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397 closures : list |
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398 List of triads of G that are triadic closures |
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399 ''' |
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400 pass |
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401 |
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402 |
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403 @not_implemented_for('undirected') |
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404 def focal_closures(G, attr_name): |
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405 '''Returns a list of order-3 subgraphs of G that are focally closed. |
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406 |
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407 Parameters |
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408 ---------- |
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409 G : digraph |
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410 A NetworkX DiGraph |
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411 attr_name : str |
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412 An attribute name |
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413 |
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414 |
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415 Returns |
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416 ------- |
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417 closures : list |
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418 List of triads of G that are focally closed on attr_name |
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419 ''' |
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420 pass |
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421 |
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422 |
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423 @not_implemented_for('undirected') |
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424 def balanced_triads(G, crit_func): |
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425 '''Returns a list of order-3 subgraphs of G that are stable. |
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426 |
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427 Parameters |
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428 ---------- |
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429 G : digraph |
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430 A NetworkX DiGraph |
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431 crit_func : function |
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432 A function that determines if a triad (order-3 digraph) is stable |
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433 |
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434 Returns |
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435 ------- |
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436 triads : list |
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437 List of triads in G that are stable |
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438 ''' |
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439 pass |
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440 """ |