Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/bipartite/projection.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 """One-mode (unipartite) projections of bipartite graphs.""" |
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2 import networkx as nx |
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3 from networkx.utils import not_implemented_for |
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4 |
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5 __all__ = [ |
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6 "project", |
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7 "projected_graph", |
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8 "weighted_projected_graph", |
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9 "collaboration_weighted_projected_graph", |
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10 "overlap_weighted_projected_graph", |
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11 "generic_weighted_projected_graph", |
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12 ] |
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13 |
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14 |
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15 def projected_graph(B, nodes, multigraph=False): |
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16 r"""Returns the projection of B onto one of its node sets. |
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17 |
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18 Returns the graph G that is the projection of the bipartite graph B |
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19 onto the specified nodes. They retain their attributes and are connected |
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20 in G if they have a common neighbor in B. |
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21 |
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22 Parameters |
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23 ---------- |
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24 B : NetworkX graph |
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25 The input graph should be bipartite. |
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26 |
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27 nodes : list or iterable |
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28 Nodes to project onto (the "bottom" nodes). |
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29 |
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30 multigraph: bool (default=False) |
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31 If True return a multigraph where the multiple edges represent multiple |
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32 shared neighbors. They edge key in the multigraph is assigned to the |
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33 label of the neighbor. |
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34 |
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35 Returns |
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36 ------- |
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37 Graph : NetworkX graph or multigraph |
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38 A graph that is the projection onto the given nodes. |
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39 |
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40 Examples |
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41 -------- |
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42 >>> from networkx.algorithms import bipartite |
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43 >>> B = nx.path_graph(4) |
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44 >>> G = bipartite.projected_graph(B, [1, 3]) |
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45 >>> list(G) |
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46 [1, 3] |
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47 >>> list(G.edges()) |
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48 [(1, 3)] |
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49 |
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50 If nodes `a`, and `b` are connected through both nodes 1 and 2 then |
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51 building a multigraph results in two edges in the projection onto |
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52 [`a`, `b`]: |
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53 |
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54 >>> B = nx.Graph() |
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55 >>> B.add_edges_from([("a", 1), ("b", 1), ("a", 2), ("b", 2)]) |
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56 >>> G = bipartite.projected_graph(B, ["a", "b"], multigraph=True) |
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57 >>> print([sorted((u, v)) for u, v in G.edges()]) |
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58 [['a', 'b'], ['a', 'b']] |
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59 |
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60 Notes |
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61 ----- |
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62 No attempt is made to verify that the input graph B is bipartite. |
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63 Returns a simple graph that is the projection of the bipartite graph B |
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64 onto the set of nodes given in list nodes. If multigraph=True then |
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65 a multigraph is returned with an edge for every shared neighbor. |
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66 |
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67 Directed graphs are allowed as input. The output will also then |
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68 be a directed graph with edges if there is a directed path between |
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69 the nodes. |
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70 |
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71 The graph and node properties are (shallow) copied to the projected graph. |
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72 |
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73 See :mod:`bipartite documentation <networkx.algorithms.bipartite>` |
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74 for further details on how bipartite graphs are handled in NetworkX. |
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75 |
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76 See Also |
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77 -------- |
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78 is_bipartite, |
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79 is_bipartite_node_set, |
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80 sets, |
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81 weighted_projected_graph, |
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82 collaboration_weighted_projected_graph, |
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83 overlap_weighted_projected_graph, |
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84 generic_weighted_projected_graph |
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85 """ |
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86 if B.is_multigraph(): |
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87 raise nx.NetworkXError("not defined for multigraphs") |
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88 if B.is_directed(): |
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89 directed = True |
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90 if multigraph: |
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91 G = nx.MultiDiGraph() |
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92 else: |
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93 G = nx.DiGraph() |
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94 else: |
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95 directed = False |
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96 if multigraph: |
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97 G = nx.MultiGraph() |
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98 else: |
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99 G = nx.Graph() |
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100 G.graph.update(B.graph) |
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101 G.add_nodes_from((n, B.nodes[n]) for n in nodes) |
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102 for u in nodes: |
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103 nbrs2 = {v for nbr in B[u] for v in B[nbr] if v != u} |
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104 if multigraph: |
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105 for n in nbrs2: |
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106 if directed: |
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107 links = set(B[u]) & set(B.pred[n]) |
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108 else: |
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109 links = set(B[u]) & set(B[n]) |
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110 for l in links: |
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111 if not G.has_edge(u, n, l): |
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112 G.add_edge(u, n, key=l) |
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113 else: |
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114 G.add_edges_from((u, n) for n in nbrs2) |
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115 return G |
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116 |
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117 |
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118 @not_implemented_for("multigraph") |
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119 def weighted_projected_graph(B, nodes, ratio=False): |
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120 r"""Returns a weighted projection of B onto one of its node sets. |
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121 |
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122 The weighted projected graph is the projection of the bipartite |
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123 network B onto the specified nodes with weights representing the |
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124 number of shared neighbors or the ratio between actual shared |
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125 neighbors and possible shared neighbors if ``ratio is True`` [1]_. |
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126 The nodes retain their attributes and are connected in the resulting |
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127 graph if they have an edge to a common node in the original graph. |
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128 |
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129 Parameters |
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130 ---------- |
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131 B : NetworkX graph |
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132 The input graph should be bipartite. |
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133 |
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134 nodes : list or iterable |
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135 Nodes to project onto (the "bottom" nodes). |
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136 |
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137 ratio: Bool (default=False) |
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138 If True, edge weight is the ratio between actual shared neighbors |
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139 and maximum possible shared neighbors (i.e., the size of the other |
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140 node set). If False, edges weight is the number of shared neighbors. |
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141 |
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142 Returns |
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143 ------- |
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144 Graph : NetworkX graph |
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145 A graph that is the projection onto the given nodes. |
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146 |
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147 Examples |
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148 -------- |
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149 >>> from networkx.algorithms import bipartite |
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150 >>> B = nx.path_graph(4) |
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151 >>> G = bipartite.weighted_projected_graph(B, [1, 3]) |
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152 >>> list(G) |
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153 [1, 3] |
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154 >>> list(G.edges(data=True)) |
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155 [(1, 3, {'weight': 1})] |
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156 >>> G = bipartite.weighted_projected_graph(B, [1, 3], ratio=True) |
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157 >>> list(G.edges(data=True)) |
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158 [(1, 3, {'weight': 0.5})] |
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159 |
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160 Notes |
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161 ----- |
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162 No attempt is made to verify that the input graph B is bipartite. |
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163 The graph and node properties are (shallow) copied to the projected graph. |
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164 |
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165 See :mod:`bipartite documentation <networkx.algorithms.bipartite>` |
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166 for further details on how bipartite graphs are handled in NetworkX. |
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167 |
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168 See Also |
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169 -------- |
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170 is_bipartite, |
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171 is_bipartite_node_set, |
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172 sets, |
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173 collaboration_weighted_projected_graph, |
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174 overlap_weighted_projected_graph, |
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175 generic_weighted_projected_graph |
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176 projected_graph |
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177 |
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178 References |
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179 ---------- |
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180 .. [1] Borgatti, S.P. and Halgin, D. In press. "Analyzing Affiliation |
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181 Networks". In Carrington, P. and Scott, J. (eds) The Sage Handbook |
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182 of Social Network Analysis. Sage Publications. |
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183 """ |
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184 if B.is_directed(): |
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185 pred = B.pred |
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186 G = nx.DiGraph() |
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187 else: |
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188 pred = B.adj |
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189 G = nx.Graph() |
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190 G.graph.update(B.graph) |
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191 G.add_nodes_from((n, B.nodes[n]) for n in nodes) |
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192 n_top = float(len(B) - len(nodes)) |
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193 for u in nodes: |
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194 unbrs = set(B[u]) |
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195 nbrs2 = {n for nbr in unbrs for n in B[nbr]} - {u} |
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196 for v in nbrs2: |
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197 vnbrs = set(pred[v]) |
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198 common = unbrs & vnbrs |
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199 if not ratio: |
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200 weight = len(common) |
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201 else: |
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202 weight = len(common) / n_top |
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203 G.add_edge(u, v, weight=weight) |
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204 return G |
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205 |
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206 |
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207 @not_implemented_for("multigraph") |
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208 def collaboration_weighted_projected_graph(B, nodes): |
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209 r"""Newman's weighted projection of B onto one of its node sets. |
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210 |
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211 The collaboration weighted projection is the projection of the |
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212 bipartite network B onto the specified nodes with weights assigned |
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213 using Newman's collaboration model [1]_: |
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214 |
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215 .. math:: |
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216 |
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217 w_{u, v} = \sum_k \frac{\delta_{u}^{k} \delta_{v}^{k}}{d_k - 1} |
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218 |
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219 where `u` and `v` are nodes from the bottom bipartite node set, |
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220 and `k` is a node of the top node set. |
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221 The value `d_k` is the degree of node `k` in the bipartite |
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222 network and `\delta_{u}^{k}` is 1 if node `u` is |
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223 linked to node `k` in the original bipartite graph or 0 otherwise. |
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224 |
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225 The nodes retain their attributes and are connected in the resulting |
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226 graph if have an edge to a common node in the original bipartite |
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227 graph. |
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228 |
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229 Parameters |
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230 ---------- |
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231 B : NetworkX graph |
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232 The input graph should be bipartite. |
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233 |
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234 nodes : list or iterable |
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235 Nodes to project onto (the "bottom" nodes). |
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236 |
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237 Returns |
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238 ------- |
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239 Graph : NetworkX graph |
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240 A graph that is the projection onto the given nodes. |
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241 |
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242 Examples |
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243 -------- |
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244 >>> from networkx.algorithms import bipartite |
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245 >>> B = nx.path_graph(5) |
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246 >>> B.add_edge(1, 5) |
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247 >>> G = bipartite.collaboration_weighted_projected_graph(B, [0, 2, 4, 5]) |
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248 >>> list(G) |
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249 [0, 2, 4, 5] |
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250 >>> for edge in sorted(G.edges(data=True)): |
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251 ... print(edge) |
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252 ... |
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253 (0, 2, {'weight': 0.5}) |
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254 (0, 5, {'weight': 0.5}) |
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255 (2, 4, {'weight': 1.0}) |
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256 (2, 5, {'weight': 0.5}) |
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257 |
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258 Notes |
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259 ----- |
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260 No attempt is made to verify that the input graph B is bipartite. |
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261 The graph and node properties are (shallow) copied to the projected graph. |
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262 |
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263 See :mod:`bipartite documentation <networkx.algorithms.bipartite>` |
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264 for further details on how bipartite graphs are handled in NetworkX. |
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265 |
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266 See Also |
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267 -------- |
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268 is_bipartite, |
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269 is_bipartite_node_set, |
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270 sets, |
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271 weighted_projected_graph, |
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272 overlap_weighted_projected_graph, |
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273 generic_weighted_projected_graph, |
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274 projected_graph |
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275 |
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276 References |
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277 ---------- |
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278 .. [1] Scientific collaboration networks: II. |
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279 Shortest paths, weighted networks, and centrality, |
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280 M. E. J. Newman, Phys. Rev. E 64, 016132 (2001). |
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281 """ |
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282 if B.is_directed(): |
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283 pred = B.pred |
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284 G = nx.DiGraph() |
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285 else: |
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286 pred = B.adj |
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287 G = nx.Graph() |
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288 G.graph.update(B.graph) |
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289 G.add_nodes_from((n, B.nodes[n]) for n in nodes) |
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290 for u in nodes: |
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291 unbrs = set(B[u]) |
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292 nbrs2 = {n for nbr in unbrs for n in B[nbr] if n != u} |
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293 for v in nbrs2: |
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294 vnbrs = set(pred[v]) |
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295 common_degree = (len(B[n]) for n in unbrs & vnbrs) |
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296 weight = sum(1.0 / (deg - 1) for deg in common_degree if deg > 1) |
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297 G.add_edge(u, v, weight=weight) |
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298 return G |
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299 |
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300 |
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301 @not_implemented_for("multigraph") |
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302 def overlap_weighted_projected_graph(B, nodes, jaccard=True): |
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303 r"""Overlap weighted projection of B onto one of its node sets. |
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304 |
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305 The overlap weighted projection is the projection of the bipartite |
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306 network B onto the specified nodes with weights representing |
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307 the Jaccard index between the neighborhoods of the two nodes in the |
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308 original bipartite network [1]_: |
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309 |
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310 .. math:: |
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311 |
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312 w_{v, u} = \frac{|N(u) \cap N(v)|}{|N(u) \cup N(v)|} |
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313 |
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314 or if the parameter 'jaccard' is False, the fraction of common |
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315 neighbors by minimum of both nodes degree in the original |
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316 bipartite graph [1]_: |
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317 |
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318 .. math:: |
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319 |
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320 w_{v, u} = \frac{|N(u) \cap N(v)|}{min(|N(u)|, |N(v)|)} |
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321 |
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322 The nodes retain their attributes and are connected in the resulting |
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323 graph if have an edge to a common node in the original bipartite graph. |
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324 |
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325 Parameters |
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326 ---------- |
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327 B : NetworkX graph |
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328 The input graph should be bipartite. |
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329 |
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330 nodes : list or iterable |
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331 Nodes to project onto (the "bottom" nodes). |
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332 |
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333 jaccard: Bool (default=True) |
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334 |
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335 Returns |
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336 ------- |
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337 Graph : NetworkX graph |
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338 A graph that is the projection onto the given nodes. |
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339 |
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340 Examples |
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341 -------- |
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342 >>> from networkx.algorithms import bipartite |
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343 >>> B = nx.path_graph(5) |
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344 >>> nodes = [0, 2, 4] |
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345 >>> G = bipartite.overlap_weighted_projected_graph(B, nodes) |
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346 >>> list(G) |
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347 [0, 2, 4] |
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348 >>> list(G.edges(data=True)) |
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349 [(0, 2, {'weight': 0.5}), (2, 4, {'weight': 0.5})] |
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350 >>> G = bipartite.overlap_weighted_projected_graph(B, nodes, jaccard=False) |
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351 >>> list(G.edges(data=True)) |
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352 [(0, 2, {'weight': 1.0}), (2, 4, {'weight': 1.0})] |
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353 |
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354 Notes |
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355 ----- |
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356 No attempt is made to verify that the input graph B is bipartite. |
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357 The graph and node properties are (shallow) copied to the projected graph. |
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358 |
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359 See :mod:`bipartite documentation <networkx.algorithms.bipartite>` |
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360 for further details on how bipartite graphs are handled in NetworkX. |
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361 |
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362 See Also |
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363 -------- |
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364 is_bipartite, |
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365 is_bipartite_node_set, |
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366 sets, |
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367 weighted_projected_graph, |
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368 collaboration_weighted_projected_graph, |
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369 generic_weighted_projected_graph, |
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370 projected_graph |
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371 |
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372 References |
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373 ---------- |
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374 .. [1] Borgatti, S.P. and Halgin, D. In press. Analyzing Affiliation |
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375 Networks. In Carrington, P. and Scott, J. (eds) The Sage Handbook |
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376 of Social Network Analysis. Sage Publications. |
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377 |
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378 """ |
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379 if B.is_directed(): |
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380 pred = B.pred |
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381 G = nx.DiGraph() |
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382 else: |
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383 pred = B.adj |
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384 G = nx.Graph() |
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385 G.graph.update(B.graph) |
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386 G.add_nodes_from((n, B.nodes[n]) for n in nodes) |
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387 for u in nodes: |
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388 unbrs = set(B[u]) |
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389 nbrs2 = {n for nbr in unbrs for n in B[nbr]} - {u} |
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390 for v in nbrs2: |
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391 vnbrs = set(pred[v]) |
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392 if jaccard: |
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393 wt = float(len(unbrs & vnbrs)) / len(unbrs | vnbrs) |
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394 else: |
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395 wt = float(len(unbrs & vnbrs)) / min(len(unbrs), len(vnbrs)) |
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396 G.add_edge(u, v, weight=wt) |
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397 return G |
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398 |
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399 |
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400 @not_implemented_for("multigraph") |
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401 def generic_weighted_projected_graph(B, nodes, weight_function=None): |
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402 r"""Weighted projection of B with a user-specified weight function. |
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403 |
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404 The bipartite network B is projected on to the specified nodes |
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405 with weights computed by a user-specified function. This function |
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406 must accept as a parameter the neighborhood sets of two nodes and |
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407 return an integer or a float. |
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408 |
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409 The nodes retain their attributes and are connected in the resulting graph |
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410 if they have an edge to a common node in the original graph. |
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411 |
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412 Parameters |
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413 ---------- |
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414 B : NetworkX graph |
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415 The input graph should be bipartite. |
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416 |
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417 nodes : list or iterable |
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418 Nodes to project onto (the "bottom" nodes). |
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419 |
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420 weight_function : function |
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421 This function must accept as parameters the same input graph |
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422 that this function, and two nodes; and return an integer or a float. |
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423 The default function computes the number of shared neighbors. |
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424 |
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425 Returns |
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426 ------- |
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427 Graph : NetworkX graph |
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428 A graph that is the projection onto the given nodes. |
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429 |
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430 Examples |
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431 -------- |
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432 >>> from networkx.algorithms import bipartite |
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433 >>> # Define some custom weight functions |
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434 >>> def jaccard(G, u, v): |
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435 ... unbrs = set(G[u]) |
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436 ... vnbrs = set(G[v]) |
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437 ... return float(len(unbrs & vnbrs)) / len(unbrs | vnbrs) |
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438 ... |
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439 >>> def my_weight(G, u, v, weight="weight"): |
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440 ... w = 0 |
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441 ... for nbr in set(G[u]) & set(G[v]): |
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442 ... w += G[u][nbr].get(weight, 1) + G[v][nbr].get(weight, 1) |
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443 ... return w |
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444 ... |
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445 >>> # A complete bipartite graph with 4 nodes and 4 edges |
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446 >>> B = nx.complete_bipartite_graph(2, 2) |
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447 >>> # Add some arbitrary weight to the edges |
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448 >>> for i, (u, v) in enumerate(B.edges()): |
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449 ... B.edges[u, v]["weight"] = i + 1 |
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450 ... |
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451 >>> for edge in B.edges(data=True): |
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452 ... print(edge) |
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453 ... |
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454 (0, 2, {'weight': 1}) |
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455 (0, 3, {'weight': 2}) |
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456 (1, 2, {'weight': 3}) |
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457 (1, 3, {'weight': 4}) |
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458 >>> # By default, the weight is the number of shared neighbors |
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459 >>> G = bipartite.generic_weighted_projected_graph(B, [0, 1]) |
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460 >>> print(list(G.edges(data=True))) |
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461 [(0, 1, {'weight': 2})] |
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462 >>> # To specify a custom weight function use the weight_function parameter |
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463 >>> G = bipartite.generic_weighted_projected_graph( |
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464 ... B, [0, 1], weight_function=jaccard |
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465 ... ) |
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466 >>> print(list(G.edges(data=True))) |
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467 [(0, 1, {'weight': 1.0})] |
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468 >>> G = bipartite.generic_weighted_projected_graph( |
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469 ... B, [0, 1], weight_function=my_weight |
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470 ... ) |
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471 >>> print(list(G.edges(data=True))) |
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472 [(0, 1, {'weight': 10})] |
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473 |
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474 Notes |
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475 ----- |
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476 No attempt is made to verify that the input graph B is bipartite. |
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477 The graph and node properties are (shallow) copied to the projected graph. |
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478 |
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479 See :mod:`bipartite documentation <networkx.algorithms.bipartite>` |
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480 for further details on how bipartite graphs are handled in NetworkX. |
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481 |
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482 See Also |
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483 -------- |
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484 is_bipartite, |
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485 is_bipartite_node_set, |
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486 sets, |
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487 weighted_projected_graph, |
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488 collaboration_weighted_projected_graph, |
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489 overlap_weighted_projected_graph, |
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490 projected_graph |
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491 |
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492 """ |
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493 if B.is_directed(): |
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494 pred = B.pred |
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495 G = nx.DiGraph() |
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496 else: |
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497 pred = B.adj |
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498 G = nx.Graph() |
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499 if weight_function is None: |
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500 |
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501 def weight_function(G, u, v): |
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502 # Notice that we use set(pred[v]) for handling the directed case. |
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503 return len(set(G[u]) & set(pred[v])) |
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504 |
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505 G.graph.update(B.graph) |
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506 G.add_nodes_from((n, B.nodes[n]) for n in nodes) |
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507 for u in nodes: |
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508 nbrs2 = {n for nbr in set(B[u]) for n in B[nbr]} - {u} |
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509 for v in nbrs2: |
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510 weight = weight_function(B, u, v) |
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511 G.add_edge(u, v, weight=weight) |
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512 return G |
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513 |
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514 |
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515 def project(B, nodes, create_using=None): |
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516 return projected_graph(B, nodes) |