Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/sitepackages/networkx/algorithms/bipartite/redundancy.py @ 0:4f3585e2f14b draft default tip
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author  shellac 

date  Mon, 22 Mar 2021 18:12:50 +0000 
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1 """Node redundancy for bipartite graphs.""" 
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2 from itertools import combinations 
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3 
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4 from networkx import NetworkXError 
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5 
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6 __all__ = ["node_redundancy"] 
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7 
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8 
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9 def node_redundancy(G, nodes=None): 
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10 r"""Computes the node redundancy coefficients for the nodes in the bipartite 
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11 graph `G`. 
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12 
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13 The redundancy coefficient of a node `v` is the fraction of pairs of 
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14 neighbors of `v` that are both linked to other nodes. In a onemode 
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15 projection these nodes would be linked together even if `v` were 
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16 not there. 
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17 
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18 More formally, for any vertex `v`, the *redundancy coefficient of `v`* is 
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19 defined by 
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20 
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21 .. math:: 
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22 
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23 rc(v) = \frac{\{\{u, w\} \subseteq N(v), 
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24 \: \exists v' \neq v,\: (v',u) \in E\: 
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25 \mathrm{and}\: (v',w) \in E\}}{ \frac{N(v)(N(v)1)}{2}}, 
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26 
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27 where `N(v)` is the set of neighbors of `v` in `G`. 
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28 
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29 Parameters 
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30  
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31 G : graph 
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32 A bipartite graph 
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33 
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34 nodes : list or iterable (optional) 
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35 Compute redundancy for these nodes. The default is all nodes in G. 
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36 
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37 Returns 
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38  
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39 redundancy : dictionary 
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40 A dictionary keyed by node with the node redundancy value. 
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41 
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42 Examples 
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43  
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44 Compute the redundancy coefficient of each node in a graph:: 
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45 
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46 >>> from networkx.algorithms import bipartite 
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47 >>> G = nx.cycle_graph(4) 
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48 >>> rc = bipartite.node_redundancy(G) 
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49 >>> rc[0] 
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50 1.0 
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51 
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52 Compute the average redundancy for the graph:: 
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53 
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54 >>> from networkx.algorithms import bipartite 
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55 >>> G = nx.cycle_graph(4) 
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56 >>> rc = bipartite.node_redundancy(G) 
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57 >>> sum(rc.values()) / len(G) 
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58 1.0 
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59 
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60 Compute the average redundancy for a set of nodes:: 
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61 
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62 >>> from networkx.algorithms import bipartite 
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63 >>> G = nx.cycle_graph(4) 
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64 >>> rc = bipartite.node_redundancy(G) 
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65 >>> nodes = [0, 2] 
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66 >>> sum(rc[n] for n in nodes) / len(nodes) 
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67 1.0 
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68 
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69 Raises 
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70  
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71 NetworkXError 
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72 If any of the nodes in the graph (or in `nodes`, if specified) has 
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73 (out)degree less than two (which would result in division by zero, 
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74 according to the definition of the redundancy coefficient). 
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75 
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76 References 
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77  
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78 .. [1] Latapy, Matthieu, ClĂ©mence Magnien, and Nathalie Del Vecchio (2008). 
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79 Basic notions for the analysis of large twomode networks. 
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80 Social Networks 30(1), 3148. 
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81 
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82 """ 
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83 if nodes is None: 
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84 nodes = G 
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85 if any(len(G[v]) < 2 for v in nodes): 
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86 raise NetworkXError( 
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87 "Cannot compute redundancy coefficient for a node" 
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88 " that has fewer than two neighbors." 
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89 ) 
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90 # TODO This can be trivially parallelized. 
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91 return {v: _node_redundancy(G, v) for v in nodes} 
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92 
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93 
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94 def _node_redundancy(G, v): 
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95 """Returns the redundancy of the node `v` in the bipartite graph `G`. 
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96 
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97 If `G` is a graph with `n` nodes, the redundancy of a node is the ratio 
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98 of the "overlap" of `v` to the maximum possible overlap of `v` 
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99 according to its degree. The overlap of `v` is the number of pairs of 
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100 neighbors that have mutual neighbors themselves, other than `v`. 
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101 
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102 `v` must have at least two neighbors in `G`. 
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103 
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104 """ 
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105 n = len(G[v]) 
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106 # TODO On Python 3, we could just use `G[u].keys() & G[w].keys()` instead 
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107 # of instantiating the entire sets. 
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108 overlap = sum( 
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109 1 for (u, w) in combinations(G[v], 2) if (set(G[u]) & set(G[w]))  {v} 
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110 ) 
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111 return (2 * overlap) / (n * (n  1)) 