Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/reciprocity.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 """Algorithms to calculate reciprocity in a directed graph.""" |
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2 from networkx import NetworkXError |
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3 from ..utils import not_implemented_for |
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4 |
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5 __all__ = ["reciprocity", "overall_reciprocity"] |
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6 |
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7 |
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8 @not_implemented_for("undirected", "multigraph") |
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9 def reciprocity(G, nodes=None): |
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10 r"""Compute the reciprocity in a directed graph. |
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11 |
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12 The reciprocity of a directed graph is defined as the ratio |
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13 of the number of edges pointing in both directions to the total |
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14 number of edges in the graph. |
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15 Formally, $r = |{(u,v) \in G|(v,u) \in G}| / |{(u,v) \in G}|$. |
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16 |
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17 The reciprocity of a single node u is defined similarly, |
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18 it is the ratio of the number of edges in both directions to |
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19 the total number of edges attached to node u. |
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20 |
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21 Parameters |
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22 ---------- |
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23 G : graph |
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24 A networkx directed graph |
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25 nodes : container of nodes, optional (default=whole graph) |
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26 Compute reciprocity for nodes in this container. |
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27 |
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28 Returns |
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29 ------- |
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30 out : dictionary |
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31 Reciprocity keyed by node label. |
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32 |
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33 Notes |
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34 ----- |
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35 The reciprocity is not defined for isolated nodes. |
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36 In such cases this function will return None. |
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37 |
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38 """ |
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39 # If `nodes` is not specified, calculate the reciprocity of the graph. |
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40 if nodes is None: |
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41 return overall_reciprocity(G) |
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42 |
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43 # If `nodes` represents a single node in the graph, return only its |
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44 # reciprocity. |
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45 if nodes in G: |
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46 reciprocity = next(_reciprocity_iter(G, nodes))[1] |
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47 if reciprocity is None: |
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48 raise NetworkXError("Not defined for isolated nodes.") |
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49 else: |
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50 return reciprocity |
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51 |
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52 # Otherwise, `nodes` represents an iterable of nodes, so return a |
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53 # dictionary mapping node to its reciprocity. |
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54 return dict(_reciprocity_iter(G, nodes)) |
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55 |
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56 |
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57 def _reciprocity_iter(G, nodes): |
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58 """ Return an iterator of (node, reciprocity). |
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59 """ |
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60 n = G.nbunch_iter(nodes) |
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61 for node in n: |
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62 pred = set(G.predecessors(node)) |
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63 succ = set(G.successors(node)) |
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64 overlap = pred & succ |
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65 n_total = len(pred) + len(succ) |
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66 |
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67 # Reciprocity is not defined for isolated nodes. |
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68 # Return None. |
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69 if n_total == 0: |
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70 yield (node, None) |
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71 else: |
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72 reciprocity = 2.0 * float(len(overlap)) / float(n_total) |
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73 yield (node, reciprocity) |
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74 |
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75 |
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76 @not_implemented_for("undirected", "multigraph") |
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77 def overall_reciprocity(G): |
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78 """Compute the reciprocity for the whole graph. |
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79 |
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80 See the doc of reciprocity for the definition. |
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81 |
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82 Parameters |
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83 ---------- |
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84 G : graph |
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85 A networkx graph |
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86 |
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87 """ |
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88 n_all_edge = G.number_of_edges() |
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89 n_overlap_edge = (n_all_edge - G.to_undirected().number_of_edges()) * 2 |
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90 |
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91 if n_all_edge == 0: |
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92 raise NetworkXError("Not defined for empty graphs") |
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93 |
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94 return float(n_overlap_edge) / float(n_all_edge) |