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annotate planemo/lib/python3.7/site-packages/networkx/algorithms/wiener.py @ 1:56ad4e20f292 draft

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"planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
author guerler
date Fri, 31 Jul 2020 00:32:28 -0400
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1 # wiener.py - functions related to the Wiener index of a graph
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2 #
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3 # Copyright 2015 NetworkX developers.
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4 #
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5 # This file is part of NetworkX.
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6 #
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7 # NetworkX is distributed under a BSD license; see LICENSE.txt for more
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8 # information.
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9 """Functions related to the Wiener index of a graph."""
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10
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11 from itertools import chain
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12
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13 from .components import is_connected
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14 from .components import is_strongly_connected
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15 from .shortest_paths import shortest_path_length as spl
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16
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17 __all__ = ['wiener_index']
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18
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19 #: Rename the :func:`chain.from_iterable` function for the sake of
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20 #: brevity.
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21 chaini = chain.from_iterable
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22
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23
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24 def wiener_index(G, weight=None):
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25 """Returns the Wiener index of the given graph.
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26
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27 The *Wiener index* of a graph is the sum of the shortest-path
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28 distances between each pair of reachable nodes. For pairs of nodes
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29 in undirected graphs, only one orientation of the pair is counted.
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30
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31 Parameters
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32 ----------
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33 G : NetworkX graph
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34
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35 weight : object
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36 The edge attribute to use as distance when computing
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37 shortest-path distances. This is passed directly to the
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38 :func:`networkx.shortest_path_length` function.
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39
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40 Returns
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41 -------
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42 float
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43 The Wiener index of the graph `G`.
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44
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45 Raises
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46 ------
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47 NetworkXError
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48 If the graph `G` is not connected.
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49
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50 Notes
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51 -----
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52 If a pair of nodes is not reachable, the distance is assumed to be
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53 infinity. This means that for graphs that are not
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54 strongly-connected, this function returns ``inf``.
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55
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56 The Wiener index is not usually defined for directed graphs, however
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57 this function uses the natural generalization of the Wiener index to
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58 directed graphs.
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59
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60 Examples
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61 --------
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62 The Wiener index of the (unweighted) complete graph on *n* nodes
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63 equals the number of pairs of the *n* nodes, since each pair of
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64 nodes is at distance one::
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65
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66 >>> import networkx as nx
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67 >>> n = 10
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68 >>> G = nx.complete_graph(n)
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69 >>> nx.wiener_index(G) == n * (n - 1) / 2
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70 True
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71
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72 Graphs that are not strongly-connected have infinite Wiener index::
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73
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74 >>> G = nx.empty_graph(2)
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75 >>> nx.wiener_index(G)
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76 inf
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77
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78 """
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79 is_directed = G.is_directed()
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80 if (is_directed and not is_strongly_connected(G)) or \
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81 (not is_directed and not is_connected(G)):
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82 return float('inf')
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83 total = sum(chaini(p.values() for v, p in spl(G, weight=weight)))
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84 # Need to account for double counting pairs of nodes in undirected graphs.
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85 return total if is_directed else total / 2