Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/wiener.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 """Functions related to the Wiener index of a graph.""" |
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2 |
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3 from itertools import chain |
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4 |
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5 from .components import is_connected |
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6 from .components import is_strongly_connected |
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7 from .shortest_paths import shortest_path_length as spl |
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8 |
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9 __all__ = ["wiener_index"] |
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10 |
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11 #: Rename the :func:`chain.from_iterable` function for the sake of |
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12 #: brevity. |
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13 chaini = chain.from_iterable |
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14 |
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15 |
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16 def wiener_index(G, weight=None): |
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17 """Returns the Wiener index of the given graph. |
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18 |
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19 The *Wiener index* of a graph is the sum of the shortest-path |
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20 distances between each pair of reachable nodes. For pairs of nodes |
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21 in undirected graphs, only one orientation of the pair is counted. |
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22 |
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23 Parameters |
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24 ---------- |
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25 G : NetworkX graph |
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26 |
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27 weight : object |
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28 The edge attribute to use as distance when computing |
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29 shortest-path distances. This is passed directly to the |
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30 :func:`networkx.shortest_path_length` function. |
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31 |
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32 Returns |
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33 ------- |
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34 float |
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35 The Wiener index of the graph `G`. |
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36 |
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37 Raises |
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38 ------ |
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39 NetworkXError |
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40 If the graph `G` is not connected. |
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41 |
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42 Notes |
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43 ----- |
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44 If a pair of nodes is not reachable, the distance is assumed to be |
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45 infinity. This means that for graphs that are not |
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46 strongly-connected, this function returns ``inf``. |
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47 |
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48 The Wiener index is not usually defined for directed graphs, however |
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49 this function uses the natural generalization of the Wiener index to |
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50 directed graphs. |
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51 |
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52 Examples |
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53 -------- |
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54 The Wiener index of the (unweighted) complete graph on *n* nodes |
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55 equals the number of pairs of the *n* nodes, since each pair of |
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56 nodes is at distance one:: |
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57 |
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58 >>> n = 10 |
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59 >>> G = nx.complete_graph(n) |
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60 >>> nx.wiener_index(G) == n * (n - 1) / 2 |
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61 True |
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62 |
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63 Graphs that are not strongly-connected have infinite Wiener index:: |
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64 |
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65 >>> G = nx.empty_graph(2) |
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66 >>> nx.wiener_index(G) |
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67 inf |
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68 |
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69 """ |
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70 is_directed = G.is_directed() |
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71 if (is_directed and not is_strongly_connected(G)) or ( |
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72 not is_directed and not is_connected(G) |
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73 ): |
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74 return float("inf") |
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75 total = sum(chaini(p.values() for v, p in spl(G, weight=weight))) |
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76 # Need to account for double counting pairs of nodes in undirected graphs. |
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77 return total if is_directed else total / 2 |