Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/vitality.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 """ |
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2 Vitality measures. |
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3 """ |
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4 from functools import partial |
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5 |
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6 import networkx as nx |
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7 |
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8 __all__ = ["closeness_vitality"] |
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9 |
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10 |
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11 def closeness_vitality(G, node=None, weight=None, wiener_index=None): |
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12 """Returns the closeness vitality for nodes in the graph. |
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13 |
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14 The *closeness vitality* of a node, defined in Section 3.6.2 of [1], |
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15 is the change in the sum of distances between all node pairs when |
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16 excluding that node. |
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17 |
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18 Parameters |
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19 ---------- |
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20 G : NetworkX graph |
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21 A strongly-connected graph. |
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22 |
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23 weight : string |
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24 The name of the edge attribute used as weight. This is passed |
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25 directly to the :func:`~networkx.wiener_index` function. |
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26 |
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27 node : object |
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28 If specified, only the closeness vitality for this node will be |
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29 returned. Otherwise, a dictionary mapping each node to its |
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30 closeness vitality will be returned. |
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31 |
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32 Other parameters |
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33 ---------------- |
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34 wiener_index : number |
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35 If you have already computed the Wiener index of the graph |
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36 `G`, you can provide that value here. Otherwise, it will be |
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37 computed for you. |
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38 |
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39 Returns |
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40 ------- |
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41 dictionary or float |
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42 If `node` is None, this function returns a dictionary |
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43 with nodes as keys and closeness vitality as the |
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44 value. Otherwise, it returns only the closeness vitality for the |
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45 specified `node`. |
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46 |
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47 The closeness vitality of a node may be negative infinity if |
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48 removing that node would disconnect the graph. |
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49 |
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50 Examples |
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51 -------- |
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52 >>> G = nx.cycle_graph(3) |
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53 >>> nx.closeness_vitality(G) |
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54 {0: 2.0, 1: 2.0, 2: 2.0} |
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55 |
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56 See Also |
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57 -------- |
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58 closeness_centrality |
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59 |
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60 References |
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61 ---------- |
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62 .. [1] Ulrik Brandes, Thomas Erlebach (eds.). |
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63 *Network Analysis: Methodological Foundations*. |
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64 Springer, 2005. |
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65 <http://books.google.com/books?id=TTNhSm7HYrIC> |
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66 |
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67 """ |
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68 if wiener_index is None: |
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69 wiener_index = nx.wiener_index(G, weight=weight) |
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70 if node is not None: |
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71 after = nx.wiener_index(G.subgraph(set(G) - {node}), weight=weight) |
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72 return wiener_index - after |
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73 vitality = partial(closeness_vitality, G, weight=weight, wiener_index=wiener_index) |
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74 # TODO This can be trivially parallelized. |
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75 return {v: vitality(node=v) for v in G} |