Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/centrality/harmonic.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 for computing the harmonic centrality of a graph.""" |
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2 from functools import partial |
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3 |
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4 import networkx as nx |
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5 |
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6 __all__ = ["harmonic_centrality"] |
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7 |
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8 |
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9 def harmonic_centrality(G, nbunch=None, distance=None): |
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10 r"""Compute harmonic centrality for nodes. |
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11 |
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12 Harmonic centrality [1]_ of a node `u` is the sum of the reciprocal |
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13 of the shortest path distances from all other nodes to `u` |
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14 |
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15 .. math:: |
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16 |
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17 C(u) = \sum_{v \neq u} \frac{1}{d(v, u)} |
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18 |
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19 where `d(v, u)` is the shortest-path distance between `v` and `u`. |
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20 |
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21 Notice that higher values indicate higher centrality. |
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22 |
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23 Parameters |
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24 ---------- |
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25 G : graph |
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26 A NetworkX graph |
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27 |
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28 nbunch : container |
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29 Container of nodes. If provided harmonic centrality will be computed |
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30 only over the nodes in nbunch. |
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31 |
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32 distance : edge attribute key, optional (default=None) |
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33 Use the specified edge attribute as the edge distance in shortest |
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34 path calculations. If `None`, then each edge will have distance equal to 1. |
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35 |
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36 Returns |
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37 ------- |
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38 nodes : dictionary |
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39 Dictionary of nodes with harmonic centrality as the value. |
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40 |
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41 See Also |
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42 -------- |
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43 betweenness_centrality, load_centrality, eigenvector_centrality, |
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44 degree_centrality, closeness_centrality |
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45 |
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46 Notes |
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47 ----- |
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48 If the 'distance' keyword is set to an edge attribute key then the |
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49 shortest-path length will be computed using Dijkstra's algorithm with |
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50 that edge attribute as the edge weight. |
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51 |
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52 References |
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53 ---------- |
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54 .. [1] Boldi, Paolo, and Sebastiano Vigna. "Axioms for centrality." |
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55 Internet Mathematics 10.3-4 (2014): 222-262. |
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56 """ |
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57 if G.is_directed(): |
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58 G = G.reverse() |
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59 spl = partial(nx.shortest_path_length, G, weight=distance) |
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60 return { |
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61 u: sum(1 / d if d > 0 else 0 for v, d in spl(source=u).items()) |
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62 for u in G.nbunch_iter(nbunch) |
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63 } |