Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/centrality/current_flow_closeness.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 """Current-flow closeness centrality measures.""" |
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2 import networkx as nx |
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3 |
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4 from networkx.utils import not_implemented_for, reverse_cuthill_mckee_ordering |
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5 from networkx.algorithms.centrality.flow_matrix import ( |
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6 CGInverseLaplacian, |
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7 FullInverseLaplacian, |
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8 laplacian_sparse_matrix, |
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9 SuperLUInverseLaplacian, |
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10 ) |
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11 |
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12 __all__ = ["current_flow_closeness_centrality", "information_centrality"] |
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13 |
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14 |
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15 @not_implemented_for("directed") |
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16 def current_flow_closeness_centrality(G, weight=None, dtype=float, solver="lu"): |
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17 """Compute current-flow closeness centrality for nodes. |
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18 |
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19 Current-flow closeness centrality is variant of closeness |
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20 centrality based on effective resistance between nodes in |
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21 a network. This metric is also known as information 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 weight : None or string, optional (default=None) |
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29 If None, all edge weights are considered equal. |
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30 Otherwise holds the name of the edge attribute used as weight. |
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31 |
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32 dtype: data type (default=float) |
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33 Default data type for internal matrices. |
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34 Set to np.float32 for lower memory consumption. |
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35 |
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36 solver: string (default='lu') |
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37 Type of linear solver to use for computing the flow matrix. |
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38 Options are "full" (uses most memory), "lu" (recommended), and |
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39 "cg" (uses least memory). |
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40 |
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41 Returns |
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42 ------- |
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43 nodes : dictionary |
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44 Dictionary of nodes with current flow closeness centrality as the value. |
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45 |
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46 See Also |
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47 -------- |
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48 closeness_centrality |
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49 |
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50 Notes |
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51 ----- |
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52 The algorithm is from Brandes [1]_. |
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53 |
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54 See also [2]_ for the original definition of information centrality. |
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55 |
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56 References |
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57 ---------- |
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58 .. [1] Ulrik Brandes and Daniel Fleischer, |
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59 Centrality Measures Based on Current Flow. |
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60 Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS '05). |
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61 LNCS 3404, pp. 533-544. Springer-Verlag, 2005. |
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62 http://algo.uni-konstanz.de/publications/bf-cmbcf-05.pdf |
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63 |
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64 .. [2] Karen Stephenson and Marvin Zelen: |
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65 Rethinking centrality: Methods and examples. |
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66 Social Networks 11(1):1-37, 1989. |
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67 https://doi.org/10.1016/0378-8733(89)90016-6 |
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68 """ |
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69 if not nx.is_connected(G): |
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70 raise nx.NetworkXError("Graph not connected.") |
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71 solvername = { |
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72 "full": FullInverseLaplacian, |
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73 "lu": SuperLUInverseLaplacian, |
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74 "cg": CGInverseLaplacian, |
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75 } |
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76 n = G.number_of_nodes() |
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77 ordering = list(reverse_cuthill_mckee_ordering(G)) |
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78 # make a copy with integer labels according to rcm ordering |
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79 # this could be done without a copy if we really wanted to |
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80 H = nx.relabel_nodes(G, dict(zip(ordering, range(n)))) |
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81 betweenness = dict.fromkeys(H, 0.0) # b[v]=0 for v in H |
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82 n = H.number_of_nodes() |
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83 L = laplacian_sparse_matrix( |
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84 H, nodelist=range(n), weight=weight, dtype=dtype, format="csc" |
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85 ) |
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86 C2 = solvername[solver](L, width=1, dtype=dtype) # initialize solver |
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87 for v in H: |
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88 col = C2.get_row(v) |
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89 for w in H: |
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90 betweenness[v] += col[v] - 2 * col[w] |
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91 betweenness[w] += col[v] |
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92 for v in H: |
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93 betweenness[v] = 1.0 / (betweenness[v]) |
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94 return {ordering[k]: float(v) for k, v in betweenness.items()} |
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95 |
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96 |
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97 information_centrality = current_flow_closeness_centrality |