Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/centrality/dispersion.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 from itertools import combinations |
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2 |
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3 __all__ = ["dispersion"] |
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4 |
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5 |
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6 def dispersion(G, u=None, v=None, normalized=True, alpha=1.0, b=0.0, c=0.0): |
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7 r"""Calculate dispersion between `u` and `v` in `G`. |
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8 |
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9 A link between two actors (`u` and `v`) has a high dispersion when their |
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10 mutual ties (`s` and `t`) are not well connected with each other. |
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11 |
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12 Parameters |
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13 ---------- |
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14 G : graph |
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15 A NetworkX graph. |
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16 u : node, optional |
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17 The source for the dispersion score (e.g. ego node of the network). |
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18 v : node, optional |
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19 The target of the dispersion score if specified. |
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20 normalized : bool |
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21 If True (default) normalize by the embededness of the nodes (u and v). |
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22 |
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23 Returns |
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24 ------- |
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25 nodes : dictionary |
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26 If u (v) is specified, returns a dictionary of nodes with dispersion |
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27 score for all "target" ("source") nodes. If neither u nor v is |
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28 specified, returns a dictionary of dictionaries for all nodes 'u' in the |
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29 graph with a dispersion score for each node 'v'. |
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30 |
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31 Notes |
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32 ----- |
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33 This implementation follows Lars Backstrom and Jon Kleinberg [1]_. Typical |
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34 usage would be to run dispersion on the ego network $G_u$ if $u$ were |
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35 specified. Running :func:`dispersion` with neither $u$ nor $v$ specified |
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36 can take some time to complete. |
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37 |
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38 References |
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39 ---------- |
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40 .. [1] Romantic Partnerships and the Dispersion of Social Ties: |
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41 A Network Analysis of Relationship Status on Facebook. |
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42 Lars Backstrom, Jon Kleinberg. |
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43 https://arxiv.org/pdf/1310.6753v1.pdf |
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44 |
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45 """ |
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46 |
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47 def _dispersion(G_u, u, v): |
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48 """dispersion for all nodes 'v' in a ego network G_u of node 'u'""" |
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49 u_nbrs = set(G_u[u]) |
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50 ST = {n for n in G_u[v] if n in u_nbrs} |
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51 set_uv = {u, v} |
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52 # all possible ties of connections that u and b share |
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53 possib = combinations(ST, 2) |
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54 total = 0 |
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55 for (s, t) in possib: |
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56 # neighbors of s that are in G_u, not including u and v |
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57 nbrs_s = u_nbrs.intersection(G_u[s]) - set_uv |
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58 # s and t are not directly connected |
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59 if t not in nbrs_s: |
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60 # s and t do not share a connection |
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61 if nbrs_s.isdisjoint(G_u[t]): |
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62 # tick for disp(u, v) |
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63 total += 1 |
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64 # neighbors that u and v share |
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65 embededness = len(ST) |
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66 |
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67 if normalized: |
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68 if embededness + c != 0: |
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69 norm_disp = ((total + b) ** alpha) / (embededness + c) |
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70 else: |
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71 norm_disp = (total + b) ** alpha |
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72 dispersion = norm_disp |
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73 |
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74 else: |
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75 dispersion = total |
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76 |
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77 return dispersion |
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78 |
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79 if u is None: |
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80 # v and u are not specified |
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81 if v is None: |
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82 results = {n: {} for n in G} |
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83 for u in G: |
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84 for v in G[u]: |
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85 results[u][v] = _dispersion(G, u, v) |
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86 # u is not specified, but v is |
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87 else: |
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88 results = dict.fromkeys(G[v], {}) |
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89 for u in G[v]: |
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90 results[u] = _dispersion(G, v, u) |
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91 else: |
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92 # u is specified with no target v |
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93 if v is None: |
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94 results = dict.fromkeys(G[u], {}) |
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95 for v in G[u]: |
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96 results[v] = _dispersion(G, u, v) |
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97 # both u and v are specified |
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98 else: |
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99 results = _dispersion(G, u, v) |
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100 |
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101 return results |