Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/non_randomness.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 r""" Computation of graph non-randomness |
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2 """ |
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3 |
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4 import math |
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5 import networkx as nx |
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6 from networkx.utils import not_implemented_for |
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7 |
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8 __all__ = ["non_randomness"] |
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9 |
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10 |
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11 @not_implemented_for("directed") |
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12 @not_implemented_for("multigraph") |
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13 def non_randomness(G, k=None): |
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14 """Compute the non-randomness of graph G. |
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15 |
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16 The first returned value nr is the sum of non-randomness values of all |
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17 edges within the graph (where the non-randomness of an edge tends to be |
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18 small when the two nodes linked by that edge are from two different |
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19 communities). |
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20 |
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21 The second computed value nr_rd is a relative measure that indicates |
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22 to what extent graph G is different from random graphs in terms |
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23 of probability. When it is close to 0, the graph tends to be more |
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24 likely generated by an Erdos Renyi model. |
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25 |
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26 Parameters |
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27 ---------- |
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28 G : NetworkX graph |
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29 Graph must be binary, symmetric, connected, and without self-loops. |
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30 |
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31 k : int |
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32 The number of communities in G. |
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33 If k is not set, the function will use a default community |
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34 detection algorithm to set it. |
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35 |
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36 Returns |
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37 ------- |
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38 non-randomness : (float, float) tuple |
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39 Non-randomness, Relative non-randomness w.r.t. |
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40 Erdos Renyi random graphs. |
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41 |
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42 Examples |
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43 -------- |
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44 >>> G = nx.karate_club_graph() |
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45 >>> nr, nr_rd = nx.non_randomness(G, 2) |
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46 |
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47 Notes |
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48 ----- |
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49 This computes Eq. (4.4) and (4.5) in Ref. [1]_. |
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50 |
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51 References |
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52 ---------- |
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53 .. [1] Xiaowei Ying and Xintao Wu, |
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54 On Randomness Measures for Social Networks, |
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55 SIAM International Conference on Data Mining. 2009 |
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56 """ |
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57 |
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58 if not nx.is_connected(G): |
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59 raise nx.NetworkXException("Non connected graph.") |
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60 if len(list(nx.selfloop_edges(G))) > 0: |
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61 raise nx.NetworkXError("Graph must not contain self-loops") |
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62 |
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63 if k is None: |
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64 k = len(tuple(nx.community.label_propagation_communities(G))) |
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65 |
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66 try: |
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67 import numpy as np |
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68 except ImportError as e: |
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69 msg = "non_randomness requires NumPy: http://numpy.org/" |
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70 raise ImportError(msg) from e |
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71 |
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72 # eq. 4.4 |
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73 nr = np.real(np.sum(np.linalg.eigvals(nx.to_numpy_array(G))[:k])) |
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74 |
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75 n = G.number_of_nodes() |
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76 m = G.number_of_edges() |
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77 p = (2 * k * m) / (n * (n - k)) |
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78 |
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79 # eq. 4.5 |
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80 nr_rd = (nr - ((n - 2 * k) * p + k)) / math.sqrt(2 * k * p * (1 - p)) |
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81 |
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82 return nr, nr_rd |