Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/linalg/spectrum.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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 Eigenvalue spectrum of graphs. |
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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__ = [ |
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7 "laplacian_spectrum", |
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8 "adjacency_spectrum", |
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9 "modularity_spectrum", |
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10 "normalized_laplacian_spectrum", |
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11 "bethe_hessian_spectrum", |
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12 ] |
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13 |
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14 |
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15 def laplacian_spectrum(G, weight="weight"): |
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16 """Returns eigenvalues of the Laplacian of G |
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17 |
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18 Parameters |
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19 ---------- |
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20 G : graph |
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21 A NetworkX graph |
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22 |
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23 weight : string or None, optional (default='weight') |
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24 The edge data key used to compute each value in the matrix. |
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25 If None, then each edge has weight 1. |
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26 |
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27 Returns |
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28 ------- |
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29 evals : NumPy array |
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30 Eigenvalues |
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31 |
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32 Notes |
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33 ----- |
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34 For MultiGraph/MultiDiGraph, the edges weights are summed. |
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35 See to_numpy_array for other options. |
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36 |
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37 See Also |
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38 -------- |
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39 laplacian_matrix |
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40 """ |
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41 from scipy.linalg import eigvalsh |
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42 |
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43 return eigvalsh(nx.laplacian_matrix(G, weight=weight).todense()) |
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44 |
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45 |
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46 def normalized_laplacian_spectrum(G, weight="weight"): |
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47 """Return eigenvalues of the normalized Laplacian of G |
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48 |
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49 Parameters |
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50 ---------- |
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51 G : graph |
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52 A NetworkX graph |
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53 |
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54 weight : string or None, optional (default='weight') |
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55 The edge data key used to compute each value in the matrix. |
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56 If None, then each edge has weight 1. |
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57 |
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58 Returns |
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59 ------- |
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60 evals : NumPy array |
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61 Eigenvalues |
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62 |
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63 Notes |
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64 ----- |
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65 For MultiGraph/MultiDiGraph, the edges weights are summed. |
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66 See to_numpy_array for other options. |
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67 |
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68 See Also |
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69 -------- |
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70 normalized_laplacian_matrix |
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71 """ |
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72 from scipy.linalg import eigvalsh |
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73 |
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74 return eigvalsh(nx.normalized_laplacian_matrix(G, weight=weight).todense()) |
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75 |
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76 |
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77 def adjacency_spectrum(G, weight="weight"): |
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78 """Returns eigenvalues of the adjacency matrix of G. |
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79 |
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80 Parameters |
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81 ---------- |
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82 G : graph |
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83 A NetworkX graph |
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84 |
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85 weight : string or None, optional (default='weight') |
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86 The edge data key used to compute each value in the matrix. |
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87 If None, then each edge has weight 1. |
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88 |
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89 Returns |
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90 ------- |
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91 evals : NumPy array |
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92 Eigenvalues |
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93 |
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94 Notes |
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95 ----- |
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96 For MultiGraph/MultiDiGraph, the edges weights are summed. |
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97 See to_numpy_array for other options. |
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98 |
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99 See Also |
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100 -------- |
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101 adjacency_matrix |
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102 """ |
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103 from scipy.linalg import eigvals |
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104 |
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105 return eigvals(nx.adjacency_matrix(G, weight=weight).todense()) |
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106 |
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107 |
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108 def modularity_spectrum(G): |
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109 """Returns eigenvalues of the modularity matrix of G. |
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110 |
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111 Parameters |
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112 ---------- |
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113 G : Graph |
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114 A NetworkX Graph or DiGraph |
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115 |
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116 Returns |
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117 ------- |
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118 evals : NumPy array |
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119 Eigenvalues |
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120 |
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121 See Also |
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122 -------- |
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123 modularity_matrix |
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124 |
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125 References |
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126 ---------- |
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127 .. [1] M. E. J. Newman, "Modularity and community structure in networks", |
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128 Proc. Natl. Acad. Sci. USA, vol. 103, pp. 8577-8582, 2006. |
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129 """ |
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130 from scipy.linalg import eigvals |
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131 |
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132 if G.is_directed(): |
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133 return eigvals(nx.directed_modularity_matrix(G)) |
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134 else: |
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135 return eigvals(nx.modularity_matrix(G)) |
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136 |
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137 |
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138 def bethe_hessian_spectrum(G, r=None): |
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139 """Returns eigenvalues of the Bethe Hessian matrix of G. |
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140 |
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141 Parameters |
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142 ---------- |
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143 G : Graph |
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144 A NetworkX Graph or DiGraph |
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145 |
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146 r : float |
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147 Regularizer parameter |
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148 |
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149 Returns |
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150 ------- |
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151 evals : NumPy array |
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152 Eigenvalues |
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153 |
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154 See Also |
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155 -------- |
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156 bethe_hessian_matrix |
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157 |
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158 References |
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159 ---------- |
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160 .. [1] A. Saade, F. Krzakala and L. Zdeborová |
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161 "Spectral clustering of graphs with the bethe hessian", |
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162 Advances in Neural Information Processing Systems. 2014. |
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163 """ |
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164 from scipy.linalg import eigvalsh |
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165 |
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166 return eigvalsh(nx.bethe_hessian_matrix(G, r).todense()) |