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comparison env/lib/python3.9/site-packages/networkx/linalg/spectrum.py @ 0:4f3585e2f14b draft default tip

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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
author shellac
date Mon, 22 Mar 2021 18:12:50 +0000
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1 """
2 Eigenvalue spectrum of graphs.
3 """
4 import networkx as nx
5
6 __all__ = [
7 "laplacian_spectrum",
8 "adjacency_spectrum",
9 "modularity_spectrum",
10 "normalized_laplacian_spectrum",
11 "bethe_hessian_spectrum",
12 ]
13
14
15 def laplacian_spectrum(G, weight="weight"):
16 """Returns eigenvalues of the Laplacian of G
17
18 Parameters
19 ----------
20 G : graph
21 A NetworkX graph
22
23 weight : string or None, optional (default='weight')
24 The edge data key used to compute each value in the matrix.
25 If None, then each edge has weight 1.
26
27 Returns
28 -------
29 evals : NumPy array
30 Eigenvalues
31
32 Notes
33 -----
34 For MultiGraph/MultiDiGraph, the edges weights are summed.
35 See to_numpy_array for other options.
36
37 See Also
38 --------
39 laplacian_matrix
40 """
41 from scipy.linalg import eigvalsh
42
43 return eigvalsh(nx.laplacian_matrix(G, weight=weight).todense())
44
45
46 def normalized_laplacian_spectrum(G, weight="weight"):
47 """Return eigenvalues of the normalized Laplacian of G
48
49 Parameters
50 ----------
51 G : graph
52 A NetworkX graph
53
54 weight : string or None, optional (default='weight')
55 The edge data key used to compute each value in the matrix.
56 If None, then each edge has weight 1.
57
58 Returns
59 -------
60 evals : NumPy array
61 Eigenvalues
62
63 Notes
64 -----
65 For MultiGraph/MultiDiGraph, the edges weights are summed.
66 See to_numpy_array for other options.
67
68 See Also
69 --------
70 normalized_laplacian_matrix
71 """
72 from scipy.linalg import eigvalsh
73
74 return eigvalsh(nx.normalized_laplacian_matrix(G, weight=weight).todense())
75
76
77 def adjacency_spectrum(G, weight="weight"):
78 """Returns eigenvalues of the adjacency matrix of G.
79
80 Parameters
81 ----------
82 G : graph
83 A NetworkX graph
84
85 weight : string or None, optional (default='weight')
86 The edge data key used to compute each value in the matrix.
87 If None, then each edge has weight 1.
88
89 Returns
90 -------
91 evals : NumPy array
92 Eigenvalues
93
94 Notes
95 -----
96 For MultiGraph/MultiDiGraph, the edges weights are summed.
97 See to_numpy_array for other options.
98
99 See Also
100 --------
101 adjacency_matrix
102 """
103 from scipy.linalg import eigvals
104
105 return eigvals(nx.adjacency_matrix(G, weight=weight).todense())
106
107
108 def modularity_spectrum(G):
109 """Returns eigenvalues of the modularity matrix of G.
110
111 Parameters
112 ----------
113 G : Graph
114 A NetworkX Graph or DiGraph
115
116 Returns
117 -------
118 evals : NumPy array
119 Eigenvalues
120
121 See Also
122 --------
123 modularity_matrix
124
125 References
126 ----------
127 .. [1] M. E. J. Newman, "Modularity and community structure in networks",
128 Proc. Natl. Acad. Sci. USA, vol. 103, pp. 8577-8582, 2006.
129 """
130 from scipy.linalg import eigvals
131
132 if G.is_directed():
133 return eigvals(nx.directed_modularity_matrix(G))
134 else:
135 return eigvals(nx.modularity_matrix(G))
136
137
138 def bethe_hessian_spectrum(G, r=None):
139 """Returns eigenvalues of the Bethe Hessian matrix of G.
140
141 Parameters
142 ----------
143 G : Graph
144 A NetworkX Graph or DiGraph
145
146 r : float
147 Regularizer parameter
148
149 Returns
150 -------
151 evals : NumPy array
152 Eigenvalues
153
154 See Also
155 --------
156 bethe_hessian_matrix
157
158 References
159 ----------
160 .. [1] A. Saade, F. Krzakala and L. Zdeborová
161 "Spectral clustering of graphs with the bethe hessian",
162 Advances in Neural Information Processing Systems. 2014.
163 """
164 from scipy.linalg import eigvalsh
165
166 return eigvalsh(nx.bethe_hessian_matrix(G, r).todense())