Coverage for /pythoncovmergedfiles/medio/medio/usr/local/lib/python3.9/dist-packages/networkx/linalg/spectrum.py: 50%

1""" 

2Eigenvalue spectrum of graphs. 

3""" 

4import 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@nx._dispatch(edge_attrs="weight") 

16def laplacian_spectrum(G, weight="weight"): 

17 """Returns eigenvalues of the Laplacian of G 

18 

19 Parameters 

20 ---------- 

21 G : graph 

22 A NetworkX graph 

23 

24 weight : string or None, optional (default='weight') 

25 The edge data key used to compute each value in the matrix. 

26 If None, then each edge has weight 1. 

27 

28 Returns 

29 ------- 

30 evals : NumPy array 

31 Eigenvalues 

32 

33 Notes 

34 ----- 

35 For MultiGraph/MultiDiGraph, the edges weights are summed. 

36 See :func:`~networkx.convert_matrix.to_numpy_array` for other options. 

37 

38 See Also 

39 -------- 

40 laplacian_matrix 

41 

42 Examples 

43 -------- 

44 The multiplicity of 0 as an eigenvalue of the laplacian matrix is equal 

45 to the number of connected components of G. 

46 

47 >>> G = nx.Graph() # Create a graph with 5 nodes and 3 connected components 

48 >>> G.add_nodes_from(range(5)) 

49 >>> G.add_edges_from([(0, 2), (3, 4)]) 

50 >>> nx.laplacian_spectrum(G) 

51 array([0., 0., 0., 2., 2.]) 

52 

53 """ 

54 import scipy as sp 

55 

56 return sp.linalg.eigvalsh(nx.laplacian_matrix(G, weight=weight).todense()) 

57 

58 

59@nx._dispatch(edge_attrs="weight") 

60def normalized_laplacian_spectrum(G, weight="weight"): 

61 """Return eigenvalues of the normalized Laplacian of G 

62 

63 Parameters 

64 ---------- 

65 G : graph 

66 A NetworkX graph 

67 

68 weight : string or None, optional (default='weight') 

69 The edge data key used to compute each value in the matrix. 

70 If None, then each edge has weight 1. 

71 

72 Returns 

73 ------- 

74 evals : NumPy array 

75 Eigenvalues 

76 

77 Notes 

78 ----- 

79 For MultiGraph/MultiDiGraph, the edges weights are summed. 

80 See to_numpy_array for other options. 

81 

82 See Also 

83 -------- 

84 normalized_laplacian_matrix 

85 """ 

86 import scipy as sp 

87 

88 return sp.linalg.eigvalsh( 

89 nx.normalized_laplacian_matrix(G, weight=weight).todense() 

90 ) 

91 

92 

93@nx._dispatch(edge_attrs="weight") 

94def adjacency_spectrum(G, weight="weight"): 

95 """Returns eigenvalues of the adjacency matrix of G. 

96 

97 Parameters 

98 ---------- 

99 G : graph 

100 A NetworkX graph 

101 

102 weight : string or None, optional (default='weight') 

103 The edge data key used to compute each value in the matrix. 

104 If None, then each edge has weight 1. 

105 

106 Returns 

107 ------- 

108 evals : NumPy array 

109 Eigenvalues 

110 

111 Notes 

112 ----- 

113 For MultiGraph/MultiDiGraph, the edges weights are summed. 

114 See to_numpy_array for other options. 

115 

116 See Also 

117 -------- 

118 adjacency_matrix 

119 """ 

120 import scipy as sp 

121 

122 return sp.linalg.eigvals(nx.adjacency_matrix(G, weight=weight).todense()) 

123 

124 

125@nx._dispatch 

126def modularity_spectrum(G): 

127 """Returns eigenvalues of the modularity matrix of G. 

128 

129 Parameters 

130 ---------- 

131 G : Graph 

132 A NetworkX Graph or DiGraph 

133 

134 Returns 

135 ------- 

136 evals : NumPy array 

137 Eigenvalues 

138 

139 See Also 

140 -------- 

141 modularity_matrix 

142 

143 References 

144 ---------- 

145 .. [1] M. E. J. Newman, "Modularity and community structure in networks", 

146 Proc. Natl. Acad. Sci. USA, vol. 103, pp. 8577-8582, 2006. 

147 """ 

148 import scipy as sp 

149 

150 if G.is_directed(): 

151 return sp.linalg.eigvals(nx.directed_modularity_matrix(G)) 

152 else: 

153 return sp.linalg.eigvals(nx.modularity_matrix(G)) 

154 

155 

156@nx._dispatch 

157def bethe_hessian_spectrum(G, r=None): 

158 """Returns eigenvalues of the Bethe Hessian matrix of G. 

159 

160 Parameters 

161 ---------- 

162 G : Graph 

163 A NetworkX Graph or DiGraph 

164 

165 r : float 

166 Regularizer parameter 

167 

168 Returns 

169 ------- 

170 evals : NumPy array 

171 Eigenvalues 

172 

173 See Also 

174 -------- 

175 bethe_hessian_matrix 

176 

177 References 

178 ---------- 

179 .. [1] A. Saade, F. Krzakala and L. Zdeborová 

180 "Spectral clustering of graphs with the bethe hessian", 

181 Advances in Neural Information Processing Systems. 2014. 

182 """ 

183 import scipy as sp 

184 

185 return sp.linalg.eigvalsh(nx.bethe_hessian_matrix(G, r).todense())