networkx关于Graph的各种操作

networkx关于Graph的各种操作

Graph DiGraph MultiGraph
https://blog.csdn.net/moodytong/article/details/7491520

import networkx as nx
G=nx.Graph()
G.add_edge(1,2,weight=1)
G.add_edge(1,3,weight=1)
for ii ,jj,kk in G.edges(data=“weight”,default=1):
… print(ii,jj,kk)
nx.adjacency_matrix()

学过线性代数的都了解矩阵,在矩阵上的文章可做的很多,什么特征矩阵,单位矩阵等.grpah存储可以使用矩阵,比如graph的邻接矩阵,权重矩阵等,
这节主要是在等到graph后,如何快速得到这些信息.详细官方文档在这里

1. #定义图的节点和边

2. nodes=[‘0’,‘1’,‘2’,‘3’,‘4’,‘5’,‘a’,‘b’,‘c’]

3. edges=[(‘0’,‘0’,1),(‘0’,‘1’,1),(‘0’,‘5’,1),(‘0’,‘5’,2),(‘1’,‘2’,3),(‘1’,‘4’,5),(‘2’,‘1’,7),(‘2’,‘4’,6),(‘a’,‘b’,0.5),(‘b’,‘c’,0.5),(‘c’,‘a’,0.5)]

5. plt.subplots(1,2,figsize=(10,3))

7. #定义一个无向图和有向图

8. G1 = nx.Graph()

9. G1.add_nodes_from(nodes)

10. G1.add_weighted_edges_from(edges)

12. G2 = nx.DiGraph()

13. G2.add_nodes_from(nodes)

14. G2.add_weighted_edges_from(edges)

16. pos1=nx.circular_layout(G1)

17. pos2=nx.circular_layout(G2)

19. #画出无向图和有向图

20. plt.subplot(121)

21. nx.draw(G1,pos1, with_labels=True, font_weight=‘bold’)

22. plt.title(‘无向图’,fontproperties=myfont)

23. plt.axis(‘on’)

24. plt.xticks([])

25. plt.yticks([])

27. plt.subplot(122)

28. nx.draw(G2,pos2, with_labels=True, font_weight=‘bold’)

29. plt.title(‘有向图’,fontproperties=myfont)

30. plt.axis(‘on’)

31. plt.xticks([])

32. plt.yticks([])

34. plt.show()

36. #控制numpy输出小数位数

37. import numpy as np

38. np.set_printoptions(precision=3)

40. #邻接矩阵

41. A = nx.adjacency_matrix(G1)

42. print(‘邻接矩阵:\n’,A.todense())

44. #关联矩阵

45. I = nx.incidence_matrix(G1)

46. print(’\n关联矩阵:\n’,I.todense())

48. #拉普拉斯矩阵

49. L=nx.laplacian_matrix(G1)

50. print(’\n拉普拉斯矩阵:\n’,L.todense())

52. #标准化的拉普拉斯矩阵

53. NL=nx.normalized_laplacian_matrix(G1)

54. print(’\n标准化的拉普拉斯矩阵:\n’,NL.todense())

56. #有向图拉普拉斯矩阵

57. DL=nx.directed_laplacian_matrix(G2)

58. print(’\n有向拉普拉斯矩阵:\n’,DL)

60. #拉普拉斯算子的特征值

61. LS=nx.laplacian_spectrum(G1)

62. print(’\n拉普拉斯算子的特征值:\n’,LS)

64. #邻接矩阵的特征值

65. AS=nx.adjacency_spectrum(G1)

66. print(’\n邻接矩阵的特征值:\n’,AS)

68. #无向图的代数连通性

69. AC=nx.algebraic_connectivity(G1)

70. print(’\n无向图的代数连通性:\n’,AC)

72. #图的光谱排序

73. SO=nx.spectral_ordering(G1)

74. print(’\n图的光谱排序:\n’,SO)

76. #两个矩阵的解释看:https://blog.csdn.net/Hanging_Gardens/article/details/55670356

77. 邻接矩阵:

78. [[0. 0. 0. 0. 5. 0. 0. 0. 6. ]

79. [0. 0. 0. 2. 0. 0. 0. 0. 0. ]

80. [0. 0. 0. 0. 0. 0.5 0.5 0. 0. ]

81. [0. 2. 0. 1. 1. 0. 0. 0. 0. ]

82. [5. 0. 0. 1. 0. 0. 0. 0. 7. ]

83. [0. 0. 0.5 0. 0. 0. 0.5 0. 0. ]

84. [0. 0. 0.5 0. 0. 0.5 0. 0. 0. ]

85. [0. 0. 0. 0. 0. 0. 0. 0. 0. ]

86. [6. 0. 0. 0. 7. 0. 0. 0. 0. ]]

88. 关联矩阵:

89. [[1. 1. 0. 0. 0. 0. 0. 0. 0.]

90. [0. 0. 1. 0. 0. 0. 0. 0. 0.]

91. [0. 0. 0. 1. 1. 0. 0. 0. 0.]

92. [0. 0. 1. 0. 0. 1. 0. 0. 0.]

93. [0. 1. 0. 0. 0. 1. 0. 1. 0.]

94. [0. 0. 0. 1. 0. 0. 0. 0. 1.]

95. [0. 0. 0. 0. 1. 0. 0. 0. 1.]

96. [0. 0. 0. 0. 0. 0. 0. 0. 0.]

97. [1. 0. 0. 0. 0. 0. 0. 1. 0.]]

99. 拉普拉斯矩阵:

100. [[11. 0. 0. 0. -5. 0. 0. 0. -6. ]

101. [ 0. 2. 0. -2. 0. 0. 0. 0. 0. ]

102. [ 0. 0. 1. 0. 0. -0.5 -0.5 0. 0. ]

103. [ 0. -2. 0. 3. -1. 0. 0. 0. 0. ]

104. [-5. 0. 0. -1. 13. 0. 0. 0. -7. ]

105. [ 0. 0. -0.5 0. 0. 1. -0.5 0. 0. ]

106. [ 0. 0. -0.5 0. 0. -0.5 1. 0. 0. ]

107. [ 0. 0. 0. 0. 0. 0. 0. 0. 0. ]

108. [-6. 0. 0. 0. -7. 0. 0. 0. 13. ]]

110. 标准化的拉普拉斯矩阵:

111. [[ 1. 0. 0. 0. -0.418 0. 0. 0. -0.502]

112. [ 0. 1. 0. -0.707 0. 0. 0. 0. 0. ]

113. [ 0. 0. 1. 0. 0. -0.5 -0.5 0. 0. ]

114. [ 0. -0.707 0. 0.75 -0.139 0. 0. 0. 0. ]

115. [-0.418 0. 0. -0.139 1. 0. 0. 0. -0.538]

116. [ 0. 0. -0.5 0. 0. 1. -0.5 0. 0. ]

117. [ 0. 0. -0.5 0. 0. -0.5 1. 0. 0. ]

118. [ 0. 0. 0. 0. 0. 0. 0. 0. 0. ]

119. [-0.502 0. 0. 0. -0.538 0. 0. 0. 1. ]]

121. 有向拉普拉斯矩阵:

122. [[ 0.889 -0.117 -0.029 -0.087 -0.319 -0.029 -0.029 -0.129 -0.242]

123. [-0.117 0.889 -0.026 -0.278 -0.051 -0.026 -0.026 -0.114 -0.056]

124. [-0.029 -0.026 0.994 -0.012 -0.009 -0.481 -0.481 -0.025 -0.01 ]

125. [-0.087 -0.278 -0.012 0.757 -0.097 -0.012 -0.012 -0.052 -0.006]

126. [-0.319 -0.051 -0.009 -0.097 0.994 -0.009 -0.009 -0.041 -0.434]

127. [-0.029 -0.026 -0.481 -0.012 -0.009 0.994 -0.481 -0.025 -0.01 ]

128. [-0.029 -0.026 -0.481 -0.012 -0.009 -0.481 0.994 -0.025 -0.01 ]

129. [-0.129 -0.114 -0.025 -0.052 -0.041 -0.025 -0.025 0.889 -0.045]

130. [-0.242 -0.056 -0.01 -0.006 -0.434 -0.01 -0.01 -0.045 0.994]]

132. 拉普拉斯算子的特征值:

133. [-1.436e-15 0.000e+00 4.610e-16 7.000e-01 1.500e+00 1.500e+00

134. 4.576e+00 1.660e+01 2.013e+01]

136. 邻接矩阵的特征值:

137. [12.068+0.000e+00j 2.588+0.000e+00j -7.219+0.000e+00j -4.925+0.000e+00j

138. -1.513+0.000e+00j 1. +0.000e+00j -0.5 +2.393e-17j -0.5 -2.393e-17j

139. 0. +0.000e+00j]

141. 无向图的代数连通性:

142. 0.0

144. 图的光谱排序:

145. [‘4’, ‘2’, ‘1’, ‘0’, ‘5’, ‘b’, ‘c’, ‘a’, ‘3’]