NetworkX系列教程(7)-对graph进行分析

小书匠Graph图论

graph构建完成后,对graph的连通等属性进行分析.

目录:

• 8.对图进行分析
  • 8.1连通子图
  • 8.2弱联通
  • 8.3强连通
  • 8.4子图
  • 8.5条件过滤

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注意:如果代码出现找不库,请返回第一个教程,把库文件导入.

8.对图进行分析

强连通：有向图中任意两点v1、v2间存在v1到v2的路径（path）及v2到v1的路径。
弱联通：将有向图的所有的有向边替换为无向边，所得到的图称为原图的基图。如果一个有向图的基图是连通图，则有向图是弱连通图。

8.1连通子图

1. #定义图的节点和边 
   

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

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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)] 
   

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4.  
   

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5. #定义graph 
   

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6. G = nx.Graph() 
   

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7. G.add_nodes_from(nodes) 
   

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8. G.add_weighted_edges_from(edges) 
   

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9.  
   

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10. #找到所有连通子图 
    

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11. print('connected_components of graph: ',list(nx.connected_components(G))) 
    

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12.  
    

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13. #显示该graph 
    

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14. nx.draw(G, with_labels=True, font_weight='bold') 
    

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15. plt.axis('on') 
    

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16. plt.xticks([]) 
    

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17. plt.yticks([]) 
    

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18. plt.show() 
    

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输出:

1. connected_components of graph: [{'a', 'b', 'c'}, {'4', '0', '5', '1', '2'}, {'3'}] 
   

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连通子图例子

8.2弱联通

1. #定义graph 
   

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2. G = nx.path_graph(4, create_using=nx.DiGraph()) 
   

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3. G.add_path([7, 8, 3]) 
   

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4. G.add_path([5, 6,9]) 
   

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5.  
   

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6. #找出所有的弱连通图 
   

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7. for c in nx.weakly_connected_components(G): 
   

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8. print(c) 
   

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9.  
   

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10. #由大到小的规模判断弱连通子图 
    

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11. print([len(c) for c in sorted(nx.weakly_connected_components(G), key=len, reverse=True)]) 
    

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12.  
    

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13. nx.draw(G, with_labels=True, font_weight='bold') 
    

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14. plt.axis('on') 
    

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15. plt.xticks([]) 
    

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16. plt.yticks([]) 
    

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17. plt.show() 
    

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输出:

1. {0, 1, 2, 3, 7, 8} 
   

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2. {9, 5, 6} 
   

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3. [6, 3] 
   

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弱联通例子

8.3强连通

1. G.clear() 
   

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2.  
   

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3. #定义图 
   

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4. G = nx.path_graph(4, create_using=nx.DiGraph()) 
   

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5. G.add_path([3, 8, 1]) 
   

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6.  
   

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7. #找出所有的强连通子图 
   

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8. con = nx.strongly_connected_components(G) 
   

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9. print(con,type(con),list(con)) 
   

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10.  
    

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11. #显示该图 
    

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12. nx.draw(G, with_labels=True, font_weight='bold') 
    

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13. plt.axis('on') 
    

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14. plt.xticks([]) 
    

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15. plt.yticks([]) 
    

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16. plt.show() 
    

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输出:

1. <generator object strongly_connected_components at 0x7fe0eefe9c50> <class 'generator'> [{8, 1, 2, 3}, {0}] 
   

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强连通例子

8.4子图

1. G.clear() 
   

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2.  
   

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3. #定义图 
   

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4. G = nx.DiGraph() 
   

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5. G.add_path([5, 6, 7, 8]) 
   

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6. #抽取图G的节点作为子图 
   

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7. sub_graph = G.subgraph([5, 6, 8]) 
   

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8.  
   

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9. plt.subplots(1,2,figsize=(15,5)) 
   

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10. #画原图 
    

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11. plt.subplot(121) 
    

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12. nx.draw(G, with_labels=True, font_weight='bold') 
    

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13. plt.title('原图',fontproperties=myfont) 
    

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14. plt.axis('on') 
    

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15. plt.xticks([]) 
    

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16. plt.yticks([]) 
    

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17.  
    

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18. #画子图 
    

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19. plt.subplot(122) 
    

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20. nx.draw(sub_graph, with_labels=True, font_weight='bold') 
    

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21. plt.title('子图',fontproperties=myfont) 
    

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22. plt.axis('on') 
    

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23. plt.xticks([]) 
    

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24. plt.yticks([]) 
    

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25.  
    

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26. plt.show() 
    

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子图例子

8.5条件过滤

1. #G.clear() 
   

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2.  
   

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3. #定义有向图 
   

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4. G = nx.DiGraph() 
   

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5. road_nodes = {'a':{'id':1}, 'b':{'id':1}, 'c':{'id':3}, 'd':{'id':4}} 
   

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6. road_edges = [('a', 'b'), ('a', 'c'), ('a', 'd'), ('b', 'd')] 
   

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7. G.add_nodes_from(road_nodes.items()) 
   

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8. G.add_edges_from(road_edges) 
   

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9.  
   

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10. #过滤函数 
    

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11. def flt_func_draw(): 
    

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12. flt_func = lambda d: d['id'] != 1 
    

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13. return flt_func 
    

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14.  
    

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15. plt.subplots(1,2,figsize=(15,5)) 
    

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16.  
    

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17. #画出原图 
    

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18. plt.subplot(121) 
    

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19. nx.draw(G, with_labels=True, font_weight='bold') 
    

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20. plt.title('过滤前',fontproperties=myfont) 
    

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21. plt.axis('on') 
    

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22. plt.xticks([]) 
    

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23. plt.yticks([]) 
    

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24.  
    

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25. #过滤原图得到子图 
    

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26. flt_func = flt_func_draw() 
    

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27. part_G = G.subgraph(n for n, d in G.nodes(data=True) if flt_func(d)) 
    

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28.  
    

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29. #画出子图 
    

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30. plt.subplot(122) 
    

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31. nx.draw(part_G, with_labels=True, font_weight='bold') 
    

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32. plt.title('过滤后',fontproperties=myfont) 
    

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33. plt.axis('on') 
    

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34. plt.xticks([]) 
    

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35. plt.yticks([]) 
    

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36.  
    

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37. plt.show() 
    

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条件过滤后的子图