NetworkX系列教程(7)-對graph進行分析

小書匠 Graph 圖論

graph構建完成后,對graph的連通等屬性進行分析.

目錄:

• 8.對圖進行分析
  • 8.1連通子圖
  • 8.2弱聯通
  • 8.3強連通
  • 8.4子圖
  • 8.5條件過濾

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注意:如果代碼出現找不庫,請返回第一個教程,把庫文件導入.

8.對圖進行分析

強連通：有向圖中任意兩點v1、v2間存在v1到v2的路徑（path）及v2到v1的路徑。
弱聯通：將有向圖的所有的有向邊替換為無向邊，所得到的圖稱為原圖的基圖。如果一個有向圖的基圖是連通圖，則有向圖是弱連通圖。

8.1連通子圖

1. #定義圖的節點和邊 
   

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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. #定義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. #找到所有連通子圖 
    

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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. #顯示該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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輸出:

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

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連通子圖例子

8.2弱聯通

1. #定義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. #找出所有的弱連通圖 
   

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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. #由大到小的規模判斷弱連通子圖 
    

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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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輸出:

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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弱聯通例子

8.3強連通

1. G.clear() 
   

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2.  
   

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3. #定義圖 
   

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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. #找出所有的強連通子圖 
   

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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. #顯示該圖 
    

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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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輸出:

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

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強連通例子

8.4子圖

1. G.clear() 
   

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2.  
   

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3. #定義圖 
   

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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. #抽取圖G的節點作為子圖 
   

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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. #畫原圖 
    

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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('原圖',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. #畫子圖 
    

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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('子圖',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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子圖例子

8.5條件過濾

1. #G.clear() 
   

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2.  
   

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3. #定義有向圖 
   

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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. #過濾函數 
    

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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. #畫出原圖 
    

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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('過濾前',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. #過濾原圖得到子圖 
    

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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. #畫出子圖 
    

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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('過濾后',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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條件過濾后的子圖