【virtual cd v9 3 0 1】专题一文读懂Python复杂网络分析库networkx

作者| yyl424525

来源| CSDN博客

文章列表

1.简介

安装

支持四种图形

绘制网络图的基本过程

2.图-无向图

节点

边缘

属性

有向图和无向图相互旋转

3.DiG raph-有向图形

精美绘画的几个例子。

圆形树视图

权重图

Giant Component

随机几何图形任意形状。

节点颜色渐变

边缘的颜色渐变

阿特拉斯

画五角形

Club

绘制多层识别器

绘制DNN结构

一些图论算法

最短路径

4.问题

一些不同的神经网络绘图工具列表

5.请参阅

1简介

Networkx是用python语言开发的图形和复杂的网络建模工具，它内置了常用的图形和复杂的网络分析算法，使分析复杂的网络数据、建模模拟等变得更加容易。

利用networkx可以以标准化和非标准化的数据格式存储网络、生成多种随机网络和经典网络、分析网络结构、建立网络模型、设计新的网络算法、进行网络绘制等。

networkx支持创建简单无向图、有向图和多重图（multigraph）；内置许多标准的图论算法，节点可为任意数据；支持任意的边值维度，功能丰富，简单易用。

networkx以图（graph）为基本数据结构。图既可以由程序生成，也可以来自在线数据源，还可以从文件与数据库中读取。

安装

安装的话，跟其他包的安装差不多，用的是anaconda就不用装了。其他就用pip install networkx。

查看版本：

1>>> import networkx

2>>> ne

3'1.11'

升级

1pip install –upgrade networkx

下面配合使用的一些库，可以选择性安装：

后面可能用到pygraphviz，安装方法如下（亲测有效）：

1sudo apt-get install graphviz

2sudo apt-get install graphviz libgraphviz-dev pkg-config

3sudo apt-get install python-pip python-virtualenv

4pip install pygraphviz

windows的安装参考这篇博客：

安装cv2：

1pip install opencv-python #安装非常慢，用下面的方式，从清华源下载

2pip3 install -i opencv-python

支持四种图

Graph：无多重边无向图
DiGraph：无多重边有向图
MultiGraph：有多重边无向图
MultiDiGraph：有多重边有向图

空图对象的创建方式

1import networkx as nx

2G=nx.Graph

3G=nx.DiGraph

4G=nx.MultiGraph

5G=nx.MultiDiGraph

6G.clear #清空图

绘制网络图基本流程

导入networkx，matplotlib包
建立网络
绘制网络 nx.draw
建立布局 pos = nx.spring_layout美化作用

最基本画图程序

1import import networkx as nx #导入networkx包

2import ma as plt

3G = nx.random_gra(100,1) #生成一个BA无标度网络G

4nx.draw(G) #绘制网络G

5("ba.png") #输出方式1: 将图像存为一个png格式的图片文件

6 #输出方式2: 在窗口中显示这幅图像

networkx 提供画图的函数

1draw（G，[pos,ax,hold]）

2draw_networkx(G，[pos,with_labels])

3draw_networkx_nodes(G,pos,[nodelist])绘制网络G的节点图

4draw_networkx_edges(G,pos[edgelist])绘制网络G的边图

5draw_networkx_edge_labels(G, pos[, …]) 绘制网络G的边图，边有label

6—有layout 布局画图函数的分界线—

7draw_circular(G, **kwargs) Draw the graph G with a circular layout.

8draw_random(G, **kwargs) Draw the graph G with a random layout.

9draw_spectral(G, **kwargs)Draw the graph G with a spectral layout.

10draw_spring(G, **kwargs)Draw the graph G with a spring layout.

11draw_shell(G, **kwargs) Draw networkx graph with shell layout.

12draw_graphviz(G[, prog])Draw networkx graph with graphviz layout.

networkx 画图函数里的一些参数

pos(dictionary, optional): 图像的布局，可选择参数；如果是字典元素，则节点是关键字，位置是对应的值。如果没有指明，则会是spring的布局；也可以使用其他类型的布局，具体可以查阅ne
arrows :布尔值，默认True; 对于有向图，如果是True则会画出箭头
with_labels: 节点是否带标签（默认为True）
ax：坐标设置，可选择参数；依照设置好的Matplotlib坐标画图
nodelist：一个列表，默认G.nodes; 给定节点
edgelist：一个列表，默认G.edges;给定边
node_size: 指定节点的尺寸大小(默认是300，单位未知，就是上图中那么大的点)
node_color: 指定节点的颜色 (默认是红色，可以用字符串简单标识颜色，例如’r’为红色，'b’为绿色等，具体可查看手册)，用“数据字典”赋值的时候必须对字典取值（.values()）后再赋值
node_shape: 节点的形状（默认是圆形，用字符串’o’标识，具体可查看手册）
alpha: 透明度 (默认是1.0，不透明，0为完全透明)
cmap：Matplotlib的颜色映射，默认None; 用来表示节点对应的强度
vmin,vmax：浮点数，默认None;节点颜色映射尺度的最大和最小值
linewidths：[None|标量|一列值];图像边界的线宽
width: 边的宽度 (默认为1.0)
edge_color: 边的颜色(默认为黑色)
edge_cmap：Matplotlib的颜色映射，默认None; 用来表示边对应的强度
edge_vmin,edge_vmax：浮点数，默认None;边的颜色映射尺度的最大和最小值
style: 边的样式(默认为实现，可选：solid|dashed|dotted,dashdot)
labels：字典元素，默认None;文本形式的节点标签
font_size: 节点标签字体大小 (默认为12)
font_color: 节点标签字体颜色（默认为黑色）
node_size：节点大小
font_weight：字符串，默认’normal’
font_family：字符串，默认’sans-serif’

布局指定节点排列形式

circular_layout：节点在一个圆环上均匀分布
random_layout：节点随机分布shell_layout：节点在同心圆上分布
spring_layout：用Fruchterman-Reingold算法排列节点，中心放射状分布
spectral_layout：根据图的拉普拉斯特征向量排列节点
布局也可用pos参数指定，例如，nx.draw(G, pos = spring_layout(G)) 这样指定了networkx上以中心放射状分布.

2 Graph-无向图

如果添加的节点和边是已经存在的，是不会报错的，NetworkX会自动忽略掉已经存在的边和节点的添加。

节点

常用函数

nodes(G)：在图节点上返回一个迭代器
number_of_nodes(G)：返回图中节点的数量
all_neighbors(graph, node)：返回图中节点的所有邻居
non_neighbors(graph, node)：返回图中没有邻居的节点
common_neighbors(G, u, v)：返回图中两个节点的公共邻居

1import networkx as nx

2import ma as plt

3G = nx.Graph # 建立一个空的无向图G

4#增加节点

5G.add_node('a') # 添加一个节点1

6G.add_nodes_from(['b', 'c', 'd', 'e']) # 加点集合

7G.add_cycle(['f', 'g', 'h', 'j']) # 加环

8H = nx.path_graph(10) # 返回由10个节点的无向图

9G.add_nodes_from(H) # 创建一个子图H加入G

10G.add_node(H) # 直接将图作为节点

12nx.draw(G, with_labels=True,node_color='red')

15#访问节点

16print('图中所有的节点', G.nodes)

17#图中所有的节点 [0, 1, 2, 3, 'a', 'c', 'f', 7, 8, 9, <ne object at 0x7fdf7d0d2780>, 'g', 'e', 'h', 'b', 4, 6, 5, 'j', 'd']

19print('图中节点的个数', G.number_of_nodes)

20#图中节点的个数 20

22#删除节点

23G.remove_node(1) #删除指定节点

24G.remove_nodes_from(['b','c','d','e']) #删除集合中的节点

边

常用函数

edges(G[, nbunch])：返回与nbunch中的节点相关的边的视图
number_of_edges(G)：返回图中边的数目
non_edges(graph)：返回图中不存在的边

1import networkx as nx

2import ma as plt

4#添加边方法1

6F = nx.Graph # 创建无向图

7F.add_edge(11,12) #一次添加一条边

9#添加边方法2

10e=(13,14) #e是一个元组

11F.add_edge(*e) #这是python中解包裹的过程

13#添加边方法3

14F.add_edges_from([(1,2),(1,3)]) #通过添加list来添加多条边

16H = nx.path_graph(10) #返回由10个节点的无向图

17#通过添加任何ebunch来添加边

18F.add_edges_from) #不能写作F.add_edges_from(H)

20nx.draw(F, with_labels=True)

23#访问边

24print('图中所有的边', F.edges)

25# 图中所有的边 [(0, 1), (1, 2), (1, 3), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), (11, 12), (13, 14)]

27print('图中边的个数', F.number_of_edges)

28# 图中边的个数 12

32#删除边

33F.remove_edge(1,2)

34F.remove_edges_from([(11,12), (13,14)])

36nx.draw(F, with_labels=True)

使用邻接迭代器遍历每一条边

1import networkx as nx

2import ma as plt

4#快速遍历每一条边，可以使用邻接迭代器实现，对于无向图，每一条边相当于两条有向边

5FG = nx.Graph

6FG.add_weighted_edges_from([(1,2,0.125), (1,3,0.75), (2,4,1.2), (3,4,0.275)])

7for n, nbrs in FG.adjacency_iter:

8 for nbr, eattr in nbrs.items:

9 data = eattr['weight']

10 print('(%d, %d, %0.3f)' % (n,nbr,data))

11 # (1, 2, 0.125)

12 # (1, 3, 0.750)

13 # (2, 1, 0.125)

14 # (2, 4, 1.200)

15 # (3, 1, 0.750)

16 # (3, 4, 0.275)

17 # (4, 2, 1.200)

18 # (4, 3, 0.275)

20print('***********************************')

22#筛选weight小于0.5的边：

23FG = nx.Graph

24FG.add_weighted_edges_from([(1,2,0.125), (1,3,0.75), (2,4,1.2), (3,4,0.275)])

25for n, nbrs in FG.adjacency_iter:

26 for nbr, eattr in nbrs.items:

27 data = eattr['weight']

28 if data < 0.5:

29 print('(%d, %d, %0.3f)' % (n,nbr,data))

30 # (1, 2, 0.125)

31 # (2, 1, 0.125)

32 # (3, 4, 0.275)

33 # (4, 3, 0.275)

35print('***********************************')

37#一种方便的访问所有边的方法:

38for u,v,d in FG.edges(data = 'weight'):

39 print((u,v,d))

40 # (1, 2, 0.125)

41 # (1, 3, 0.75)

42 # (2, 4, 1.2)

43 # (3, 4, 0.275)

属性

属性诸如weight,labels,colors,或者任何对象，都可以附加到图、节点或边上。

对于每一个图、节点和边都可以在关联的属性字典中保存一个（多个）键-值对。

默认情况下这些是一个空的字典，但是可以增加或者是改变这些属性。

图的属性

1#图的属性

3import networkx as nx

5G = nx.Graph(day='Monday') #可以在创建图时分配图的属性

6prin)

8G.graph['day'] = 'Friday' #也可以修改已有的属性

9prin)

11G.graph['name'] = 'time' #可以随时添加新的属性到图中

12prin)

14输出：

15{'day': 'Monday'}

16{'day': 'Friday'}

17{'day': 'Friday', 'name': 'time'}

节点的属性

1#节点的属性

2import networkx as nx

4G = nx.Graph(day='Monday')

5G.add_node(1, index='1th') #在添加节点时分配节点属性

6# prin(data=True)) #TypeError: 'dict' object is not callable

7prin)

8#{1: {'index': '1th'}}

11G.node[1]['index'] = '0th' #通过G.node来添加或修改属性

12prin)

13# {1: {'index': '0th'}}

16G.add_nodes_from([2,3], index='2/3th') #从集合中添加节点时分配属性

17prin)

18# {1: {'index': '0th'}, 2: {'index': '2/3th'}, 3: {'index': '2/3th'}}

边的属性

1#边的属性

2import networkx as nx

4G = nx.Graph(day='manday')

5G.add_edge(1,2,weight=10) #在添加边时分配属性

6prin(data=True))

7#[(1, 2, {'weight': 10})]

9G.add_edges_from([(1,3), (4,5)], len=22) #从集合中添加边时分配属性

10prin(data='len'))

11# [(1, 2, None), (1, 3, 22), (4, 5, 22)]

13G.add_edges_from([(3,4,{'hight':10}),(1,4,{'high':'unknow'})])

14prin(data=True))

15# [(1, 2, {'weight': 10}), (1, 3, {'len': 22}), (1, 4, {'high': 'unknow'}), (3, 4, {'hight': 10}), (4, 5, {'len': 22})]

18G[1][2]['weight'] = 100000 #通过G来添加或修改属性

19prin(data=True))

20# [(1, 2, {'weight': 100000}), (1, 3, {'len': 22}), (1, 4, {'high': 'unknow'}), (3, 4, {'hight': 10}), (4, 5, {'len': 22})]

有向图和无向图互转

有向图和多重图的基本操作与无向图一致。

无向图与有向图之间可以相互转换，转化方法如下：

1#有向图转化成无向图

3H=DG.to_undirected

4#或者

5H=nx.Graph(DG)

7#无向图转化成有向图

9F = H.to_directed

10#或者

11F = nx.DiGraph(H)

3、DiGraph-有向图

1import networkx as nx

2import ma as plt

4G = nx.DiGraph

5G.add_node(1)

6G.add_node(2)

7G.add_nodes_from([3,4,5,6])

8G.add_cycle([1,2,3,4])

9G.add_edge(1,3)

10G.add_edges_from([(3,5),(3,6),(6,7)])

11nx.draw(G,node_color = 'red')

12("youxiang;)

1from __future__ import division

2import ma as plt

3import networkx as nx

5G = nx.genera(10, 3, 0.5)

6pos = nx.layout.spring_layout(G)

8node_sizes = [3 + 10 * i for i in range(len(G))]

9M = G.number_of_edges

10edge_colors = range(2, M + 2)

11edge_alphas = [(5 + i) / (M + 4) for i in range(M)]

13nodes = nx.draw_networkx_nodes(G, pos, node_size=node_sizes, node_color='blue')

14edges = nx.draw_networkx_edges(G, pos, node_size=node_sizes, arrowstyle='->',

15 arrowsize=10, edge_color=edge_colors,

16 edge_cmap=, width=2)

17# set alpha value for each edge

18for i in range(M):

19 edges[i].set_alpha(edge_alphas[i])

21ax =

22ax.set_axis_off

23("direc;)

一些精美的图例子

环形树状图

1import ma as plt

2import networkx as nx

4try:

5 import pygraphviz

6 from ne import graphviz_layout

7except ImportError:

8 try:

9 import pydot

10 from ne import graphviz_layout

11 except ImportError:

12 raise ImportError("This example needs Graphviz and either "

13 "PyGraphviz or pydot")

15G = nx.balanced_tree(3, 5)

16pos = graphviz_layout(G, prog='twopi', args='')

17(figsize=(8, 8))

18nx.draw(G, pos, node_size=20, alpha=0.5, node_color="blue", with_labels=False)

19('equal')

权重图

1import ma as plt

2import networkx as nx

4G = nx.Graph

6G.add_edge('a', 'b', weight=0.6)

7G.add_edge('a', 'c', weight=0.2)

8G.add_edge('c', 'd', weight=0.1)

9G.add_edge('c', 'e', weight=0.7)

10G.add_edge('c', 'f', weight=0.9)

11G.add_edge('a', 'd', weight=0.3)

13elarge = [(u, v) for (u, v, d) in G.edges(data=True) if d['weight'] > 0.5]

14esmall = [(u, v) for (u, v, d) in G.edges(data=True) if d['weight'] <= 0.5]

16pos = nx.spring_layout(G) # positions for all nodes

18# nodes

19nx.draw_networkx_nodes(G, pos, node_size=700)

21# edges

22nx.draw_networkx_edges(G, pos, edgelist=elarge,

23 width=6)

24nx.draw_networkx_edges(G, pos, edgelist=esmall,

25 width=6, alpha=0.5, edge_color='b', style='dashed')

27# labels

28nx.draw_networkx_labels(G, pos, font_size=20, font_family='sans-serif')

30('off')

31("weig;)

Giant Component

1import math

4import ma as plt

5import networkx as nx

7try:

8 import pygraphviz

9 from ne import graphviz_layout

10 layout = graphviz_layout

11except ImportError:

12 try:

13 import pydot

14 from ne import graphviz_layout

15 layout = graphviz_layout

16 except ImportError:

17 print("PyGraphviz and pydot not found;n"

18 "drawing with spring layout;n"

19 "will be slow.")

20 layout = nx.spring_layout

22n = 150 # 150 nodes

23# p value at which giant component (of size log(n) nodes) is expected

24p_giant = 1.0 / (n – 1)

25# p value at which graph is expected to become completely connected

26p_conn = ma(n) / float(n)

28# the following range of p values should be close to the threshold

29pvals = [0.003, 0.006, 0.008, 0.015]

31region = 220 # for pylab 2×2 subplot layout

32(left=0, right=1, bottom=0, top=0.95, wspace=0.01, hspace=0.01)

33for p in pvals:

34 G = nx.binomial_graph(n, p)

35 pos = layout(G)

36 region += 1

37 (region)

38 ("p = %6.3f" % (p))

39 nx.draw(G, pos,

40 with_labels=False,

41 node_size=10

42 )

43 # identify largest connected component

44 Gcc = sorted(G), key=len, reverse=True)

45 G0 = Gcc[0]

46 nx.draw_networkx_edges(G0, pos,

47 with_labels=False,

48 edge_color='r',

49 width=6.0

50 )

51 # show other connected components

52 for Gi in Gcc[1:]:

53 if len(Gi) > 1:

54 nx.draw_networkx_edges(Gi, pos,

55 with_labels=False,

56 edge_color='r',

57 alpha=0.3,

58 width=5.0

59 )

Random Geometric Graph 随机几何图

1import ma as plt

2import networkx as nx

4G = nx.random_geometric_graph(200, 0.125)

5# position is stored as node attribute data for random_geometric_graph

6pos = nx.get_node_attributes(G, 'pos')

8# find node near center )

9dmin = 1

10ncenter = 0

11for n in pos:

12 x, y = pos[n]

13 d = (x – 0.5)**2 + (y – 0.5)**2

14 if d < dmin:

15 ncenter = n

16 dmin = d

18# color by path length from node near center

19p = dic(G, ncenter))

21(figsize=(8, 8))

22nx.draw_networkx_edges(G, pos, nodelist=[ncenter], alpha=0.4)

23nx.draw_networkx_nodes(G, pos, nodelist=li),

24 node_size=80,

25 node_color=li),

26 cmap=)

28, 1.05)

29, 1.05)

30#('off')

节点颜色渐变

1import networkx as nx

2import ma as plt

3G = nx.cycle_graph(24)

4pos = nx.spring_layout(G, iterations=200)

5nx.draw(G, pos, node_color=range(24), node_size=800, cmap=)

6("node.jpg")

边的颜色渐变

1import ma as plt

2import networkx as nx

4G = nx.star_graph(20)

5pos = nx.spring_layout(G) #布局为中心放射状

6colors = range(20)

7nx.draw(G, pos, node_color='#A0CBE2', edge_color=colors,

8 width=4, edge_cmap=, with_labels=False)

Atlas

1import random

3try:

4 import pygraphviz

5 from ne import graphviz_layout

6except ImportError:

7 try:

8 import pydot

9 from ne import graphviz_layout

10 except ImportError:

11 raise ImportError("This example needs Graphviz and either "

12 "PyGraphviz or pydot.")

14import ma as plt

16import networkx as nx

17from ne import graph_could_be_isomorphic as isomorphic

18from ne import graph_atlas_g

21 def atlas6:

22 """ Return the atlas of all connected graphs of 6 nodes or less.

23 Attempt to check for isomorphisms and remove.

24 """

26 Atlas = graph_atlas_g[0:208] # 208

27 # remove isolated nodes, only connected graphs are left

28 U = nx.Graph # graph for union of all graphs in atlas

29 for G in Atlas:

30 zerodegree = [n for n in G if G.degree(n) == 0]

31 for n in zerodegree:

32 G.remove_node(n)

33 U = nx.disjoint_union(U, G)

35 # iterator of graphs of all connected components

36 C = (c) for c in nx.connected_components(U))

38 UU = nx.Graph

39 # do quick isomorphic-like check, not a true isomorphism checker

40 nlist = # list of nonisomorphic graphs

41 for G in C:

42 # check against all nonisomorphic graphs so far

43 if not iso(G, nlist):

44 nli(G)

45 UU = nx.disjoint_union(UU, G) # union the nonisomorphic graphs

46 return UU

49 def iso(G1, glist):

50 """Quick and dirty nonisomorphism checker used to check isomorphisms."""

51 for G2 in glist:

52 if isomorphic(G1, G2):

53 return True

54 return False

57if __name__ == '__main__':

58 G = atlas6

60 print("graph has %d nodes with %d edges"

61 % (G), nx.number_of_edges(G)))

62 prin(G), "connected components")

64 (1, figsize=(8, 8))

65 # layout graphs with positions using graphviz neato

66 pos = graphviz_layout(G, prog="neato")

67 # color nodes the same in each connected subgraph

68 C = (c) for c in nx.connected_components(G))

69 for g in C:

70 c = [random.random()] * nx.number_of_nodes(g) # random color…

71 nx.draw(g,

72 pos,

73 node_size=40,

74 node_color=c,

75 vmin=0.0,

76 vmax=1.0,

77 with_labels=False

78 )

画个五角星

1import networkx as nx

2import ma as plt

3#画图！

4G=nx.Graph

5G.add_node(1)

6G.add_nodes_from([2,3,4,5])

7for i in range(5):

8 for j in range(i):

9 if (abs(i-j) not in (1,4)):

10 G.add_edge(i+1, j+1)

11nx.draw(G,

12 with_labels=True, #这个选项让节点有名称

13 edge_color='b', # b stands for blue!

14 pos=nx.circular_layout(G), # 这个是选项选择点的排列方式，具体可以用 hel) 查看

15 # 主要有spring_layout (default), random_layout, circle_layout, shell_layout

16 # 这里是环形排布，还有随机排列等其他方式

17 node_color='r', # r = red

18 node_size=1000, # 节点大小

19 width=3, # 边的宽度

20 )

21(";)

Club

1import ma as plt

2import networkx as nx

3import ne as bipartite

5G = nx.davis_southern_women_graph

6women = G.graph['top']

7clubs = G.graph['bottom']

9print("Biadjacency matrix")

10prin(G, women, clubs))

12# project bipartite graph onto women nodes

13W = bi(G, women)

14print('')

15print("#Friends, Member")

16for w in women:

17 print('%d %s' % (w), w))

19# project bipartite graph onto women nodes keeping number of co-occurence

20# the degree computed is weighted and counts the total number of shared contacts

21W = bi(G, women)

22print('')

23print("#Friend meetings, Member")

24for w in women:

25 print('%d %s' % (w, weight='weight'), w))

27nx.draw(G,node_color="red")

28("club.jpg")

画一个多层感知机

1import ma as plt

2import networkx as nx

3left, right, bottom, top, layer_sizes = .1, .9, .1, .9, [4, 7, 7, 2]

4# 网络离上下左右的距离

5# layter_sizes可以自己调整

6import random

7G = nx.Graph

8v_spacing = (top – bottom)/float(max(layer_sizes))

9h_spacing = (right – left)/float(len(layer_sizes) – 1)

10node_count = 0

11for i, v in enumerate(layer_sizes):

12 layer_top = v_spacing*(v-1)/2. + (top + bottom)/2.

13 for j in range(v):

14 G.add_node(node_count, pos=(left + i*h_spacing, layer_top – j*v_spacing))

15 node_count += 1

16# 这上面的数字调整我想了好半天，汗

17for x, (left_nodes, right_nodes) in enumerate(zip(layer_sizes[:-1], layer_sizes[1:])):

18 for i in range(left_nodes):

19 for j in range(right_nodes):

20 G.add_edge(i+sum(layer_sizes[:x]), j+sum(layer_sizes[:x+1]))

22pos=nx.get_node_attributes(G,'pos')

23# 把每个节点中的位置pos信息导出来

24nx.draw(G, pos,

25 node_color=range(node_count),

26 with_labels=True,

27 node_size=200,

28 edge_color=[random.random() for i in range(len))],

29 width=3,

30 cmap=, # matplotlib的调色板，可以搜搜，很多颜色

31 edge_cmap=

32 )

33("mlp.jpg")

绘制一个DNN结构图

1# -*- coding:utf-8 -*-

2import networkx as nx

3import ma as plt

5# 创建DAG

6G = nx.DiGraph

8# 顶点列表

9vertex_list = ['v'+str(i) for i in range(1, 22)]

10# 添加顶点

11G.add_nodes_from(vertex_list)

13# 边列表

14edge_list = [

15 ('v1', 'v5'), ('v1', 'v6'), ('v1', 'v7'),('v1', 'v8'),('v1', 'v9'),

16 ('v2', 'v5'), ('v2', 'v6'), ('v2', 'v7'),('v2', 'v8'),('v2', 'v9'),

17 ('v3', 'v5'), ('v3', 'v6'), ('v3', 'v7'),('v3', 'v8'),('v3', 'v9'),

18 ('v4', 'v5'), ('v4', 'v6'), ('v4', 'v7'),('v4', 'v8'),('v4', 'v9'),

19 ('v5','v10'),('v5','v11'),('v5','v12'),('v5','v13'),('v5','v14'),('v5','v15'),

20 ('v6','v10'),('v6','v11'),('v6','v12'),('v6','v13'),('v6','v14'),('v6','v15'),

21 ('v7','v10'),('v7','v11'),('v7','v12'),('v7','v13'),('v7','v14'),('v7','v15'),

22 ('v8','v10'),('v8','v11'),('v8','v12'),('v8','v13'),('v8','v14'),('v8','v15'),

23 ('v9','v10'),('v9','v11'),('v9','v12'),('v9','v13'),('v9','v14'),('v9','v15'),

24 ('v10','v16'),('v10','v17'),('v10','v18'),

25 ('v11','v16'),('v11','v17'),('v11','v18'),

26 ('v12','v16'),('v12','v17'),('v12','v18'),

27 ('v13','v16'),('v13','v17'),('v13','v18'),

28 ('v14','v16'),('v14','v17'),('v14','v18'),

29 ('v15','v16'),('v15','v17'),('v15','v18'),

30 ('v16','v19'),

31 ('v17','v20'),

32 ('v18','v21')

33 ]

34# 通过列表形式来添加边

35G.add_edges_from(edge_list)

37# 绘制DAG图

38('DNN for iris') #图片标题

40nx.draw(

41 G,

42 node_color = 'red', # 顶点颜色

43 edge_color = 'black', # 边的颜色

44 with_labels = True, # 显示顶点标签

45 font_size =10, # 文字大小

46 node_size =300 # 顶点大小

47 )

48# 显示图片

可以看到，在代码中已经设置好了这22个神经元以及它们之间的连接情况，但绘制出来的结构如却是这样的：

这显然不是想要的结果，因为各神经的连接情况不明朗，而且很多神经都挤在了一起，看不清楚。之所以出现这种情况，是因为没有给神经元设置坐标，导致每个神经元都是随机放置的。

接下来，引入坐标机制，即设置好每个神经元节点的坐标，使得它们的位置能够按照事先设置好的来放置，其Python代码如下：