python 解析网络包（一文读懂Python复杂网络分析库networkx）

作者 | yyl424525

来源 | CSDN博客

文章目录

1. 简介

• 安装

• 支持四种图

• 绘制网络图基本流程

2. Graph-无向图

节点

边

属性

有向图和无向图互转

3. DiGraph-有向图

• 一些精美的图例子

• 环形树状图

• 权重图

• Giant Component

• Random Geometric Graph 随机几何图

• 节点颜色渐变

• 边的颜色渐变

• Atlas

• 画个五角星

• Club

• 画一个多层感知机

• 绘制一个DNN结构图

• 一些图论算法

• 最短路径

4. 问题

• 一些其他神经网络绘制工具列表

5. 参考

1 简介

networkx是一个用Python语言开发的图论与复杂网络建模工具，内置了常用的图与复杂网络分析算法，可以方便的进行复杂网络数据分析、仿真建模等工作。

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>>> networkx.__version__

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：https://blog.csdn.net/fadai1993/article/details/82491657#2____linux_9

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 https://pypi.tuna.tsinghua.edu.cn/simple 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 matplotlib.pyplot as plt

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

4nx.draw(G) #绘制网络G

5plt.savefig("ba.png") #输出方式1: 将图像存为一个png格式的图片文件

6plt.show #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networkx.layout

• 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 matplotlib.pyplot 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

11

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

13plt.show

14

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, <networkx.classes.graph.Graph object at 0x7fdf7d0d2780>, 'g', 'e', 'h', 'b', 4, 6, 5, 'j', 'd']

18

19print('图中节点的个数', G.number_of_nodes)

20#图中节点的个数 20

21

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 matplotlib.pyplot as plt

3

4#添加边方法1

5

6F = nx.Graph # 创建无向图

7F.add_edge(11,12) #一次添加一条边

8

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

12

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

15

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(H.edges) #不能写作F.add_edges_from(H)

19

20nx.draw(F, with_labels=True)

21plt.show

22

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)]

26

27print('图中边的个数', F.number_of_edges)

28# 图中边的个数 12

29

30

31

32#删除边

33F.remove_edge(1,2)

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

35

36nx.draw(F, with_labels=True)

37plt.show

使用邻接迭代器遍历每一条边

1import networkx as nx

2import matplotlib.pyplot as plt

3

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)

19

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

21

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)

34

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

36

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

2

3import networkx as nx

4

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

6print(G.graph)

7

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

9print(G.graph)

10

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

12print(G.graph)

13

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

3

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

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

6# print(G.node(data=True)) #TypeError: 'dict' object is not callable

7print(G.node)

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

9

10

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

12print(G.node)

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

14

15

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

17print(G.node)

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

3

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

5G.add_edge(1,2,weight=10) #在添加边时分配属性

6print(G.edges(data=True))

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

8

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

10print(G.edges(data='len'))

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

12

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

14print(G.edges(data=True))

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

16

17

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

19print(G.edges(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

2

3H=DG.to_undirected

4#或者

5H=nx.Graph(DG)

6

7#无向图转化成有向图

8

9F = H.to_directed

10#或者

11F = nx.DiGraph(H)

3、DiGraph-有向图

1import networkx as nx

2import matplotlib.pyplot as plt

3

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')

12plt.savefig("youxiangtu.png")

13plt.show

1from __future__ import division

2import matplotlib.pyplot as plt

3import networkx as nx

4

5G = nx.generators.directed.random_k_out_graph(10, 3, 0.5)

6pos = nx.layout.spring_layout(G)

7

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)]

12

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=plt.cm.Blues, width=2)

17# set alpha value for each edge

18for i in range(M):

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

20

21ax = plt.gca

22ax.set_axis_off

23plt.savefig("directed.jpg")

24plt.show

一些精美的图例子

环形树状图

1import matplotlib.pyplot as plt

2import networkx as nx

3

4try:

5 import pygraphviz

6 from networkx.drawing.nx_agraph import graphviz_layout

7except ImportError:

8 try:

9 import pydot

10 from networkx.drawing.nx_pydot import graphviz_layout

11 except ImportError:

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

13 "PyGraphviz or pydot")

14

15G = nx.balanced_tree(3, 5)

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

17plt.figure(figsize=(8, 8))

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

19plt.axis('equal')

20plt.show

权重图

1import matplotlib.pyplot as plt

2import networkx as nx

3

4G = nx.Graph

5

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)

12

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]

15

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

17

18# nodes

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

20

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')

26

27# labels

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

29

30plt.axis('off')

31plt.savefig("weight.jpg")

32plt.show

Giant Component

1import math

3

4import matplotlib.pyplot as plt

5import networkx as nx

6

7try:

8 import pygraphviz

9 from networkx.drawing.nx_agraph import graphviz_layout

10 layout = graphviz_layout

11except ImportError:

12 try:

13 import pydot

14 from networkx.drawing.nx_pydot 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

21

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 = math.log(n) / float(n)

27

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

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

30

31region = 220 # for pylab 2x2 subplot layout

32plt.subplots_adjust(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 plt.subplot(region)

38 plt.title("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(nx.connected_component_subgraphs(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 )

60plt.show

Random Geometric Graph 随机几何图

1import matplotlib.pyplot as plt

2import networkx as nx

3

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')

7

8# find node near center (0.5,0.5)

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

17

18# color by path length from node near center

19p = dict(nx.single_source_shortest_path_length(G, ncenter))

20

21plt.figure(figsize=(8, 8))

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

23nx.draw_networkx_nodes(G, pos, nodelist=list(p.keys),

24 node_size=80,

25 node_color=list(p.values),

26 cmap=plt.cm.Reds_r)

27

28plt.xlim(-0.05, 1.05)

29plt.ylim(-0.05, 1.05)

30#plt.axis('off')

31plt.show

节点颜色渐变

1import networkx as nx

2import matplotlib.pyplot 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=plt.cm.Blues)

6plt.savefig("node.jpg")

7plt.show

边的颜色渐变

1import matplotlib.pyplot as plt

2import networkx as nx

3

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=plt.cm.Blues, with_labels=False)

9plt.show

Atlas

1import random

2

3try:

4 import pygraphviz

5 from networkx.drawing.nx_agraph import graphviz_layout

6except ImportError:

7 try:

8 import pydot

9 from networkx.drawing.nx_pydot import graphviz_layout

10 except ImportError:

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

12 "PyGraphviz or pydot.")

13

14import matplotlib.pyplot as plt

15

16import networkx as nx

17from networkx.algorithms.isomorphism.isomorph import graph_could_be_isomorphic as isomorphic

18from networkx.generators.atlas import graph_atlas_g

19

20

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 """

25

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)

34

35 # iterator of graphs of all connected components

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

37

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 nlist.append(G)

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

46 return UU

47

48

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

55

56

57if __name__ == '__main__':

58 G = atlas6

59

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

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

62 print(nx.number_connected_components(G), "connected components")

63

64 plt.figure(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 = (G.subgraph(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 )

79 plt.show

画个五角星

1import networkx as nx

2import matplotlib.pyplot 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 help(nx.drawing.layout) 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 )

21plt.savefig("star.jpg")

22plt.show

Club

1import matplotlib.pyplot as plt

2import networkx as nx

3import networkx.algorithms.bipartite as bipartite

4

5G = nx.davis_southern_women_graph

6women = G.graph['top']

7clubs = G.graph['bottom']

8

9print("Biadjacency matrix")

10print(bipartite.biadjacency_matrix(G, women, clubs))

11

12# project bipartite graph onto women nodes

13W = bipartite.projected_graph(G, women)

14print('')

15print("#Friends, Member")

16for w in women:

17 print('%d %s' % (W.degree(w), w))

18

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 = bipartite.weighted_projected_graph(G, women)

22print('')

23print("#Friend meetings, Member")

24for w in women:

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

26

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

28plt.savefig("club.jpg")

29plt.show

画一个多层感知机

1import matplotlib.pyplot 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]))

21

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(G.edges))],

29 width=3,

30 cmap=plt.cm.Dark2, # matplotlib的调色板，可以搜搜，很多颜色

31 edge_cmap=plt.cm.Blues

32 )

33plt.savefig("mlp.jpg")

34plt.show

绘制一个DNN结构图

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

2import networkx as nx

3import matplotlib.pyplot as plt

4

5# 创建DAG

6G = nx.DiGraph

7

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)

12

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)

36

37# 绘制DAG图

38plt.title('DNN for iris') #图片标题

39

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

49plt.show

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：

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

2import networkx as nx

3import matplotlib.pyplot as plt

4

5# 创建DAG

6G = nx.DiGraph

7

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)

12

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)

36

37# 指定绘制DAG图时每个顶点的位置

38pos = {

39 'v1':(-2,1.5),

40 'v2':(-2,0.5),

41 'v3':(-2,-0.5),

42 'v4':(-2,-1.5),

43 'v5':(-1,2),

44 'v6': (-1,1),

45 'v7':(-1,0),

46 'v8':(-1,-1),

47 'v9':(-1,-2),

48 'v10':(0,2.5),

49 'v11':(0,1.5),

50 'v12':(0,0.5),

51 'v13':(0,-0.5),

52 'v14':(0,-1.5),

53 'v15':(0,-2.5),

54 'v16':(1,1),

55 'v17':(1,0),

56 'v18':(1,-1),

57 'v19':(2,1),

58 'v20':(2,0),

59 'v21':(2,-1)

60 }

61# 绘制DAG图

62plt.title('DNN for iris') #图片标题

63plt.xlim(-2.2, 2.2) #设置X轴坐标范围

64plt.ylim(-3, 3) #设置Y轴坐标范围

65nx.draw(

66 G,

67 pos = pos, # 点的位置

68 node_color = 'red', # 顶点颜色

69 edge_color = 'black', # 边的颜色

70 with_labels = True, # 显示顶点标签

71 font_size =10, # 文字大小

72 node_size =300 # 顶点大小

73 )

74# 显示图片

75plt.show

可以看到，在代码中，通过pos字典已经规定好了每个神经元节点的位置。

接下来，需要对这个框架图进行更为细致地修改，需要修改的地方为：

• 去掉神经元节点的标签；

• 添加模型层的文字注释（比如Input layer）

其中，第二步的文字注释，我们借助opencv来完成。完整的Python代码如下：

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

2import cv2

3import networkx as nx

4import matplotlib.pyplot as plt

5

6# 创建DAG

7G = nx.DiGraph

8

9# 顶点列表

10vertex_list = ['v' str(i) for i in range(1, 22)]

11# 添加顶点

12G.add_nodes_from(vertex_list)

13

14# 边列表

15edge_list = [

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

31 ('v16','v19'),

32 ('v17','v20'),

33 ('v18','v21')

34 ]

35# 通过列表形式来添加边

36G.add_edges_from(edge_list)

37

38# 指定绘制DAG图时每个顶点的位置

39pos = {

40 'v1':(-2,1.5),

41 'v2':(-2,0.5),

42 'v3':(-2,-0.5),

43 'v4':(-2,-1.5),

44 'v5':(-1,2),

45 'v6': (-1,1),

46 'v7':(-1,0),

47 'v8':(-1,-1),

48 'v9':(-1,-2),

49 'v10':(0,2.5),

50 'v11':(0,1.5),

51 'v12':(0,0.5),

52 'v13':(0,-0.5),

53 'v14':(0,-1.5),

54 'v15':(0,-2.5),

55 'v16':(1,1),

56 'v17':(1,0),

57 'v18':(1,-1),

58 'v19':(2,1),

59 'v20':(2,0),

60 'v21':(2,-1)

61 }

62# 绘制DAG图

63plt.title('DNN for iris') #图片标题

64plt.xlim(-2.2, 2.2) #设置X轴坐标范围

65plt.ylim(-3, 3) #设置Y轴坐标范围

66nx.draw(

67 G,

68 pos = pos, # 点的位置

69 node_color = 'red', # 顶点颜色

70 edge_color = 'black', # 边的颜色

71 font_size =10, # 文字大小

72 node_size =300 # 顶点大小

73 )

74

75# 保存图片，图片大小为640*480

76plt.savefig('DNN_sketch.png')

77

78# 利用opencv模块对DNN框架添加文字注释

79

80# 读取图片

81imagepath = 'DNN_sketch.png'

82image = cv2.imread(imagepath, 1)

83

84# 输入层

85cv2.rectangle(image, (85, 130), (120, 360), (255,0,0), 2)

86cv2.putText(image, "Input Layer", (15, 390), 1, 1.5, (0, 255, 0), 2, 1)

87

88# 隐藏层

89cv2.rectangle(image, (190, 70), (360, 420), (255,0,0), 2)

90cv2.putText(image, "Hidden Layer", (210, 450), 1, 1.5, (0, 255, 0), 2, 1)

91

92# 输出层

93cv2.rectangle(image, (420, 150), (460, 330), (255,0,0), 2)

94cv2.putText(image, "Output Layer", (380, 360), 1, 1.5, (0, 255, 0), 2, 1)

95

96# sofrmax层

97cv2.rectangle(image, (530, 150), (570, 330), (255,0,0), 2)

98cv2.putText(image, "Softmax Func", (450, 130), 1, 1.5, (0, 0, 255), 2, 1)

99

100# 保存修改后的图片

101cv2.imwrite('DNN.png', image)

一些图论算法

最短路径

函数调用：

1dijkstra_path(G, source, target, weight=‘weight’) ————求最短路径

2dijkstra_path_length(G, source, target, weight=‘weight’) ————求最短距离

3

4import networkx as nx

5import pylab

6import numpy as np

7#自定义网络

8row=np.array([0,0,0,1,2,3,6])

9col=np.array([1,2,3,4,5,6,7])

10value=np.array([1,2,1,8,1,3,5])

11

12print('生成一个空的有向图')

13G=nx.DiGraph

14print('为这个网络添加节点...')

15for i in range(0,np.size(col) 1):

16 G.add_node(i)

17print('在网络中添加带权中的边...')

18for i in range(np.size(row)):

19 G.add_weighted_edges_from([(row[i],col[i],value[i])])

20

21print('给网路设置布局...')

22pos=nx.shell_layout(G)

23print('画出网络图像：')

24nx.draw(G,pos,with_labels=True, node_color='white', edge_color='red', node_size=400, alpha=0.5 )

25pylab.title('Self_Define Net',fontsize=15)

26pylab.show

27

28

29'''

30Shortest Path with dijkstra_path

31'''

32print('dijkstra方法寻找最短路径：')

33path=nx.dijkstra_path(G, source=0, target=7)

34print('节点0到7的路径：', path)

35print('dijkstra方法寻找最短距离：')

36distance=nx.dijkstra_path_length(G, source=0, target=7)

37print('节点0到7的距离为：', distance)

输出：

1生成一个空的有向图

2为这个网络添加节点...

3在网络中添加带权中的边...

4给网路设置布局...

5画出网络图像：

6dijkstra方法寻找最短路径：

7节点0到7的路径： [0, 3, 6, 7]

8dijkstra方法寻找最短距离：

9节点0到7的距离为： 9

问题

本人在pycharm中运行下列程序：

1import networkx as nx

2import matplotlib.pyplot as plt

3

4G = nx.Graph # 建立一个空的无向图G

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个节点挨个连接的无向图，所以有9条边

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

11

12nx.draw(G, with_labels=True)

13plt.show

发现在Pycharm下使用matploylib库绘制3D图的时候，在最后需要显示图像的时候，每当输入plt.show 都会报错

1plt.show

2/yyl/Python/3.6/lib/python/site-packages/matplotlib/figure.py:1743: UserWarning: This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.

3warnings.warn("This figure includes Axes that are not "

4...

5ValueError: max arg is an empty sequence

网上的解决方案：File -> Setting -> Tools -> Python Scientific中去掉对Show plots in tool window的勾选就好了

一些其他神经网络绘制工具列表

上面都是一些这个网络库使用的一点总结，更多内容可以参考下面的官方链接。

参考

官方教程：https://networkx.github.io/documentation/stable/_downloads/networkx_reference.pdf

官方网站：https://networkx.github.io/documentation/latest/index.html

官方githu博客：http://networkx.github.io/

用Python的networkx绘制精美网络图：https://blog.csdn.net/qq951127336/article/details/54586869

networkx整理：https://www.cnblogs.com/minglex/p/9205160.html

Networkx使用指南：https://blog.csdn.net/Zhili_wang/article/details/89368177

论文中绘制神经网络工具汇总：https://blog.csdn.net/WZZ18191171661/article/details/87886588

networkx Cytoscape构建及可视化网络图：https://www.jianshu.com/p/f62991aa1f8a

用python graphviz/networkx画目录结构树状图：https://blog.csdn.net/XiaoPANGXia/article/details/53043664

（*本文为 AI科技大本营转载文章，转载请联系原作者）

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