python复杂网络分析库networkx

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：

>>> import networkx
>>> networkx.__version__
'1.11'

升级

pip 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）：

sudo apt-get install graphviz
sudo apt-get install graphviz libgraphviz-dev pkg-config
sudo apt-get install python-pip python-virtualenv
pip 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：

pip install opencv-python #安装非常慢，用下面的方式，从清华源下载
pip3 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

import networkx as nx
G=nx.Graph()
G=nx.DiGraph()
G=nx.MultiGraph()
G=nx.MultiDiGraph()
G.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
 
import import networkx as nx             #导入networkx包
import matplotlib.pyplot as plt 
G = nx.random_graphs.barabasi_albert_graph(100,1)   #生成一个BA无标度网络G
nx.draw(G)                               #绘制网络G
plt.savefig("ba.png")           #输出方式1: 将图像存为一个png格式的图片文件
plt.show()                            #输出方式2: 在窗口中显示这幅图像 

networkx 提供画图的函数

• draw（G，[pos,ax,hold]）
• draw_networkx(G，[pos,with_labels])
• draw_networkx_nodes(G,pos,[nodelist])绘制网络G的节点图
• draw_networkx_edges(G,pos[edgelist])绘制网络G的边图
• draw_networkx_edge_labels(G, pos[, …]) 绘制网络G的边图，边有label
  —有layout 布局画图函数的分界线—
• draw_circular(G, **kwargs) Draw the graph G with a circular layout.
• draw_random(G, **kwargs) Draw the graph G with a random layout.
• draw_spectral(G, **kwargs)Draw the graph G with a spectral layout.
• draw_spring(G, **kwargs)Draw the graph G with a spring layout.
• draw_shell(G, **kwargs) Draw networkx graph with shell layout.
• draw_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

import networkx as nx
import matplotlib.pyplot as plt

G = nx.Graph()  # 建立一个空的无向图G

#增加节点
G.add_node('a')  # 添加一个节点1
G.add_nodes_from(['b', 'c', 'd', 'e'])  # 加点集合
G.add_cycle(['f', 'g', 'h', 'j'])  # 加环
H = nx.path_graph(10)  # 返回由10个节点的无向图
G.add_nodes_from(H)  # 创建一个子图H加入G
G.add_node(H)  # 直接将图作为节点

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

#访问节点
print('图中所有的节点', G.nodes())
#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']

print('图中节点的个数', G.number_of_nodes())
#图中节点的个数 20

#删除节点
G.remove_node(1)    #删除指定节点
G.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

import networkx as nx
import matplotlib.pyplot as plt

#添加边方法1

F = nx.Graph() # 创建无向图
F.add_edge(11,12)   #一次添加一条边

#添加边方法2
e=(13,14)        #e是一个元组
F.add_edge(*e) #这是python中解包裹的过程

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

H = nx.path_graph(10)          #返回由10个节点的无向图
#通过添加任何ebunch来添加边
F.add_edges_from(H.edges()) #不能写作F.add_edges_from(H)

nx.draw(F, with_labels=True)
plt.show()

#访问边
print('图中所有的边', F.edges())
# 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)]

print('图中边的个数', F.number_of_edges()) 
# 图中边的个数 12



#删除边
F.remove_edge(1,2)
F.remove_edges_from([(11,12), (13,14)])

nx.draw(F, with_labels=True)
plt.show()

使用邻接迭代器遍历每一条边

import networkx as nx
import matplotlib.pyplot as plt

#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
FG = nx.Graph()
FG.add_weighted_edges_from([(1,2,0.125), (1,3,0.75), (2,4,1.2), (3,4,0.275)])
for n, nbrs in FG.adjacency_iter():
    for nbr, eattr in nbrs.items():
        data = eattr['weight']
        print('(%d, %d, %0.3f)' % (n,nbr,data))
        # (1, 2, 0.125)
        # (1, 3, 0.750)
        # (2, 1, 0.125)
        # (2, 4, 1.200)
        # (3, 1, 0.750)
        # (3, 4, 0.275)
        # (4, 2, 1.200)
        # (4, 3, 0.275)

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

#筛选weight小于0.5的边：
FG = nx.Graph()
FG.add_weighted_edges_from([(1,2,0.125), (1,3,0.75), (2,4,1.2), (3,4,0.275)])
for n, nbrs in FG.adjacency_iter():
    for nbr, eattr in nbrs.items():
        data = eattr['weight']
        if data < 0.5:
            print('(%d, %d, %0.3f)' % (n,nbr,data))
            # (1, 2, 0.125)
            # (2, 1, 0.125)
            # (3, 4, 0.275)
            # (4, 3, 0.275)
            
print('***********************************')

#一种方便的访问所有边的方法:
for u,v,d in FG.edges(data = 'weight'):
    print((u,v,d))
    # (1, 2, 0.125)
    # (1, 3, 0.75)
    # (2, 4, 1.2)
    # (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

#图的属性

import networkx as nx

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

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

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

输出：
{'day': 'Monday'}
{'day': 'Friday'}
{'day': 'Friday', 'name': 'time'}

节点的属性

#节点的属性
import networkx as nx

G = nx.Graph(day='Monday')
G.add_node(1, index='1th')             #在添加节点时分配节点属性
# print(G.node(data=True))  #TypeError: 'dict' object is not callable
print(G.node) 
#{1: {'index': '1th'}}


G.node[1]['index'] = '0th'             #通过G.node[][]来添加或修改属性
print(G.node)
# {1: {'index': '0th'}}


G.add_nodes_from([2,3], index='2/3th') #从集合中添加节点时分配属性
print(G.node)
# {1: {'index': '0th'}, 2: {'index': '2/3th'}, 3: {'index': '2/3th'}}

边的属性

#边的属性
import networkx as nx

G = nx.Graph(day='manday')
G.add_edge(1,2,weight=10)                    #在添加边时分配属性
print(G.edges(data=True))
#[(1, 2, {'weight': 10})]

G.add_edges_from([(1,3), (4,5)], len=22)     #从集合中添加边时分配属性
print(G.edges(data='len'))
# [(1, 2, None), (1, 3, 22), (4, 5, 22)]

G.add_edges_from([(3,4,{'hight':10}),(1,4,{'high':'unknow'})])
print(G.edges(data=True))
# [(1, 2, {'weight': 10}), (1, 3, {'len': 22}), (1, 4, {'high': 'unknow'}), (3, 4, {'hight': 10}), (4, 5, {'len': 22})]


G[1][2]['weight'] = 100000                   #通过G[][][]来添加或修改属性
print(G.edges(data=True))
# [(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：

#有向图转化成无向图

H=DG.to_undirected()
#或者
H=nx.Graph(DG)

#无向图转化成有向图

F = H.to_directed()
#或者
F = nx.DiGraph(H)

3 DiGraph-有向图

import networkx as nx
import matplotlib.pyplot as plt

G = nx.DiGraph()
G.add_node(1)
G.add_node(2)
G.add_nodes_from([3,4,5,6])
G.add_cycle([1,2,3,4])
G.add_edge(1,3)
G.add_edges_from([(3,5),(3,6),(6,7)])
nx.draw(G,node_color = 'red')
plt.savefig("youxiangtu.png")
plt.show()

from __future__ import division
import matplotlib.pyplot as plt
import networkx as nx

G = nx.generators.directed.random_k_out_graph(10, 3, 0.5)
pos = nx.layout.spring_layout(G)

node_sizes = [3 + 10 * i for i in range(len(G))]
M = G.number_of_edges()
edge_colors = range(2, M + 2)
edge_alphas = [(5 + i) / (M + 4) for i in range(M)]

nodes = nx.draw_networkx_nodes(G, pos, node_size=node_sizes, node_color='blue')
edges = nx.draw_networkx_edges(G, pos, node_size=node_sizes, arrowstyle='->',
                               arrowsize=10, edge_color=edge_colors,
                               edge_cmap=plt.cm.Blues, width=2)
# set alpha value for each edge
for i in range(M):
    edges[i].set_alpha(edge_alphas[i])

ax = plt.gca()
ax.set_axis_off()
plt.savefig("directed.jpg")
plt.show()

一些精美的图例子

环形树状图

import matplotlib.pyplot as plt
import networkx as nx

try:
    import pygraphviz
    from networkx.drawing.nx_agraph import graphviz_layout
except ImportError:
    try:
        import pydot
        from networkx.drawing.nx_pydot import graphviz_layout
    except ImportError:
        raise ImportError("This example needs Graphviz and either "
                          "PyGraphviz or pydot")

G = nx.balanced_tree(3, 5)
pos = graphviz_layout(G, prog='twopi', args='')
plt.figure(figsize=(8, 8))
nx.draw(G, pos, node_size=20, alpha=0.5, node_color="blue", with_labels=False)
plt.axis('equal')
plt.show()

权重图

import matplotlib.pyplot as plt
import networkx as nx

G = nx.Graph()

G.add_edge('a', 'b', weight=0.6)
G.add_edge('a', 'c', weight=0.2)
G.add_edge('c', 'd', weight=0.1)
G.add_edge('c', 'e', weight=0.7)
G.add_edge('c', 'f', weight=0.9)
G.add_edge('a', 'd', weight=0.3)

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

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

# nodes
nx.draw_networkx_nodes(G, pos, node_size=700)

# edges
nx.draw_networkx_edges(G, pos, edgelist=elarge,
                       width=6)
nx.draw_networkx_edges(G, pos, edgelist=esmall,
                       width=6, alpha=0.5, edge_color='b', style='dashed')

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

plt.axis('off')
plt.savefig("weight.jpg")
plt.show()

Giant Component

import math

import matplotlib.pyplot as plt
import networkx as nx

try:
    import pygraphviz
    from networkx.drawing.nx_agraph import graphviz_layout
    layout = graphviz_layout
except ImportError:
    try:
        import pydot
        from networkx.drawing.nx_pydot import graphviz_layout
        layout = graphviz_layout
    except ImportError:
        print("PyGraphviz and pydot not found;\n"
              "drawing with spring layout;\n"
              "will be slow.")
        layout = nx.spring_layout


n = 150  # 150 nodes
# p value at which giant component (of size log(n) nodes) is expected
p_giant = 1.0 / (n - 1)
# p value at which graph is expected to become completely connected
p_conn = math.log(n) / float(n)

# the following range of p values should be close to the threshold
pvals = [0.003, 0.006, 0.008, 0.015]

region = 220  # for pylab 2x2 subplot layout
plt.subplots_adjust(left=0, right=1, bottom=0, top=0.95, wspace=0.01, hspace=0.01)
for p in pvals:
    G = nx.binomial_graph(n, p)
    pos = layout(G)
    region += 1
    plt.subplot(region)
    plt.title("p = %6.3f" % (p))
    nx.draw(G, pos,
            with_labels=False,
            node_size=10
           )
    # identify largest connected component
    Gcc = sorted(nx.connected_component_subgraphs(G), key=len, reverse=True)
    G0 = Gcc[0]
    nx.draw_networkx_edges(G0, pos,
                           with_labels=False,
                           edge_color='r',
                           width=6.0
                          )
    # show other connected components
    for Gi in Gcc[1:]:
        if len(Gi) > 1:
            nx.draw_networkx_edges(Gi, pos,
                                   with_labels=False,
                                   edge_color='r',
                                   alpha=0.3,
                                   width=5.0
                                  )
plt.show()

Random Geometric Graph 随机几何图

import matplotlib.pyplot as plt
import networkx as nx

G = nx.random_geometric_graph(200, 0.125)
# position is stored as node attribute data for random_geometric_graph
pos = nx.get_node_attributes(G, 'pos')

# find node near center (0.5,0.5)
dmin = 1
ncenter = 0
for n in pos:
    x, y = pos[n]
    d = (x - 0.5)**2 + (y - 0.5)**2
    if d < dmin:
        ncenter = n
        dmin = d

# color by path length from node near center
p = dict(nx.single_source_shortest_path_length(G, ncenter))

plt.figure(figsize=(8, 8))
nx.draw_networkx_edges(G, pos, nodelist=[ncenter], alpha=0.4)
nx.draw_networkx_nodes(G, pos, nodelist=list(p.keys()),
                       node_size=80,
                       node_color=list(p.values()),
                       cmap=plt.cm.Reds_r)

plt.xlim(-0.05, 1.05)
plt.ylim(-0.05, 1.05)
#plt.axis('off')
plt.show()

节点颜色渐变

import networkx as nx
import matplotlib.pyplot as plt
G = nx.cycle_graph(24)
pos = nx.spring_layout(G, iterations=200)
nx.draw(G, pos, node_color=range(24), node_size=800, cmap=plt.cm.Blues)
plt.savefig("node.jpg")
plt.show()

边的颜色渐变

import matplotlib.pyplot as plt
import networkx as nx

G = nx.star_graph(20)
pos = nx.spring_layout(G) #布局为中心放射状
colors = range(20)
nx.draw(G, pos, node_color='#A0CBE2', edge_color=colors,
        width=4, edge_cmap=plt.cm.Blues, with_labels=False)
plt.show()

Atlas

import random

try:
    import pygraphviz
    from networkx.drawing.nx_agraph import graphviz_layout
except ImportError:
    try:
        import pydot
        from networkx.drawing.nx_pydot import graphviz_layout
    except ImportError:
        raise ImportError("This example needs Graphviz and either "
                          "PyGraphviz or pydot.")

import matplotlib.pyplot as plt

import networkx as nx
from networkx.algorithms.isomorphism.isomorph import graph_could_be_isomorphic as isomorphic
from networkx.generators.atlas import graph_atlas_g


def atlas6():
    """ Return the atlas of all connected graphs of 6 nodes or less.
        Attempt to check for isomorphisms and remove.
    """

    Atlas = graph_atlas_g()[0:208]  # 208
    # remove isolated nodes, only connected graphs are left
    U = nx.Graph()  # graph for union of all graphs in atlas
    for G in Atlas:
        zerodegree = [n for n in G if G.degree(n) == 0]
        for n in zerodegree:
            G.remove_node(n)
        U = nx.disjoint_union(U, G)

    # iterator of graphs of all connected components
    C = (U.subgraph(c) for c in nx.connected_components(U))

    UU = nx.Graph()
    # do quick isomorphic-like check, not a true isomorphism checker
    nlist = []  # list of nonisomorphic graphs
    for G in C:
        # check against all nonisomorphic graphs so far
        if not iso(G, nlist):
            nlist.append(G)
            UU = nx.disjoint_union(UU, G)  # union the nonisomorphic graphs
    return UU


def iso(G1, glist):
    """Quick and dirty nonisomorphism checker used to check isomorphisms."""
    for G2 in glist:
        if isomorphic(G1, G2):
            return True
    return False


if __name__ == '__main__':
    G = atlas6()

    print("graph has %d nodes with %d edges"
          % (nx.number_of_nodes(G), nx.number_of_edges(G)))
    print(nx.number_connected_components(G), "connected components")

    plt.figure(1, figsize=(8, 8))
    # layout graphs with positions using graphviz neato
    pos = graphviz_layout(G, prog="neato")
    # color nodes the same in each connected subgraph
    C = (G.subgraph(c) for c in nx.connected_components(G))
    for g in C:
        c = [random.random()] * nx.number_of_nodes(g)  # random color...
        nx.draw(g,
                pos,
                node_size=40,
                node_color=c,
                vmin=0.0,
                vmax=1.0,
                with_labels=False
               )
    plt.show()

画个五角星

import networkx as nx
import matplotlib.pyplot as plt
#画图！
G=nx.Graph()
G.add_node(1)
G.add_nodes_from([2,3,4,5])
for i in range(5):
    for j in range(i):
        if (abs(i-j) not in (1,4)):
            G.add_edge(i+1, j+1)
nx.draw(G,
        with_labels=True, #这个选项让节点有名称
        edge_color='b', # b stands for blue!
        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
     # 主要有spring_layout  (default), random_layout, circle_layout, shell_layout
     # 这里是环形排布，还有随机排列等其他方式
        node_color='r', # r = red
        node_size=1000, # 节点大小
        width=3, # 边的宽度
       )
plt.savefig("star.jpg")
plt.show()

Club

import matplotlib.pyplot as plt
import networkx as nx
import networkx.algorithms.bipartite as bipartite

G = nx.davis_southern_women_graph()
women = G.graph['top']
clubs = G.graph['bottom']

print("Biadjacency matrix")
print(bipartite.biadjacency_matrix(G, women, clubs))

# project bipartite graph onto women nodes
W = bipartite.projected_graph(G, women)
print('')
print("#Friends, Member")
for w in women:
    print('%d %s' % (W.degree(w), w))

# project bipartite graph onto women nodes keeping number of co-occurence
# the degree computed is weighted and counts the total number of shared contacts
W = bipartite.weighted_projected_graph(G, women)
print('')
print("#Friend meetings, Member")
for w in women:
    print('%d %s' % (W.degree(w, weight='weight'), w))

nx.draw(G,node_color="red")
plt.savefig("club.jpg")
plt.show()

画一个多层感知机

import matplotlib.pyplot as plt
import networkx as nx
left, right, bottom, top, layer_sizes = .1, .9, .1, .9, [4, 7, 7, 2]
# 网络离上下左右的距离
# layter_sizes可以自己调整
import random
G = nx.Graph()
v_spacing = (top - bottom)/float(max(layer_sizes))
h_spacing = (right - left)/float(len(layer_sizes) - 1)
node_count = 0
for i, v in enumerate(layer_sizes):
    layer_top = v_spacing*(v-1)/2. + (top + bottom)/2.
    for j in range(v):
        G.add_node(node_count, pos=(left + i*h_spacing, layer_top - j*v_spacing))
        node_count += 1
# 这上面的数字调整我想了好半天，汗
for x, (left_nodes, right_nodes) in enumerate(zip(layer_sizes[:-1], layer_sizes[1:])):
    for i in range(left_nodes):
        for j in range(right_nodes):
            G.add_edge(i+sum(layer_sizes[:x]), j+sum(layer_sizes[:x+1]))

pos=nx.get_node_attributes(G,'pos')
# 把每个节点中的位置pos信息导出来
nx.draw(G, pos,
        node_color=range(node_count),
        with_labels=True,
        node_size=200,
        edge_color=[random.random() for i in range(len(G.edges))],
        width=3,
        cmap=plt.cm.Dark2, # matplotlib的调色板，可以搜搜，很多颜色
        edge_cmap=plt.cm.Blues
       )
plt.savefig("mlp.jpg")
plt.show()

绘制一个DNN结构图

# -*- coding:utf-8 -*-
import networkx as nx
import matplotlib.pyplot as plt

# 创建DAG
G = nx.DiGraph()

# 顶点列表
vertex_list = ['v'+str(i) for i in range(1, 22)]
# 添加顶点
G.add_nodes_from(vertex_list)

# 边列表
edge_list = [
             ('v1', 'v5'), ('v1', 'v6'), ('v1', 'v7'),('v1', 'v8'),('v1', 'v9'),
             ('v2', 'v5'), ('v2', 'v6'), ('v2', 'v7'),('v2', 'v8'),('v2', 'v9'),
             ('v3', 'v5'), ('v3', 'v6'), ('v3', 'v7'),('v3', 'v8'),('v3', 'v9'),
             ('v4', 'v5'), ('v4', 'v6'), ('v4', 'v7'),('v4', 'v8'),('v4', 'v9'),
             ('v5','v10'),('v5','v11'),('v5','v12'),('v5','v13'),('v5','v14'),('v5','v15'),
             ('v6','v10'),('v6','v11'),('v6','v12'),('v6','v13'),('v6','v14'),('v6','v15'),
             ('v7','v10'),('v7','v11'),('v7','v12'),('v7','v13'),('v7','v14'),('v7','v15'),
             ('v8','v10'),('v8','v11'),('v8','v12'),('v8','v13'),('v8','v14'),('v8','v15'),
             ('v9','v10'),('v9','v11'),('v9','v12'),('v9','v13'),('v9','v14'),('v9','v15'),
             ('v10','v16'),('v10','v17'),('v10','v18'),
             ('v11','v16'),('v11','v17'),('v11','v18'),
             ('v12','v16'),('v12','v17'),('v12','v18'),
             ('v13','v16'),('v13','v17'),('v13','v18'),
             ('v14','v16'),('v14','v17'),('v14','v18'),
             ('v15','v16'),('v15','v17'),('v15','v18'),
             ('v16','v19'),
             ('v17','v20'),
             ('v18','v21')
            ]
# 通过列表形式来添加边
G.add_edges_from(edge_list)

# 绘制DAG图
plt.title('DNN for iris')    #图片标题

nx.draw(
        G,
        node_color = 'red',             # 顶点颜色
        edge_color = 'black',           # 边的颜色
        with_labels = True,             # 显示顶点标签
        font_size =10,                  # 文字大小
        node_size =300                  # 顶点大小
       )
# 显示图片
plt.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：

# -*- coding:utf-8 -*-
import networkx as nx
import matplotlib.pyplot as plt

# 创建DAG
G = nx.DiGraph()

# 顶点列表
vertex_list = ['v'+str(i) for i in range(1, 22)]
# 添加顶点
G.add_nodes_from(vertex_list)

# 边列表
edge_list = [
             ('v1', 'v5'), ('v1', 'v6'), ('v1', 'v7'),('v1', 'v8'),('v1', 'v9'),
             ('v2', 'v5'), ('v2', 'v6'), ('v2', 'v7'),('v2', 'v8'),('v2', 'v9'),
             ('v3', 'v5'), ('v3', 'v6'), ('v3', 'v7'),('v3', 'v8'),('v3', 'v9'),
             ('v4', 'v5'), ('v4', 'v6'), ('v4', 'v7'),('v4', 'v8'),('v4', 'v9'),
             ('v5','v10'),('v5','v11'),('v5','v12'),('v5','v13'),('v5','v14'),('v5','v15'),
             ('v6','v10'),('v6','v11'),('v6','v12'),('v6','v13'),('v6','v14'),('v6','v15'),
             ('v7','v10'),('v7','v11'),('v7','v12'),('v7','v13'),('v7','v14'),('v7','v15'),
             ('v8','v10'),('v8','v11'),('v8','v12'),('v8','v13'),('v8','v14'),('v8','v15'),
             ('v9','v10'),('v9','v11'),('v9','v12'),('v9','v13'),('v9','v14'),('v9','v15'),
             ('v10','v16'),('v10','v17'),('v10','v18'),
             ('v11','v16'),('v11','v17'),('v11','v18'),
             ('v12','v16'),('v12','v17'),('v12','v18'),
             ('v13','v16'),('v13','v17'),('v13','v18'),
             ('v14','v16'),('v14','v17'),('v14','v18'),
             ('v15','v16'),('v15','v17'),('v15','v18'),
             ('v16','v19'),
             ('v17','v20'),
             ('v18','v21')
            ]
# 通过列表形式来添加边
G.add_edges_from(edge_list)

# 指定绘制DAG图时每个顶点的位置
pos = {
        'v1':(-2,1.5),
        'v2':(-2,0.5),
        'v3':(-2,-0.5),
        'v4':(-2,-1.5),
        'v5':(-1,2),
        'v6': (-1,1),
        'v7':(-1,0),
        'v8':(-1,-1),
        'v9':(-1,-2),
        'v10':(0,2.5),
        'v11':(0,1.5),
        'v12':(0,0.5),
        'v13':(0,-0.5),
        'v14':(0,-1.5),
        'v15':(0,-2.5),
        'v16':(1,1),
        'v17':(1,0),
        'v18':(1,-1),
        'v19':(2,1),
        'v20':(2,0),
        'v21':(2,-1)
       }
# 绘制DAG图
plt.title('DNN for iris')    #图片标题
plt.xlim(-2.2, 2.2)                     #设置X轴坐标范围
plt.ylim(-3, 3)                     #设置Y轴坐标范围
nx.draw(
        G,
        pos = pos,                      # 点的位置
        node_color = 'red',             # 顶点颜色
        edge_color = 'black',           # 边的颜色
        with_labels = True,             # 显示顶点标签
        font_size =10,                  # 文字大小
        node_size =300                  # 顶点大小
       )
# 显示图片
plt.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：

# -*- coding:utf-8 -*-
import cv2
import networkx as nx
import matplotlib.pyplot as plt

# 创建DAG
G = nx.DiGraph()

# 顶点列表
vertex_list = ['v'+str(i) for i in range(1, 22)]
# 添加顶点
G.add_nodes_from(vertex_list)

# 边列表
edge_list = [
             ('v1', 'v5'), ('v1', 'v6'), ('v1', 'v7'),('v1', 'v8'),('v1', 'v9'),
             ('v2', 'v5'), ('v2', 'v6'), ('v2', 'v7'),('v2', 'v8'),('v2', 'v9'),
             ('v3', 'v5'), ('v3', 'v6'), ('v3', 'v7'),('v3', 'v8'),('v3', 'v9'),
             ('v4', 'v5'), ('v4', 'v6'), ('v4', 'v7'),('v4', 'v8'),('v4', 'v9'),
             ('v5','v10'),('v5','v11'),('v5','v12'),('v5','v13'),('v5','v14'),('v5','v15'),
             ('v6','v10'),('v6','v11'),('v6','v12'),('v6','v13'),('v6','v14'),('v6','v15'),
             ('v7','v10'),('v7','v11'),('v7','v12'),('v7','v13'),('v7','v14'),('v7','v15'),
             ('v8','v10'),('v8','v11'),('v8','v12'),('v8','v13'),('v8','v14'),('v8','v15'),
             ('v9','v10'),('v9','v11'),('v9','v12'),('v9','v13'),('v9','v14'),('v9','v15'),
             ('v10','v16'),('v10','v17'),('v10','v18'),
             ('v11','v16'),('v11','v17'),('v11','v18'),
             ('v12','v16'),('v12','v17'),('v12','v18'),
             ('v13','v16'),('v13','v17'),('v13','v18'),
             ('v14','v16'),('v14','v17'),('v14','v18'),
             ('v15','v16'),('v15','v17'),('v15','v18'),
             ('v16','v19'),
             ('v17','v20'),
             ('v18','v21')
            ]
# 通过列表形式来添加边
G.add_edges_from(edge_list)

# 指定绘制DAG图时每个顶点的位置
pos = {
        'v1':(-2,1.5),
        'v2':(-2,0.5),
        'v3':(-2,-0.5),
        'v4':(-2,-1.5),
        'v5':(-1,2),
        'v6': (-1,1),
        'v7':(-1,0),
        'v8':(-1,-1),
        'v9':(-1,-2),
        'v10':(0,2.5),
        'v11':(0,1.5),
        'v12':(0,0.5),
        'v13':(0,-0.5),
        'v14':(0,-1.5),
        'v15':(0,-2.5),
        'v16':(1,1),
        'v17':(1,0),
        'v18':(1,-1),
        'v19':(2,1),
        'v20':(2,0),
        'v21':(2,-1)
       }
# 绘制DAG图
plt.title('DNN for iris')    #图片标题
plt.xlim(-2.2, 2.2)                     #设置X轴坐标范围
plt.ylim(-3, 3)                     #设置Y轴坐标范围
nx.draw(
        G,
        pos = pos,                      # 点的位置
        node_color = 'red',             # 顶点颜色
        edge_color = 'black',           # 边的颜色
        font_size =10,                  # 文字大小
        node_size =300                  # 顶点大小
       )

# 保存图片，图片大小为640*480
plt.savefig('DNN_sketch.png')

# 利用opencv模块对DNN框架添加文字注释

# 读取图片
imagepath = 'DNN_sketch.png'
image = cv2.imread(imagepath, 1)

# 输入层
cv2.rectangle(image, (85, 130), (120, 360), (255,0,0), 2)
cv2.putText(image, "Input Layer", (15, 390), 1, 1.5, (0, 255, 0), 2, 1)

# 隐藏层
cv2.rectangle(image, (190, 70), (360, 420), (255,0,0), 2)
cv2.putText(image, "Hidden Layer", (210, 450), 1, 1.5, (0, 255, 0), 2, 1)

# 输出层
cv2.rectangle(image, (420, 150), (460, 330), (255,0,0), 2)
cv2.putText(image, "Output Layer", (380, 360), 1, 1.5, (0, 255, 0), 2, 1)

# sofrmax层
cv2.rectangle(image, (530, 150), (570, 330), (255,0,0), 2)
cv2.putText(image, "Softmax Func", (450, 130), 1, 1.5, (0, 0, 255), 2, 1)

# 保存修改后的图片
cv2.imwrite('DNN.png', image)

一些图论算法

最短路径

函数调用：
dijkstra_path(G, source, target, weight=‘weight’) ————求最短路径
dijkstra_path_length(G, source, target, weight=‘weight’) ————求最短距离

import networkx as nx
import pylab 
import numpy as np
#自定义网络
row=np.array([0,0,0,1,2,3,6])
col=np.array([1,2,3,4,5,6,7])
value=np.array([1,2,1,8,1,3,5])

print('生成一个空的有向图')
G=nx.DiGraph()
print('为这个网络添加节点...')
for i in range(0,np.size(col)+1):
    G.add_node(i)
print('在网络中添加带权中的边...')
for i in range(np.size(row)):
    G.add_weighted_edges_from([(row[i],col[i],value[i])])

print('给网路设置布局...')
pos=nx.shell_layout(G)
print('画出网络图像：')
nx.draw(G,pos,with_labels=True, node_color='white', edge_color='red', node_size=400, alpha=0.5 )
pylab.title('Self_Define Net',fontsize=15)
pylab.show()


'''
Shortest Path with dijkstra_path
'''
print('dijkstra方法寻找最短路径：')
path=nx.dijkstra_path(G, source=0, target=7)
print('节点0到7的路径：', path)
print('dijkstra方法寻找最短距离：')
distance=nx.dijkstra_path_length(G, source=0, target=7)
print('节点0到7的距离为：', distance)

输出：

生成一个空的有向图
为这个网络添加节点...
在网络中添加带权中的边...
给网路设置布局...
画出网络图像：
dijkstra方法寻找最短路径：
节点0到7的路径： [0, 3, 6, 7]
dijkstra方法寻找最短距离：
节点0到7的距离为： 9

问题

本人在pycharm中运行下列程序：

import networkx as nx
import matplotlib.pyplot as plt

G = nx.Graph()  # 建立一个空的无向图G
G.add_node('a')  # 添加一个节点1
G.add_nodes_from(['b', 'c', 'd', 'e'])  # 加点集合
G.add_cycle(['f', 'g', 'h', 'j'])  # 加环
H = 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
G.add_nodes_from(H)  # 创建一个子图H加入G
G.add_node(H)  # 直接将图作为节点

nx.draw(G, with_labels=True)
plt.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

plt.show()
/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.
warnings.warn("This figure includes Axes that are not "
...
ValueError: 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

名称	描述	推荐指数
Python+Graphviz	graphviz的python版本(亲测)	****
PlotNeuralNet	第一步生成tex文件，然后调用LaTeX命令行生成图形(亲测)	****
NetworkX	这是个专门的复杂网络图的Python包	****
Matplotlib’s Viznet	利用Matplotlib的Viznet	****
LaTeX tikz	绘制网络结点图的tikz库	***
Graphviz	专业绘图软件，dot描述语言	***
Inkscape	属于绘图软件	***
Omnigraffle	由The Omni Group制作的一款绘图软件	***
netron	支持ONNX (.onnx, .pb, .pbtxt), Keras (.h5, .keras), CoreML (.mlmodel), Caffe2 (predict_net.pb, predict_net.pbtxt), MXNet (.model, -symbol.json) and TensorFlow Lite (.tflite)，在前面链接处下载文件，在这里演示	***
TensorBoard	配合Tensorflow一起使用的	***
Keras	自带plot方法，例子，也需要安装graphviz，pydot等	***
Netscope for Caffe	只支持Caffe格式，例子	***
draw_convnet	这个其实是利用Matplotlib的绘图功能写了一个Python脚本	**
dnngraph	仅使用于Caffe框架	**
ConvNetDraw	灵活性差,没有更新了	**

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
• networkx整理
• Networkx使用指南
• 论文中绘制神经网络工具汇总
• networkx + Cytoscape 构建及可视化网络图
• 用python+graphviz/networkx画目录结构树状图