python复杂网络结构可视化——matplotlib+networkx

什么是networkx？

networkx在02年5月产生，是用python语言编写的软件包，便于用户对复杂网络进行创建、操作和学习。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。 ——百度百科

我们可以用networkx做什么？

Examples - NetworkX 2.1 documentation

1. 画图

2. 有向图，无向图，网络图……

3. 总之各种图

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看到这你是不是心动了呢？今天的教程就是要教会你画出封面上的三层感知机模型图！

Let's get started!

首先导入networkx和matplotlib模块

import networkx as nx

import matplotlib.pyplot as plt

>>> import networkx as nx
>>> G = nx.Graph() 定义了一个空图
>>> G.add_node(1) 这个图中增加了1节点
>>> G.add_node('A') 增加'A'节点
>>> G.add_nodes_from([2, 3]) 同时加2和3两个节点
>>> G.add_edges_from([(1,2),(1,3),(2,4),(2,5),(3,6),(4,8),(5,8),(3,7)]) 
# 增加这么多条边，在下面有举例
>>> H = nx.path_graph(10) 
>>> G.add_nodes_from(H)
>>> G.add_node(H)
G.add_node('a')#添加点a
G.add_node(1,1)#用坐标来添加点
G.add_edge('x','y')#添加边,起点为x，终点为y
G.add_weight_edges_from([('x','y',1.0)])#第三个输入量为权值
#也可以
list = [[('a','b',5.0),('b','c',3.0),('a','c',1.0)]
G.add_weight_edges_from([(list)])

我们来看看上面最后一句是什么意思

import matplotlib.pyplot as plt
import networkx as nx
H = nx.path_graph(10) 
G.add_nodes_from(H)
nx.draw(G, with_labels=True)
plt.show()

生成了标号为0到9的十个点！别急，丑是丑了点，一会我们再给他化妆。

#再举个栗子
G=nx.Graph()
#导入所有边，每条边分别用tuple表示
G.add_edges_from([(1,2),(1,3),(2,4),(2,5),(3,6),(4,8),(5,8),(3,7)]) 
nx.draw(G, with_labels=True, edge_color='b', node_color='g', node_size=1000)
plt.show()
#plt.savefig('./generated_image.png') 如果你想保存图片，去除这句的注释

好了，你现在已经知道如何给图添加边和节点了，接下来是构造环：

画个圈圈

import matplotlib.pyplot as plt
import networkx as nx
# H = nx.path_graph(10) 
# G.add_nodes_from(H)
G = nx.Graph()
G.add_cycle([0,1,2,3,4])
nx.draw(G, with_labels=True)
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.show()

import random
G = nx.gnp_random_graph(10,0.3)
for u,v,d in G.edges(data=True):
    d['weight'] = random.random()

edges,weights = zip(*nx.get_edge_attributes(G,'weight').items())

pos = nx.spring_layout(G)
nx.draw(G, pos, node_color='b', edgelist=edges, edge_color=weights, width=10.0, edge_cmap=plt.cm.Blues)
# plt.savefig('edges.png')
plt.show()

加入权重

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.show()

有向图

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.show()

颜色渐变的节点

import matplotlib.pyplot as plt
import networkx as nx

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.show()

颜色渐变的边

import matplotlib.pyplot as plt
import networkx as nx

G = nx.star_graph(20)
pos = nx.spring_layout(G)
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()

如何画一个多层感知机？

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]))    
# 慢慢研究吧
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，很多颜色呢
        edge_cmap=plt.cm.Blues
       )
plt.show() 

差不多就是这个效果了。

后续我会封装为一个类，加入动态演示，比如通过颜色深浅，显示神经网络在优化的时候权重变化。应该会很好玩，嘿嘿。

上面你也可以改变layer_sizes

比如改为233333

完。