# 【3】数据分析-4-1-由煮面条到图论到图论--NetworkX

## 一、NetworkX概论

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。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。

pip install networkx


import networkx as nx
print nx


#!-*- coding:utf8-*-
import networkx as nx
#linux系统下没有作图系统，需要如下生成图片
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
#windows下直接
import matplotlib.pyplot as plt
G = nx.Graph() #建立一个空的无向图G G.add_node(1) #添加一个节点1
print "nodes:", G.nodes() #输出全部的节点： [1, 2, 3]
print "edges:", G.edges() #输出全部的边：[(2, 3)]
print "number of edges:", G.number_of_edges() #输出边的数量：1
nx.draw(G,with_labels=True) #nodes的标签加上
plt.savefig("wuxiangtu.png")
plt.show()


nodes: [1, 2, 3]
edges: [(2, 3)]
number of edges: 1


#-*- coding:utf8-*-

import networkx as nx
import matplotlib.pyplot as plt
G = nx.DiGraph()
nx.draw(G)
plt.savefig("youxiangtu.png")
plt.show()


#!-*- coding:utf8-*-

import networkx as nx
import matplotlib.pyplot as plt

G = nx.DiGraph()
nx.draw(G)
plt.savefig("youxiangtu.png")
plt.show()


Graph.to_undirected()
Graph.to_directed()


#!-*- coding:utf8-*-

import networkx as nx
import matplotlib.pyplot as plt

G = nx.DiGraph()
G = G.to_undirected()
nx.draw(G)
plt.savefig("wuxiangtu.png")
plt.show()


#-*- coding:utf8-*-

import networkx as nx
import matplotlib.pyplot as plt

G = nx.DiGraph()

road_nodes = {'a': 1, 'b': 2, 'c': 3}
road_edges = [('a', 'b'), ('b', 'c')]

nx.draw(G)
plt.savefig("youxiangtu.png")
plt.show()


#-*- coding:utf8-*-

import networkx as nx
import matplotlib.pyplot as plt

G = nx.DiGraph()

#road_nodes = {'a': 1, 'b': 2, 'c': 3}
road_edges = [('a', 'b'), ('b', 'c')]

nx.draw(G)
plt.savefig("youxiangtu.png")
plt.show()


import networkx as nx
import matplotlib.pyplot as plt
G = nx.Graph()                                        #建立一个空的无向图G
G.add_weighted_edges_from([(3, 4, 3.5),(3, 5, 7.0)])                                     #对于无向图，边3-2与边2-3被认为是一条边

print G.get_edge_data(2, 3)
print G.get_edge_data(3, 4)
print G.get_edge_data(3, 5)

nx.draw(G)
plt.savefig("wuxiangtu.png")
plt.show()


{}
{'weight': 3.5}
{'weight': 7.0}


import networkx as nx
import matplotlib.pyplot as plt

#计算1：求无向图的任意两点间的最短路径
G = nx.Graph()
path = nx.all_pairs_shortest_path(G)
print path[1]


• 强连通：有向图中任意两点v1、v2间存在v1到v2的路径（path）及v2到v1的路径。
• 弱联通：将有向图的所有的有向边替换为无向边，所得到的图称为原图的基图。如果一个有向图的基图是连通图，则有向图是弱连通图。

import networkx as nx
import matplotlib.pyplot as plt
#G = nx.path_graph(4, create_using=nx.Graph())
#0 1 2 3
G = nx.path_graph(4, create_using=nx.DiGraph())    #默认生成节点0 1 2 3，生成有向变0->1,1->2,2->3

for c in nx.weakly_connected_components(G):
print c

print [len(c) for c in sorted(nx.weakly_connected_components(G), key=len, reverse=True)]

nx.draw(G)
plt.savefig("youxiangtu.png")
plt.show()


set([0, 1, 2, 3, 7, 8])
[6]


import networkx as nx
import matplotlib.pyplot as plt
#G = nx.path_graph(4, create_using=nx.Graph())
#0 1 2 3
G = nx.path_graph(4, create_using=nx.DiGraph())

#for c in nx.strongly_connected_components(G):
#    print c
#
#print [len(c) for c in sorted(nx.strongly_connected_components(G), key=len, reverse=True)]

con = nx.strongly_connected_components(G)
print con
print type(con)
print list(con)

nx.draw(G)
plt.savefig("youxiangtu.png")
plt.show()


<type 'generator'>
[set([8, 1, 2, 3]), set([0])]


import networkx as nx
import matplotlib.pyplot as plt
G = nx.DiGraph()
sub_graph = G.subgraph([5, 6, 8])
#sub_graph = G.subgraph((5, 6, 8))  #ok  一样

nx.draw(sub_graph)
plt.savefig("youxiangtu.png")
plt.show()


## 二、其他函数

### planted_partition_graph

planted_partition_graph(l, k, p_in, p_out, seed=None, directed=False)

Return the planted l-partition graph.

This model partitions a graph with n=l*k vertices in l groups with k vertices each. Vertices of the same group are linked with a probability p_in, and vertices of different groups are linked with probability p_out.

Parameters:
l (int) – Number of groups
k (int) – Number of vertices in each group
p_in (float) – probability of connecting vertices within a group
p_out (float) – probability of connected vertices between groups
seed (int,optional) – Seed for random number generator(default=None)
directed (bool,optional (default=False)) – If True return a directed graph
Returns:
G – planted l-partition graph

Return type:
NetworkX Graph or DiGraph

Raises:
NetworkXError: – If p_in,p_out are not in [0,1] or


import networkx as nx
gene_net = nx.planted_partition_graph(50, 10, 0.2, 0.05, seed=42)  # 50组，每10个，算是500个了吧

## 理解这是什么图

# ## 1.把图做出来
# nx.draw(gene_net)
# plt.savefig('test.png')
# plt.show()

# 2.查看nodes
# print gene_net.nodes()
#看到了0-499 的list，说明应该是 500个nodes，难道是 50 *10 ？

# 3.输出图的边值
# print gene_net.edges()
# 出来的是 0-499任意两个数的set。

# 其他属性

# print gene_net.degree()
# print gene_net.degree_histogram()
# print gene_net.density()

# print nx.info(gene_net)
# Type: Graph
# Number of nodes: 500
# Number of edges: 6566
# Average degree:  26.2640

# print nx.is_directed(gene_net)
# False

## 获得Nodes
# print len(nx.nodes(gene_net))
# 500


### 2.2 独立的node，即没有Node与其形成edge

import networkx as nx
G = nx.path_graph(4)
graphs = list(nx.isolates(G))
for one_part in graphs:
print(one_part)


7
8


### 2.3 连通子图，子图里面不需要任意两两之间相连

import networkx as nx
G = nx.path_graph(4)
graphs = list(nx.connected_component_subgraphs(G))
for one_part in graphs:
print(one_part.nodes)


[0, 1, 2, 3]
[5, 6, 7]


### 2.4 任意两点之间的联通

G = nx.complete_graph(4)
for path in nx.all_simple_paths(G, source=0, target=3):
print(path)

[0, 1, 2, 3]
[0, 1, 3]
[0, 2, 1, 3]
[0, 2, 3]
[0, 3]

paths = nx.all_simple_paths(G, source=0, target=3, cutoff=2)
print(list(paths))
[[0, 1, 3], [0, 2, 3], [0, 3]]


source :起点Node
target: 终点node
cutoff:  Depth to stop the search. Only paths of length <= cutoff are returned


### 2.5 最短path

G = nx.path_graph(5)
path = nx.all_pairs_shortest_path(G)

print(path[0][4])
[0, 1, 2, 3, 4]


### 2.6 最长path

def longest_path(G):
dist = {} # stores [node, distance] pair
for node in nx.topological_sort(G):
# pairs of dist,node for all incoming edges
pairs = [(dist[v][0]+1,v) for v in G.pred[node]]
if pairs:
dist[node] = max(pairs)
else:
dist[node] = (0, node)
node,(length,_)  = max(dist.items(), key=lambda x:x[1])
path = []
while length > 0:
path.append(node)
length,node = dist[node]
return list(reversed(path))

if __name__=='__main__':
G = nx.DiGraph()
nx.draw(G, with_labels=True,font_size=20)
print(longest_path(G))


## 三、案例：

import networkx as nx
from networkx.algorithms.approximation.clique import max_clique, clique_removal

G = nx.Graph()
nx.draw(G, with_labels=True)
plt.savefig('temp/network.png')
plt.show()

cliques_primers1 = list(nx.find_cliques(G))

cliques_primers2 = list(list(clique_removal(G))[1])


## 四、讨论：

1.加颜色

import networkx as nx
import numpy as np
import matplotlib.pyplot as plt

G = nx.Graph()
[('A', 'B'), ('A', 'C'), ('D', 'B'), ('E', 'C'), ('E', 'F'),
('B', 'H'), ('B', 'G'), ('B', 'F'), ('C', 'G')])

val_map = {'A': 1.0,
'D': 0.5714285714285714,
'H': 0.0}

values = [val_map.get(node, 0.25) for node in G.nodes()]

nx.draw(G, cmap=plt.get_cmap('jet'), node_color=values)

# nx.draw(G, cmap=plt.get_cmap('viridis'), node_color=values, with_labels=True, font_color='white')  #其他颜色： PuBuGn , PuBuGn_r

plt.show()