NetworkX

常用网站：

• 官方文档
• Github (latest development)

NetworkX官方介绍：

========

NetworkX (NX) is a Python package for the creation, manipulation, andstudy of the structure, dynamics, and functions of complex networks.<https://networkx.lanl.gov/>

    Just write in Python    >>> import networkx as nx    >>> G=nx.Graph()    >>> G.add_edge(1,2)    >>> G.add_node(42)    >>> print(sorted(G.nodes()))    [1, 2, 42]    >>> print(sorted(G.edges()))    [(1, 2)]

• 用来处理无向图、有向图、多重图的Python数据结构
• 包含许多标准的图算法
• 包括网络结构和分析方法
• 用于产生经典图、随机图和综合网络
• 节点可以是任何事物（如text, images, XML records）
• 边能保存任意起算值（如weights, time-series）
• 开源证书 BSD license
• 很好的测试结果：超过1800个单元测试，90%的结点覆盖
• 从Python获得的额外优势：快速原型开发方法，容易学，支持多平台。

import networkx as nxG = nx.Graph()G.add_edge('A', 'B', weight=4)G.add_edge('B', 'D', weight=2)G.add_edge('A', 'C', weight=3)G.add_edge('C', 'D', weight=4)nx.shortest_path(G, 'A', 'D', weight='weight')

['A', 'B', 'D']

import networkx as nxG=nx.Graph()G.add_edge(1,2)G.add_node(42)print(sorted(G.nodes()))print(sorted(G.edges()))

[1, 2, 42][(1, 2)]

创建图

import networkx as nxG=nx.Graph()

• Graph是结点（向量）与确定的结点对（称作边、链接等）的集合。
  在Networkx中，结点可以是任何可哈希的对象，如文本字符串、图片、XML对象、其他图，自定义对象等。
  注意:python的None对象不应该用作结点，

可哈希的：一个对象在它的生存期从来不会被改变（拥有一个哈希方法），能和其他对象区别（有比较方法）

结点

Neatworkx包含很多图生成器函数和工具，可用来以多种格式来读写图。

一次增加一个节点：

G.add_node(1)

用序列增加一系列的节点

G.add_nodes_from([2,3])

增加 nbunch结点。

nbunch是可迭代的结点容器 （序列、集合、图、文件等），其本身不是图的某个节点

import networkx as nxG=nx.Graph()G.add_node(1)G.add_nodes_from([2,3])H=nx.path_graph(10)      # type(H) networkx.classes.graph.GraphG.add_nodes_from(H)     # 这是将H中的许多结点作为G的节点G.add_node(H)          # 这是将H作为G中的一个节点#查看结点G.node

{1: {}, 2: {}, 3: {}, 0: {}, 4: {}, 5: {}, 6: {}, 7: {}, 8: {}, 9: {}, <networkx.classes.graph.Graph at 0x18ecbb89940>: {}}

#G能够一次增加一条边G.add_edge(1,2)     #只能增加边，有属性，除非指定属性名和值“属性名=值”e=(2,3)G.add_edge(*e)      #注意！ G.add_edge(e)会报错！G.add_edge(e)#用序列增加一系列结点G.add_edges_from([(1,2),(1,3)])#增加 ebunch边。ebunch：包含边元组的容器，比如序列、迭代器、文件等#这个元组可以是2维元组或 三维元组 （node1，node2，an_edge_attribute_dictionary）,an_edge_attribute_dictionary比如：#{‘weight’:3.1415}G.add_edges_from(H.edges())

删除

G.remove_node(),G.remove_nodes_from()G.remove_edge(),G.remove_edges_from()G.remove_node(H)      #删除不存在的东西会报错#移除所有的节点和边G.clear()G.add_edges_from([(1,2),(1,3)])G.add_node(1)G.add_edge(1,2)G.add_node("spam")G.add_nodes_from("spam")    # adds 4 nodes: 's', 'p', 'a', 'm'G.edges(),G.nodes(),G.number_of_edges(),G.number_of_nodes()

import networkx as nx

<module 'networkx' from 'D:\\ProgramData\\Anaconda3\\lib\\site-packages\\networkx\\__init__.py'>

无向图

import networkx as nximport matplotlib.pyplot as pltG = nx.Graph()                 #建立一个空的无向图GG.add_node(1)                  #添加一个节点1G.add_edge(2,3)                #添加一条边2-3（隐含着添加了两个节点2、3）G.add_edge(3,2)                #对于无向图，边3-2与边2-3被认为是一条边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：1nx.draw(G)plt.savefig("wuxiangtu.png")plt.show()

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

#-*- coding:utf8-*- import networkx as nximport matplotlib.pyplot as pltG = nx.DiGraph()G.add_node(1)G.add_node(2)                  #加点G.add_nodes_from([3,4,5,6])    #加点集合G.add_cycle([1,2,3,4])         #加环G.add_edge(1,3)     G.add_edges_from([(3,5),(3,6),(6,7)])  #加边集合nx.draw(G)plt.savefig("youxiangtu.png")plt.show()

有向图

#!-*- coding:utf8-*- import networkx as nximport matplotlib.pyplot as pltG = 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)plt.savefig("youxiangtu.png")plt.show()

注：有向图和无向图可以互相转换，使用函数：

• Graph.to_undirected()
• Graph.to_directed()

# 例子中把有向图转化为无向图import networkx as nximport matplotlib.pyplot as pltG = 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)])G = G.to_undirected()nx.draw(G)plt.savefig("wuxiangtu.png")plt.show()

#-*- coding:utf8-*-import networkx as nximport matplotlib.pyplot as pltG = nx.DiGraph()road_nodes = {'a': 1, 'b': 2, 'c': 3}#road_nodes = {'a':{1:1}, 'b':{2:2}, 'c':{3:3}}road_edges = [('a', 'b'), ('b', 'c')]G.add_nodes_from(road_nodes.items())G.add_edges_from(road_edges)nx.draw(G)plt.savefig("youxiangtu.png")plt.show()

#-*- coding:utf8-*-import networkx as nximport matplotlib.pyplot as pltG = nx.DiGraph()#road_nodes = {'a': 1, 'b': 2, 'c': 3}road_nodes = {'a':{1:1}, 'b':{2:2}, 'c':{3:3}}road_edges = [('a', 'b'), ('b', 'c')]G.add_nodes_from(road_nodes.items())G.add_edges_from(road_edges)nx.draw(G)plt.savefig("youxiangtu.png")plt.show()

加权图

有向图和无向图都可以给边赋予权重，用到的方法是add_weighted_edges_from，它接受1个或多个三元组[u,v,w]作为参数，
其中u是起点，v是终点，w是权重

#!-*- coding:utf8-*- import networkx as nximport matplotlib.pyplot as pltG = nx.Graph()                                        #建立一个空的无向图GG.add_edge(2,3)                                     #添加一条边2-3（隐含着添加了两个节点2、3）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 nximport matplotlib.pyplot as pltG = nx.DiGraph()

经典图论算法计算

计算1：求无向图的任意两点间的最短路径

# -*- coding: cp936 -*-import networkx as nximport 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()G.add_edges_from([(1,2),(1,3),(1,4),(1,5),(4,5),(4,6),(5,6)])path = nx.all_pairs_shortest_path(G)print(path[1])

{1: [1], 2: [1, 2], 3: [1, 3], 4: [1, 4], 5: [1, 5], 6: [1, 4, 6]}

计算2：找图中两个点的最短路径

import networkx as nxG=nx.Graph()G.add_nodes_from([1,2,3,4])G.add_edge(1,2)G.add_edge(3,4)try:    n=nx.shortest_path_length(G,1,4)    print (n)except nx.NetworkXNoPath:    print ('No path')

No path

强连通、弱连通

• 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。

距离

例1：弱连通

#-*- coding:utf8-*- import networkx as nximport matplotlib.pyplot as plt#G = nx.path_graph(4, create_using=nx.Graph())#0 1 2 3G = 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->3G.add_path([7, 8, 3])  #生成有向边：7->8->3for 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()

{0, 1, 2, 3, 7, 8}[6]

例2：强连通

#-*- coding:utf8-*- import networkx as nximport matplotlib.pyplot as plt#G = nx.path_graph(4, create_using=nx.Graph())#0 1 2 3G = nx.path_graph(4, create_using=nx.DiGraph())G.add_path([3, 8, 1])#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()

<generator object strongly_connected_components at 0x0000018ECC82DD58><class 'generator'>[{8, 1, 2, 3}, {0}]

子图

#-*- coding:utf8-*- import networkx as nximport matplotlib.pyplot as pltG = nx.DiGraph()G.add_path([5, 6, 7, 8])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()

条件过滤

原图

#-*- coding:utf8-*-import networkx as nximport matplotlib.pyplot as pltG = nx.DiGraph()road_nodes = {'a':{'id':1}, 'b':{'id':1}, 'c':{'id':3}, 'd':{'id':4}}road_edges = [('a', 'b'), ('a', 'c'), ('a', 'd'), ('b', 'd')]G.add_nodes_from(road_nodes)G.add_edges_from(road_edges)nx.draw(G)plt.savefig("youxiangtu.png")plt.show()

过滤函数

#-*- coding:utf8-*-import networkx as nximport matplotlib.pyplot as pltG = nx.DiGraph()def flt_func_draw():    flt_func = lambda d: d['id'] != 1    return flt_funcroad_nodes = {'a':{'id':1}, 'b':{'id':1}, 'c':{'id':3}, 'd':{'id':4}}road_edges = [('a', 'b'), ('a', 'c'), ('a', 'd'), ('b', 'd')]G.add_nodes_from(road_nodes.items())G.add_edges_from(road_edges)flt_func = flt_func_draw()part_G = G.subgraph(n for n, d in G.nodes_iter(data=True) if flt_func(d))nx.draw(part_G)plt.savefig("youxiangtu.png")plt.show()

pred，succ

#-*- coding:utf8-*-import networkx as nximport matplotlib.pyplot as pltG = nx.DiGraph()road_nodes = {'a':{'id':1}, 'b':{'id':1}, 'c':{'id':3}}road_edges = [('a', 'b'), ('a', 'c'), ('c', 'd')]G.add_nodes_from(road_nodes.items())G.add_edges_from(road_edges)print( G.nodes())print (G.edges())print ("a's pred ", G.pred['a'])print ("b's pred ", G.pred['b'])print ("c's pred ", G.pred['c'])print ("d's pred ", G.pred['d'])print ("a's succ ", G.succ['a'])print ("b's succ ", G.succ['b'])print ("c's succ ", G.succ['c'])print ("d's succ ", G.succ['d'])nx.draw(G)plt.savefig("wuxiangtu.png")plt.draw()

['a', 'b', 'c', 'd'][('a', 'b'), ('a', 'c'), ('c', 'd')]a's pred  {}b's pred  {'a': {}}c's pred  {'a': {}}d's pred  {'c': {}}a's succ  {'b': {}, 'c': {}}b's succ  {}c's succ  {'d': {}}d's succ  {}