python复杂网络分析库NetworkX-白红宇

阅读目录

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。

引入模块

import networkx as nxprint nx

无向图

例1：

#!-*- coding:utf8-*- 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()

输出

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

例2：

#-*- 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

例1：

#!-*- 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2，例子中把有向图转化为无向图：

#!-*- 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)])G = G.to_undirected()nx.draw(G)plt.savefig("wuxiangtu.png")plt.show()

注意区分以下2例

例3-1

#-*- 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.iteritems())G.add_edges_from(road_edges)nx.draw(G)plt.savefig("youxiangtu.png")plt.show()

例3-2

#-*- 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.iteritems())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。

例1：

#!-*- 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()

输出

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

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]

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 nexcept nx.NetworkXNoPath:    print '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 cprint [len(c) for c in sorted(nx.weakly_connected_components(G), key=len, reverse=True)]nx.draw(G)plt.savefig("youxiangtu.png")plt.show()

执行结果

set([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 conprint type(con)print list(con)nx.draw(G)plt.savefig("youxiangtu.png")plt.show()

执行结果


     
      
       [set([8, 1, 2, 3]), set([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()

图

#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.iteritems())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()

图

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.iteritems())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()

结果

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

本文转自jihite博客园博客，原文链接：http://www.cnblogs.com/kaituorensheng/p/5423131.html，如需转载请自行联系原作者