python複雜網絡分析庫NetworkX

NetworkX是一個用Python語言開發的圖論與複雜網絡建模工具，內置了經常使用的圖與複雜網絡分析算法，能夠方便的進行復雜網絡數據分析、仿真建模等工做。networkx支持建立簡單無向圖、有向圖和多重圖（multigraph）；內置許多標準的圖論算法，節點可爲任意數據；支持任意的邊值維度，功能豐富，簡單易用。

引入模塊

import networkx as nx
print nx

無向圖

例1：

#!-*- coding:utf8-*-
 
import networkx as nx
import matplotlib.pyplot as plt

G = nx.Graph()                 #創建一個空的無向圖G
G.add_node(1)                  #添加一個節點1
G.add_edge(2,3)                #添加一條邊2-3（隱含着添加了兩個節點二、3）
G.add_edge(3,2)                #對於無向圖，邊3-2與邊2-3被認爲是一條邊
print "nodes:", G.nodes()      #輸出所有的節點： [1, 2, 3]
print "edges:", G.edges()      #輸出所有的邊：[(2, 3)]
print "number of edges:", G.number_of_edges()   #輸出邊的數量：1
nx.draw(G)
plt.savefig("wuxiangtu.png")
plt.show()

輸出

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

例2：

#-*- coding:utf8-*-
 
import networkx as nx
import matplotlib.pyplot as plt
G = nx.DiGraph()
G.add_node(1)
G.add_node(2)                  #加點
G.add_nodes_from([3,4,5,6])    #加點集合
G.add_cycle([1,2,3,4])         #加環
G.add_edge(1,3)     
G.add_edges_from([(3,5),(3,6),(6,7)])  #加邊集合
nx.draw(G)
plt.savefig("youxiangtu.png")
plt.show()

有向圖

例1：

#!-*- coding:utf8-*-
 
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)
plt.savefig("youxiangtu.png")
plt.show()

注：有向圖和無向圖能夠互相轉換，使用函數：

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

例2，例子中把有向圖轉化爲無向圖：

#!-*- coding:utf8-*-
 
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)])
G = G.to_undirected()
nx.draw(G)
plt.savefig("wuxiangtu.png")
plt.show()

注意區分如下2例

例3-1

#-*- coding:utf8-*-

import networkx as nx
import matplotlib.pyplot as plt

G = 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 nx
import matplotlib.pyplot as plt

G = 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()

加權圖

有向圖和無向圖均可以給邊賦予權重，用到的方法是add_weighted_edges_from，它接受1個或多個三元組[u,v,w]做爲參數，其中u是起點，v是終點，w是權重。

例1：

#!-*- coding:utf8-*-
 
import networkx as nx
import matplotlib.pyplot as plt
G = nx.Graph()                                        #創建一個空的無向圖G
G.add_edge(2,3)                                     #添加一條邊2-3（隱含着添加了兩個節點二、3）
G.add_weighted_edges_from([(3, 4, 3.5),(3, 5, 7.0)])                                     #對於無向圖，邊3-2與邊2-3被認爲是一條邊


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()

輸出

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

 

經典圖論算法計算

計算1：求無向圖的任意兩點間的最短路徑

# -*- coding: cp936 -*-
import networkx as nx
import matplotlib.pyplot as plt
 
#計算1：求無向圖的任意兩點間的最短路徑
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]

計算2：找圖中兩個點的最短路徑

import networkx as nx
G=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'

強連通、弱連通

• 強連通：有向圖中任意兩點v一、v2間存在v1到v2的路徑（path）及v2到v1的路徑。
• 弱聯通：將有向圖的全部的有向邊替換爲無向邊，所獲得的圖稱爲原圖的基圖。若是一個有向圖的基圖是連通圖，則有向圖是弱連通圖。

距離

例1：弱連通

#-*- coding:utf8-*-
 
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())    #默認生成節點0 1 2 3，生成有向變0->1,1->2,2->3
G.add_path([7, 8, 3])  #生成有向邊：7->8->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()

執行結果

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

例2：強連通

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

執行結果

<generator object strongly_connected_components at 0x0000000008AA1D80>
<type 'generator'>
[set([8, 1, 2, 3]), set([0])]

子圖

#-*- coding:utf8-*-
 
import networkx as nx
import matplotlib.pyplot as plt
G = nx.DiGraph()
G.add_path([5, 6, 7, 8])
sub_graph = G.subgraph([5, 6, 8])
#sub_graph = G.subgraph((5, 6, 8))  #ok  同樣

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

條件過濾

#原圖

#-*- coding:utf8-*-

import networkx as nx
import matplotlib.pyplot as plt
G = 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()

圖

#過濾函數

#-*- coding:utf8-*-

import networkx as nx
import matplotlib.pyplot as plt
G = nx.DiGraph()
def flt_func_draw():
    flt_func = lambda d: d['id'] != 1
    return flt_func

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.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()

圖

pred，succ

#-*- coding:utf8-*-

import networkx as nx
import matplotlib.pyplot as plt
G = 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()

結果

['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  {}