NetworkX是一個用Python語言開發的圖論與復雜網絡建模工具，內置了常用的圖與復雜網絡分析算法，可以方便的進行復雜網絡數據分析、仿真建模等工作。networkx支持創建簡單無向圖、有向圖和多重圖（multigraph）；內置許多標準的圖論算法，節點可為任意數據；支持任意的邊值維度，功能豐富，簡單易用。

引入模塊

importnetworkx as nxprint nx

無向圖

例1：

#!-*- coding:utf8-*-

importnetworkx as nximportmatplotlib.pyplot as plt

G= nx.Graph() #建立一個空的無向圖G

G.add_node(1) #添加一個節點1

G.add_edge(2,3) #添加一條邊2-3（隱含著添加了兩個節點2、3）

G.add_edge(3,2) #對于無向圖，邊3-2與邊2-3被認為是一條邊

print "nodes:", G.nodes() #輸出全部的節點： [1, 2, 3]

print "edges:", G.edges() #輸出全部的邊：[(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-*-

importnetworkx as nximportmatplotlib.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-*-

importnetworkx as nximportmatplotlib.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：有向圖和無向圖可以互相轉換，使用函數：

Graph.to_undirected()

Graph.to_directed()

例2，例子中把有向圖轉化為無向圖：

#!-*- coding:utf8-*-

importnetworkx as nximportmatplotlib.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()

注意區分以下2例

例3-1

#-*- coding:utf8-*-

importnetworkx as nximportmatplotlib.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-*-

importnetworkx as nximportmatplotlib.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

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

例1：

#!-*- coding:utf8-*-

importnetworkx as nximportmatplotlib.pyplot as plt

G= nx.Graph() #建立一個空的無向圖G

G.add_edge(2,3) #添加一條邊2-3（隱含著添加了兩個節點2、3）

G.add_weighted_edges_from([(3, 4, 3.5),(3, 5, 7.0)]) #對于無向圖，邊3-2與邊2-3被認為是一條邊

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 -*-

importnetworkx as nximportmatplotlib.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

importnetworkx 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)printnexceptnx.NetworkXNoPath:print 'No path'

強連通、弱連通

強連通：有向圖中任意兩點v1、v2間存在v1到v2的路徑（path）及v2到v1的路徑。

弱聯通：將有向圖的所有的有向邊替換為無向邊，所得到的圖稱為原圖的基圖。如果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-*-

importnetworkx as nximportmatplotlib.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 innx.weakly_connected_components(G):printcprint [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-*-

importnetworkx as nximportmatplotlib.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)printconprinttype(con)printlist(con)

nx.draw(G)

plt.savefig("youxiangtu.png")

plt.show()

執行結果

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

子圖

#-*- coding:utf8-*-

importnetworkx as nximportmatplotlib.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 一樣

nx.draw(sub_graph)

plt.savefig("youxiangtu.png")

plt.show()

條件過濾

#原圖

#-*- coding:utf8-*-

importnetworkx as nximportmatplotlib.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-*-

importnetworkx as nximportmatplotlib.pyplot as plt

G=nx.DiGraph()defflt_func_draw():

flt_func= lambda d: d['id'] != 1

returnflt_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) ifflt_func(d))

nx.draw(part_G)

plt.savefig("youxiangtu.png")

plt.show()

圖

pred，succ

#-*- coding:utf8-*-import networkxasnx

import matplotlib.pyplotasplt

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 {}

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