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。
利用networkx可以以标准化和非标准化的数据格式存储网络、生成多种随机网络和经典网络、分析网络结构、建立网络模型、设计新的网络算法、进行网络绘制等。
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。
networkx以图（graph）为基本数据结构。图既可以由程序生成，也可以来自在线数据源，还可以从文件与数据库中读取。
基本流程：
1. 导入networkx，matplotlib包
2. 建立网络
3. 绘制网络 nx.draw()
4. 建立布局 pos = nx.spring_layout美化作用
import networkx as nx
import matplotlib.pyplot as plt
# G = nx.random_graphs.barabasi_albert_graph(100, 1) # 生成一个BA无向图
# G = nx.MultiGraph() # 有多重边无向图
# G = nx.MultiDiGraph() # 有多重边有向图
# G = nx.Graph() # 无多重边无向图
G = nx.DiGraph() # 无多重边有向图
...
G.clear() # 清空图draw（G，[pos,ax,hold]）draw_networkx(G，[pos,with_labels])draw_networkx_nodes(G,pos,[nodelist]) 绘制网络G的节点图draw_networkx_edges(G,pos[edgelist]) 绘制网络G的边图draw_networkx_edge_labels(G, pos[, ...]) 绘制网络G的边图，边有labeldraw_circular(G, **kwargs) Draw the graph G with a circular layout.draw_random(G, **kwargs) Draw the graph G with a random layout.draw_spectral(G, **kwargs) Draw the graph G with a spectral layout.draw_spring(G, **kwargs) Draw the graph G with a spring layout.draw_shell(G, **kwargs) Draw networkx graph with shell layout.draw_graphviz(G[, prog]) Draw networkx graph with graphviz layout.nx.draw(G,node_size = 30, with_label = False)上例，绘制节点的尺寸为30，不带标签的网络图。
node_size: 指定节点的尺寸大小(默认是300，单位未知，就是上图中那么大的点)node_color: 指定节点的颜色 (默认是红色，可以用字符串简单标识颜色，例如'r'为红色，'b'为绿色等，具体可查看手册)，用“数据字典”赋值的时候必须对字典取值（.values()）后再赋值node_shape: 节点的形状（默认是圆形，用字符串'o'标识，具体可查看手册）alpha: 透明度 (默认是1.0，不透明，0为完全透明)width: 边的宽度 (默认为1.0)edge_color: 边的颜色(默认为黑色)style: 边的样式(默认为实现，可选： solid|dashed|dotted,dashdot)with_labels: 节点是否带标签（默认为True）font_size: 节点标签字体大小 (默认为12)font_color: 节点标签字体颜色（默认为黑色）pos = nx.spring_layout
建立布局，对图进行布局美化，networkx 提供的布局方式有：
布局也可用pos参数指定，例如，nx.draw(G, pos = spring_layout(G)) 这样指定了networkx上以中心放射状分布.
G = nx.DiGraph() # 无多重边有向图
G.add_node(2) # 添加一个节点
G.add_nodes_from([3, 4, 5, 6, 8, 9, 10, 11, 12]) # 添加多个节点
G.add_cycle([1, 2, 3, 4]) # 添加环
G.add_edge(1, 3) # 添加一条边
G.add_edges_from([(3, 5), (3, 6), (6, 7)]) # 添加多条边
G.remove_node(8) # 删除一个节点
G.remove_nodes_from([9, 10, 11, 12]) # 删除多个节点
print("nodes: ", G.nodes()) # 输出所有的节点
print("edges: ", G.edges()) # 输出所有的边
print("number_of_edges: ", G.number_of_edges()) # 边的条数，只有一条边，就是（2，3）
print("degree: ", G.degree) # 返回节点的度
print("in_degree: ", G.in_degree) # 返回节点的入度
print("out_degree: ", G.out_degree) # 返回节点的出度
print("degree_histogram: ", nx.degree_histogram(G)) # 返回所有节点的分布序列输出>>
nodes: [2, 3, 4, 5, 6, 1, 7]
edges: [(2, 3), (3, 4), (3, 5), (3, 6), (4, 1), (6, 7), (1, 2), (1, 3)]
number_of_edges: 8
degree: [(2, 2), (3, 5), (4, 2), (5, 1), (6, 2), (1, 3), (7, 1)]
in_degree: [(2, 1), (3, 2), (4, 1), (5, 1), (6, 1), (1, 1), (7, 1)]
out_degree: [(2, 1), (3, 3), (4, 1), (5, 0), (6, 1), (1, 2), (7, 0)]
degree_histogram: [0, 2, 3, 1, 0, 1]
# 增加节点
G.add_node('a') # 添加一个节点1
G.add_nodes_from(['b', 'c', 'd', 'e']) # 加点集合
G.add_cycle(['f', 'g', 'h', 'j']) # 加环
H = nx.path_graph(10) # 返回由10个节点的无向图
G.add_nodes_from(H) # 创建一个子图H加入G
G.add_node(H) # 直接将图作为节点
# print("non_edges: ", G.non_edges) # 返回图中不存在的边
print("all_neighbors: ") # 返回图中节点的所有邻居
a = nx.all_neighbors(G, "f")
for i, node in enumerate(a):
print(i, node)
print("non_neighbors: ") # 返回图中没有邻居的节点
b = nx.non_neighbors(G, "f")
for i, node in enumerate(b):
print(i, node)
print("common_neighbors: ") # 返回图中两个节点的公共邻居
c = nx.common_neighbors(G, "j", "g")
for i, node in enumerate(c):
print(i, node)
print("non_edges: ") # 返回图中不存在的边
d = nx.non_edges(G)
for i, node in enumerate(d):
print(i, node)
nx.draw(G, with_labels=True, node_color='red')
plt.show()输出>>
all_neighbors:
0 g
1 j
non_neighbors:
0 a 1 b 2 c 3 d 4 e 5 h 6 0 7 1 8 2 9
common_neighbors:
0 h
1 f
non_edges:
0 (0, 'g')
1 (0, 'h')
2 (0, 1)
3 (0, 2)
4 (0, 'e')
...太多了1、图的属性：
G = nx.Graph(day='Monday') # 可以在创建图时分配图的属性
print(G.graph)
G.graph['day'] = 'Friday' # 也可以修改已有的属性
print(G.graph)
G.graph['name'] = 'time' # 可以随时添加新的属性到图中
print(G.graph)输出>>
{'day': 'Monday'}
{'day': 'Friday'}
{'day': 'Friday', 'name': 'time'}2、节点的属性：
G = nx.Graph(day='Monday')
G.add_node(1, index='1th') # 在添加节点时分配节点属性
print(G.node(data=True))
G.node[1]['index'] = '0th' # 通过G.node[][]来添加或修改属性
print(G.node(data=True))
G.add_nodes_from([2, 3], index='2/3th') # 从集合中添加节点时分配属性
print(G.node(data=True))输出>>
[(1, {'index': '1th'})]
[(1, {'index': '0th'})]
[(1, {'index': '0th'}), (2, {'index': '2/3th'}), (3, {'index': '2/3th'})]3、边的属性：
G.add_edge(1, 2, weight=10) # 在添加边时分配属性
print(G.edges(data=True))
G.add_edges_from([(1, 3), (4, 5)], len=22) # 从集合中添加边时分配属性
print(G.edges(data='len'))
G.add_edges_from([(3, 4, {'hight': 10}), (1, 4, {'high': 'unknow'})])
print(G.edges(data=True))
G[1][2]['weight'] = 100000 # 通过G[][][]来添加或修改属性
print(G.edges(data=True))输出>>
[(1, 2, {'weight': 10})]
[(1, 2, None), (1, 3, 22), (4, 5, 22)]
[(1, 2, {'weight': 10}), (1, 3, {'len': 22}), (1, 4, {'high': 'unknow'}), (3, 4, {'hight': 10}), (4, 5, {'len': 22})]
[(1, 2, {'weight': 100000}), (1, 3, {'len': 22}), (1, 4, {'high': 'unknow'}), (3, 4, {'hight': 10}), (4, 5, {'len': 22})]有向图和多重图的基本操作与无向图一致。
无向图与有向图之间可以相互转换。
G = nx.DiGraph()
H = G.to_undirected() # 有向图转化成无向图-方法1
H = nx.Graph(G) # 有向图转化成无向图-方法2
F = H.to_directed() # 无向图转化成有向图-方法1
F = nx.DiGraph(H) # 无向图转化成有向图-方法2使用pydot时会遇见如下的错误：
FileNotFoundError: [WinError 2] "twopi" not found in path.
解决参考：
1、 环形树状图
# 环形树状图
import os
import pydot
from networkx.drawing.nx_pydot import graphviz_layout
def set_prog(prog="dot"):
path = r'C:\Program Files (x86)\Graphviz 2.28\bin' # graphviz的bin目录
prog = os.path.join(path, prog) + '.exe'
return prog
G = nx.balanced_tree(3, 5)
pos = graphviz_layout(G, prog=set_prog("twopi"))
plt.figure(figsize=(8, 8))
nx.draw(G, pos, node_size=20, alpha=0.5, node_color="blue", with_labels=False)
plt.axis('equal')
plt.show()2、权重图
G = nx.Graph()
G.add_edge('a', 'b', weight=0.6)
G.add_edge('a', 'c', weight=0.2)
G.add_edge('c', 'd', weight=0.1)
G.add_edge('c', 'e', weight=0.7)
G.add_edge('c', 'f', weight=0.9)
G.add_edge('a', 'd', weight=0.3)
elarge = [(u, v) for (u, v, d) in G.edges(data=True) if d['weight'] > 0.5]
esmall = [(u, v) for (u, v, d) in G.edges(data=True) if d['weight'] <= 0.5]
pos = nx.spring_layout(G) # positions for all nodes
# nodes
nx.draw_networkx_nodes(G, pos, node_size=700)
# edges
nx.draw_networkx_edges(G, pos, edgelist=elarge, width=6)
nx.draw_networkx_edges(G, pos, edgelist=esmall, width=6, alpha=0.5, edge_color='b', style='dashed')
# labels-标签
# nx.draw_networkx_labels(G, pos, font_size=20, font_family='sans-serif')
plt.axis('off')
plt.show()3、Giant Component
import pydot
from networkx.drawing.nx_pydot import graphviz_layout
def set_prog(prog="dot"):
path = r'C:\Program Files (x86)\Graphviz 2.28\bin' # graphviz的bin目录
prog = os.path.join(path, prog) + '.exe'
return prog
pvals = [0.003, 0.006, 0.008, 0.015] # the range of p values should be close to the threshold
plt.subplots_adjust(left=0, right=1, bottom=0, top=0.95, wspace=0.01, hspace=0.01)
for i, p in enumerate(pvals):
G = nx.binomial_graph(150, p) # 150 nodes
pos = graphviz_layout(G, prog=set_prog("neato"))
plt.subplot(2, 2, i + 1)
plt.title("p = %6.3f" % (p,))
nx.draw(G, pos, with_labels=False, node_size=10)
# 找出最大连通数的子图
Gcc = sorted(nx.connected_component_subgraphs(G), key=len, reverse=True)
G0 = Gcc[0]
nx.draw_networkx_edges(G0, pos, with_labels=False, edge_color='r', width=6.0)
# 画出其他连通数子图
[nx.draw_networkx_edges(Gi, pos, with_labels=False, edge_color='r', alpha=0.3, width=5.0) for Gi in Gcc[1:] if
len(Gi) > 1]
plt.show()
4、Random Geometric Graph 随机几何图
G = nx.random_geometric_graph(200, 0.125)
pos = nx.get_node_attributes(G, 'pos') # position is stored as node attribute data for random_geometric_graph
# find node near center (0.5,0.5)
dmin = 1
ncenter = 0
for n in pos:
x, y = pos[n]
d = (x - 0.5) ** 2 + (y - 0.5) ** 2
if d < dmin:
ncenter = n
dmin = d
# color by path length from node near center
p = dict(nx.single_source_shortest_path_length(G, ncenter))
plt.figure(figsize=(8, 8))
nx.draw_networkx_edges(G, pos, nodelist=[ncenter], alpha=0.4)
nx.draw_networkx_nodes(G, pos, nodelist=list(p.keys()), node_size=80, node_color=list(p.values()), cmap=plt.cm.Reds_r)
plt.xlim(-0.05, 1.05)
plt.ylim(-0.05, 1.05)
plt.show()5、节点颜色渐变
G = nx.cycle_graph(24)
pos = nx.spring_layout(G, iterations=200)
nx.draw(G, pos, node_color=range(24), node_size=800, cmap=plt.cm.Blues)
plt.show()6、边颜色渐变
G = nx.star_graph(20)
pos = nx.spring_layout(G) # 布局为中心放射状
colors = range(20)
nx.draw(G, pos, node_color='#A0CBE2', edge_color=colors, width=2, edge_cmap=plt.cm.Blues, with_labels=False)
plt.show()7、Atlas
import os
import pydot
import random
from networkx.generators.atlas import graph_atlas_g
from networkx.drawing.nx_pydot import graphviz_layout
from networkx.algorithms.isomorphism.isomorph import graph_could_be_isomorphic as isomorphic
def set_prog(prog="dot"):
path = r'C:\Program Files (x86)\Graphviz 2.28\bin' # graphviz的bin目录
prog = os.path.join(path, prog) + '.exe'
return prog
def atlas6():
""" Return the atlas of all connected graphs of 6 nodes or less.
Attempt to check for isomorphisms and remove.
"""
Atlas = graph_atlas_g()[0:208] # 208
# remove isolated nodes, only connected graphs are left
U = nx.Graph() # graph for union of all graphs in atlas
for G in Atlas:
for n in [n for n in G if G.degree(n) == 0]:
G.remove_node(n)
U = nx.disjoint_union(U, G)
# iterator of graphs of all connected components
C = (U.subgraph(c) for c in nx.connected_components(U))
UU = nx.Graph()
# do quick isomorphic-like check, not a true isomorphism checker
nlist = [] # list of nonisomorphic graphs
for G in C:
# check against all nonisomorphic graphs so far
if not iso(G, nlist):
nlist.append(G)
UU = nx.disjoint_union(UU, G) # union the nonisomorphic graphs
return UU
def iso(G1, glist):
"""Quick and dirty nonisomorphism checker used to check isomorphisms."""
if any(isomorphic(G1, G2) for G2 in glist):
return True
return False
G = atlas6()
print("graph has %d nodes with %d edges" % (nx.number_of_nodes(G), nx.number_of_edges(G)))
print(nx.number_connected_components(G), "connected components")
plt.figure(1, figsize=(8, 8))
pos = graphviz_layout(G, prog=set_prog("neato"))
# color nodes the same in each connected subgraph
C = (G.subgraph(c) for c in nx.connected_components(G))
for g in C:
c = [random.random()] * nx.number_of_nodes(g) # random color...
nx.draw(g, pos, node_size=40, node_color=c, vmin=0.0, vmax=1.0, with_labels=False)
plt.show()8、Club
import networkx.algorithms.bipartite as bipartite
G = nx.davis_southern_women_graph()
women = G.graph['top']
clubs = G.graph['bottom']
print("Biadjacency matrix")
print(bipartite.biadjacency_matrix(G, women, clubs))
# project bipartite graph onto women nodes
W = bipartite.projected_graph(G, women)
print('')
print("#Friends, Member")
for w in women:
print('%d %s' % (W.degree(w), w))
# project bipartite graph onto women nodes keeping number of co-occurence
# the degree computed is weighted and counts the total number of shared contacts
W = bipartite.weighted_projected_graph(G, women)
print('')
print("#Friend meetings, Member")
for w in women:
print('%d %s' % (W.degree(w, weight='weight'), w))
nx.draw(G, node_color="red")
plt.show()
参考：