本文目录导读：
我来为你详细介绍使用 NetworkX 进行图分析的典型案例。
基础安装和导入
# 安装 # pip install networkx matplotlib import networkx as nx import matplotlib.pyplot as plt import numpy as np
创建不同类型的图
# 创建无向图
G = nx.Graph()
# 创建有向图
DG = nx.DiGraph()
# 添加节点
G.add_nodes_from([1, 2, 3, 4, 5])
# 添加边
G.add_edges_from([(1, 2), (1, 3), (2, 3), (3, 4), (4, 5)])
# 添加带权重的边
G.add_edge(1, 2, weight=4.0)
G.add_edge(2, 3, weight=2.0)
# 可视化
nx.draw(G, with_labels=True, node_color='lightblue',
node_size=500, font_size=16)
plt.show()
案例一：社交网络分析
import networkx as nx
import matplotlib.pyplot as plt
# 创建社交网络
def create_social_network():
G = nx.Graph()
# 添加用户（节点）和关系（边）
users = ['Alice', 'Bob', 'Charlie', 'David', 'Eve', 'Frank']
G.add_nodes_from(users)
# 添加朋友关系
friendships = [
('Alice', 'Bob'), ('Alice', 'Charlie'),
('Bob', 'Charlie'), ('Bob', 'David'),
('David', 'Eve'), ('Eve', 'Frank'),
('Charlie', 'Frank')
]
G.add_edges_from(friendships)
return G
# 分析社交网络
def analyze_social_network(G):
print("=== 社交网络分析 ===")
# 基本统计
print(f"用户数量: {G.number_of_nodes()}")
print(f"好友关系数量: {G.number_of_edges()}")
# 计算度中心性（好友数量）
degree_centrality = nx.degree_centrality(G)
print("\n度中心性（影响力）:")
for user, centrality in sorted(degree_centrality.items(),
key=lambda x: x[1], reverse=True):
print(f"{user}: {centrality:.3f}")
# 找出最有人气的人
most_popular = max(degree_centrality, key=degree_centrality.get)
print(f"\n最受欢迎的人: {most_popular}")
# 计算最短路径
print("\n最短路径:")
print(f"Alice到Frank: {nx.shortest_path(G, 'Alice', 'Frank')}")
# 检测社区
communities = nx.community.greedy_modularity_communities(G)
print(f"\n检测到的社区数量: {len(communities)}")
for i, community in enumerate(communities, 1):
print(f"社区 {i}: {sorted(community)}")
# 可视化
plt.figure(figsize=(10, 8))
pos = nx.spring_layout(G, seed=42)
nx.draw(G, pos, with_labels=True, node_color='lightgreen',
node_size=2000, font_size=10, font_weight='bold',
edge_color='gray')
plt.title("社交网络图")
plt.show()
# 执行分析
G = create_social_network()
analyze_social_network(G)
案例二：交通网络最短路径
import networkx as nx
import matplotlib.pyplot as plt
# 创建交通网络
def create_transport_network():
G = nx.Graph()
# 添加城市节点和距离（权重）
cities = ['北京', '上海', '广州', '深圳', '成都', '武汉', '西安']
# 添加带权重的边（距离km）
routes = [
('北京', '上海', 1200),
('北京', '西安', 1100),
('北京', '武汉', 1150),
('上海', '广州', 1400),
('上海', '深圳', 1300),
('广州', '深圳', 100),
('广州', '武汉', 850),
('武汉', '成都', 1100),
('西安', '成都', 700),
('成都', '深圳', 1500)
]
G.add_weighted_edges_from(routes)
return G
# 路径分析
def analyze_routes(G):
print("=== 交通网络分析 ===")
# 查找最短路径
start, end = '北京', '深圳'
shortest_path = nx.shortest_path(G, start, end, weight='weight')
shortest_distance = nx.shortest_path_length(G, start, end, weight='weight')
print(f"从{start}到{end}的最短路径:")
print(f"路径: {' -> '.join(shortest_path)}")
print(f"总距离: {shortest_distance}km")
# 计算所有最短路径
print(f"\n从{start}到所有城市的最短距离:")
for city, distance in nx.single_source_dijkstra_path_length(G, start, weight='weight'):
if city != start:
print(f"{start} -> {city}: {distance}km")
# 查找最小生成树（最经济的网络连接）
mst = nx.minimum_spanning_tree(G, weight='weight')
print(f"\n最小生成树总距离: {sum(weight for _, _, weight in mst.edges(data='weight'))}km")
# 可视化
plt.figure(figsize=(12, 8))
pos = nx.spring_layout(G, seed=42)
# 绘制原始网络
nx.draw(G, pos, with_labels=True, node_color='lightblue',
node_size=1500, font_size=12)
# 添加边权重标签
edge_labels = nx.get_edge_attributes(G, 'weight')
nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels)
# 高亮最短路径
path_edges = list(zip(shortest_path, shortest_path[1:]))
nx.draw_networkx_edges(G, pos, edgelist=path_edges,
edge_color='red', width=3)
plt.title(f"交通网络 - 红色为{start}到{end}最短路径")
plt.show()
# 执行分析
G = create_transport_network()
analyze_routes(G)
案例三：推荐系统（协同过滤）
import networkx as nx
import matplotlib.pyplot as plt
def create_recommendation_graph():
G = nx.Graph()
# 用户和商品
users = ['User_A', 'User_B', 'User_C']
products = ['商品1', '商品2', '商品3', '商品4', '商品5']
# 用户-商品购买关系
purchases = [
('User_A', '商品1'), ('User_A', '商品2'), ('User_A', '商品4'),
('User_B', '商品1'), ('User_B', '商品3'), ('User_B', '商品5'),
('User_C', '商品2'), ('User_C', '商品4'), ('User_C', '商品5')
]
G.add_nodes_from(users, bipartite='users')
G.add_nodes_from(products, bipartite='products')
G.add_edges_from(purchases)
return G, users, products
def generate_recommendations(G, users, products, target_user):
print(f"\n=== 为{target_user}推荐商品 ===")
# 找到目标用户购买的商品
user_products = list(G.neighbors(target_user))
print(f"{target_user}已购买: {user_products}")
# 找到购买了相同商品的其他用户
recommended_products = set()
for product in user_products:
similar_users = list(G.neighbors(product))
for user in similar_users:
if user != target_user:
# 找出这些用户购买的其他商品
other_products = list(G.neighbors(user))
for p in other_products:
if p not in user_products:
recommended_products.add(p)
print(f"推荐商品: {recommended_products}")
return recommended_products
# 执行推荐
G, users, products = create_recommendation_graph()
recommendations = generate_recommendations(G, users, products, 'User_A')
# 可视化
plt.figure(figsize=(10, 6))
pos = nx.bipartite_layout(G, users)
nx.draw(G, pos, with_labels=True, node_color=['lightblue' if n in users else 'lightgreen'
for n in G.nodes()], node_size=1500)"用户-商品二分图")
plt.show()
案例四：网络传播模拟
import networkx as nx
import matplotlib.pyplot as plt
import random
def simulate_information_spread(G, start_node, probability=0.3, max_steps=5):
"""模拟信息传播"""
infected = set([start_node])
newly_infected = set([start_node])
history = [list(infected)]
for step in range(max_steps):
next_infected = set()
for node in newly_infected:
# 对每个邻居以一定概率传播
for neighbor in G.neighbors(node):
if neighbor not in infected and random.random() < probability:
next_infected.add(neighbor)
infected.update(next_infected)
newly_infected = next_infected
history.append(list(infected))
if not newly_infected:
break
return infected, history
# 创建随机网络
G = nx.erdos_renyi_graph(20, 0.15, seed=42)
# 模拟信息传播
start_node = 0
infected, history = simulate_information_spread(G, start_node, probability=0.4)
print(f"传播前的节点数: {1}")
print(f"传播后的节点数: {len(infected)}")
print(f"传播率: {len(infected)/G.number_of_nodes()*100:.1f}%")
# 可视化传播过程
plt.figure(figsize=(8, 6))
pos = nx.spring_layout(G, seed=42)
colors = ['red' if n in infected else 'lightblue' for n in G.nodes()]
nx.draw(G, pos, with_labels=True, node_color=colors,
node_size=500, font_size=10)f"信息传播结果（从节点{start_node}开始）")
plt.show()
高级分析功能
import networkx as nx
def advanced_analysis(G):
"""高级图分析功能"""
# 1. 中心性分析
print("\n=== 中心性分析 ===")
degree_cent = nx.degree_centrality(G)
betweenness_cent = nx.betweenness_centrality(G)
closeness_cent = nx.closeness_centrality(G)
eigenvector_cent = nx.eigenvector_centrality(G)
print(f"度中心性（前3名）: {dict(sorted(degree_cent.items(), key=lambda x: x[1], reverse=True)[:3])}")
print(f"介数中心性（前3名）: {dict(sorted(betweenness_cent.items(), key=lambda x: x[1], reverse=True)[:3])}")
# 2. 聚类系数
print(f"\n全局聚类系数: {nx.average_clustering(G):.3f}")
# 3. 密度
print(f"网络密度: {nx.density(G):.3f}")
# 4. 连通性分析
if nx.is_connected(G):
print("网络是连通的")
print(f"直径: {nx.diameter(G)}")
print(f"平均最短路径长度: {nx.average_shortest_path_length(G):.3f}")
# 5. 检测桥接边（关键连接）
bridges = list(nx.bridges(G))
print(f"桥接边数量: {len(bridges)}")
if bridges:
print(f"桥接边: {bridges[:5]}...") # 只显示前5个
# 创建示例图并分析
G = nx.karate_club_graph() # 使用经典的Zachary's Karate Club数据集
advanced_analysis(G)
# 可视化
plt.figure(figsize=(10, 8))
pos = nx.spring_layout(G, seed=42)
nx.draw(G, pos, with_labels=True, node_color='lightcoral',
node_size=500, font_size=8)"Zachary's Karate Club Network")
plt.show()
常用操作速查表
# 创建图 G = nx.Graph() # 无向图 DG = nx.DiGraph() # 有向图 # 添加节点/边 G.add_node(1) # 添加单个节点 G.add_nodes_from([1,2,3]) # 添加多个节点 G.add_edge(1, 2) # 添加单条边 G.add_edges_from([(1,2), (2,3)]) # 添加多条边 # 基本属性 G.number_of_nodes() # 节点数 G.number_of_edges() # 边数 G.nodes() # 所有节点 G.edges() # 所有边 G.degree() # 度 # 路径分析 nx.shortest_path(G, 1, 3) # 最短路径 nx.shortest_path_length(G, 1, 3) # 最短路径长度 nx.connected_components(G) # 连通分量 # 中心性 nx.degree_centrality(G) # 度中心性 nx.betweenness_centrality(G) # 介数中心性 nx.closeness_centrality(G) # 接近中心性
这些案例覆盖了 NetworkX 的主要功能,你可以根据实际需求调整和使用。
