Network Analysis

网络分析

概述

此技能可分析网络结构，以识别社群、衡量中心性、检测有影响力的节点，并可视化社交网络、组织结构和互联系统中的复杂关系。

适用场景

• 分析社交网络，识别有影响力的用户和社群结构
• 绘制组织层级图，识别关键连接者或瓶颈
• 研究引文网络，寻找有影响力的研究论文和协作模式
• 基于网络关系和相似性构建推荐系统
• 分析供应链网络，优化物流并识别薄弱环节
• 通过分析金融交易网络检测欺诈模式

网络概念

• 节点：单个实体
• 边：连接／关系
• 度：连接数量
• 中心性：衡量节点重要性的指标
• 社群：连接紧密的群组
• 聚类系数：局部密度

关键指标

• 度中心性：连接数量
• 介数中心性：对路径的控制程度
• 接近中心性：到其他节点的平均距离
• 特征向量中心性：与重要节点的连接
• 模块度：社群结构的强度

使用 Python 实现

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import networkx as nx
from collections import defaultdict, Counter
import seaborn as sns

# Create sample network (social network)
G = nx.Graph()

# Add nodes with attributes
nodes = [
    ('Alice', {'role': 'Manager', 'dept': 'Sales'}),
    ('Bob', {'role': 'Engineer', 'dept': 'Tech'}),
    ('Carol', {'role': 'Designer', 'dept': 'Design'}),
    ('David', {'role': 'Engineer', 'dept': 'Tech'}),
    ('Eve', {'role': 'Analyst', 'dept': 'Sales'}),
    ('Frank', {'role': 'Manager', 'dept': 'HR'}),
    ('Grace', {'role': 'Designer', 'dept': 'Design'}),
    ('Henry', {'role': 'Engineer', 'dept': 'Tech'}),
    ('Iris', {'role': 'Analyst', 'dept': 'Sales'}),
    ('Jack', {'role': 'Manager', 'dept': 'Finance'}),
]

for node, attrs in nodes:
    G.add_node(node, **attrs)

# Add edges (relationships)
edges = [
    ('Alice', 'Bob'), ('Alice', 'Carol'), ('Alice', 'Eve'),
    ('Bob', 'David'), ('Bob', 'Henry'), ('Carol', 'Grace'),
    ('David', 'Henry'), ('Eve', 'Iris'), ('Frank', 'Jack'),
    ('Grace', 'Carol'), ('Alice', 'Frank'), ('Bob', 'Carol'),
    ('Eve', 'Alice'), ('Iris', 'Eve'), ('Jack', 'Frank'),
    ('Henry', 'David'), ('Carol', 'David'),
]

G.add_edges_from(edges)

print("Network Summary:")
print(f"Nodes: {G.number_of_nodes()}")
print(f"Edges: {G.number_of_edges()}")
print(f"Density: {nx.density(G):.2%}")

# 1. Degree Centrality
degree_centrality = nx.degree_centrality(G)
print("\n1. Degree Centrality (Top 5):")
for node, score in sorted(degree_centrality.items(), key=lambda x: x[1], reverse=True)[:5]:
    print(f"  {node}: {score:.3f}")

# 2. Betweenness Centrality (control over network)
betweenness_centrality = nx.betweenness_centrality(G)
print("\n2. Betweenness Centrality (Top 5):")
for node, score in sorted(betweenness_centrality.items(), key=lambda x: x[1], reverse=True)[:5]:
    print(f"  {node}: {score:.3f}")

# 3. Closeness Centrality (average distance to others)
closeness_centrality = nx.closeness_centrality(G)
print("\n3. Closeness Centrality (Top 5):")
for node, score in sorted(closeness_centrality.items(), key=lambda x: x[1], reverse=True)[:5]:
    print(f"  {node}: {score:.3f}")

# 4. Eigenvector Centrality
try:
    eigenvector_centrality = nx.eigenvector_centrality(G, max_iter=100)
    print("\n4. Eigenvector Centrality (Top 5):")
    for node, score in sorted(eigenvector_centrality.items(), key=lambda x: x[1], reverse=True)[:5]:
        print(f"  {node}: {score:.3f}")
except:
    print("\n4. Eigenvector Centrality: Not converged")

# 5. Community Detection (using modularity)
from networkx.algorithms import community

communities = list(community.greedy_modularity_communities(G))
print(f"\n5. Community Detection:")
print(f"Number of communities: {len(communities)}")
for i, comm in enumerate(communities):
    print(f"  Community {i+1}: {list(comm)}")

# 6. Network Statistics
degrees = [G.degree(n) for n in G.nodes()]
print(f"\n6. Network Statistics:")
print(f"Average Degree: {np.mean(degrees):.2f}")
print(f"Max Degree: {max(degrees)}")
print(f"Min Degree: {min(degrees)}")
print(f"Clustering Coefficient: {nx.average_clustering(G):.3f}")
print(f"Number of Triangles: {sum(nx.triangles(G).values()) // 3}")

# Visualization
fig, axes = plt.subplots(2, 2, figsize=(15, 12))

# Network layout
pos = nx.spring_layout(G, k=0.5, iterations=50, seed=42)

# 1. Network Graph (colored by degree)
ax = axes[0, 0]
node_colors = [degree_centrality[node] for node in G.nodes()]
nx.draw_networkx_nodes(G, pos, node_color=node_colors, node_size=1000, cmap='YlOrRd', ax=ax)
nx.draw_networkx_edges(G, pos, alpha=0.5, ax=ax)
nx.draw_networkx_labels(G, pos, font_size=8, ax=ax)
ax.set_title('Network Graph (Colored by Degree Centrality)')
ax.axis('off')

# 2. Network Graph (colored by communities)
ax = axes[0, 1]
color_map = []
colors = plt.cm.Set3(np.linspace(0, 1, len(communities)))
node_to_color = {}
for i, comm in enumerate(communities):
    for node in comm:
        node_to_color[node] = colors[i]
color_map = [node_to_color[node] for node in G.nodes()]

nx.draw_networkx_nodes(G, pos, node_color=color_map, node_size=1000, ax=ax)
nx.draw_networkx_edges(G, pos, alpha=0.5, ax=ax)
nx.draw_networkx_labels(G, pos, font_size=8, ax=ax)
ax.set_title('Network Graph (Colored by Community)')
ax.axis('off')

# 3. Centrality Comparison
ax = axes[1, 0]
centrality_df = pd.DataFrame({
    'Degree': degree_centrality,
    'Betweenness': betweenness_centrality,
    'Closeness': closeness_centrality,
}).head(8)

centrality_df.plot(kind='barh', ax=ax, width=0.8)
ax.set_xlabel('Centrality Score')
ax.set_title('Top 8 Nodes - Centrality Comparison')
ax.legend(loc='lower right')
ax.grid(True, alpha=0.3, axis='x')

# 4. Degree Distribution
ax = axes[1, 1]
degree_sequence = sorted([d for n, d in G.degree()], reverse=True)
degree_count = Counter(degree_sequence)
degrees_unique = sorted(degree_count.keys())
counts = [degree_count[d] for d in degrees_unique]

ax.bar(degrees_unique, counts, color='steelblue', edgecolor='black', alpha=0.7)
ax.set_xlabel('Degree')
ax.set_ylabel('Count')
ax.set_title('Degree Distribution')
ax.grid(True, alpha=0.3, axis='y')

plt.tight_layout()
plt.show()

# 7. Path Analysis
print(f"\n7. Path Analysis:")
try:
    shortest_path = nx.shortest_path_length(G, 'Alice', 'Jack')
    print(f"Shortest path from Alice to Jack: {shortest_path}")
except nx.NetworkXNoPath:
    print("No path exists between nodes")

# 8. Connectivity Analysis
print(f"\n8. Connectivity Analysis:")
print(f"Is connected: {nx.is_connected(G)}")
num_components = nx.number_connected_components(G)
print(f"Number of connected components: {num_components}")

# 9. Similarity Measures
def jaccard_similarity(node1, node2):
    neighbors1 = set(G.neighbors(node1)) | {node1}
    neighbors2 = set(G.neighbors(node2)) | {node2}
    intersection = len(neighbors1 & neighbors2)
    union = len(neighbors1 | neighbors2)
    return intersection / union if union > 0 else 0

print(f"\n9. Node Similarity (Jaccard):")
print(f"Alice & Bob: {jaccard_similarity('Alice', 'Bob'):.3f}")
print(f"Alice & Jack: {jaccard_similarity('Alice', 'Jack'):.3f}")

# 10. Influence Score (Combination of metrics)
influence_score = {}
for node in G.nodes():
    score = (degree_centrality[node] * 0.4 +
             betweenness_centrality[node] * 0.3 +
             closeness_centrality[node] * 0.3)
    influence_score[node] = score

print(f"\n10. Influence Score (Top 5):")
for node, score in sorted(influence_score.items(), key=lambda x: x[1], reverse=True)[:5]:
    print(f"  {node}: {score:.3f}")

# Summary
print("\n" + "="*50)
print("NETWORK ANALYSIS SUMMARY")
print("="*50)
print(f"Most influential: {max(influence_score, key=influence_score.get)}")
print(f"Most connected: {max(degree_centrality, key=degree_centrality.get)}")
print(f"Network bottleneck: {max(betweenness_centrality, key=betweenness_centrality.get)}")
print(f"Closest to all: {max(closeness_centrality, key=closeness_centrality.get)}")
print("="*50)

中心性指标

• 度：仅统计直接连接
• 介数：群组之间的桥梁
• 接近度：对网络的可达性
• 特征向量：连接到重要节点
• PageRank：随机游走概率

社群检测

• 模块度优化：查找紧密群组
• Louvain 算法：层级社群
• K-clique：重叠社群
• 谱方法：基于特征值的方法

应用场景

• 社交网络分析
• 组织结构分析
• 引文网络
• 推荐网络
• 供应链分析

交付成果

• 网络可视化
• 中心性分析
• 社群检测结果
• 连通性指标
• 影响力排名
• 关键节点识别
• 网络统计摘要