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434 lines
16 KiB
434 lines
16 KiB
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import pickle
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import pandas as pd
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import networkx as nx
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import numpy as np
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from tqdm import tqdm
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import os
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import matplotlib.pyplot as plt
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import seaborn as sns
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from collections import defaultdict
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def load_graph(graph_file):
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"""
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加载保存的图结构
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Args:
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graph_file (str): 图文件路径
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Returns:
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nx.Graph: 网络图对象
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"""
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print(f"正在加载图结构: {graph_file}")
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with open(graph_file, 'rb') as f:
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G = pickle.load(f)
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print(f"图加载完成 - 节点数: {G.number_of_nodes()}, 边数: {G.number_of_edges()}")
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return G
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def calculate_degree_centrality(G):
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"""
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计算度中心性
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Args:
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G (nx.Graph): 网络图对象
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Returns:
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dict: 节点度中心性字典
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"""
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print("计算度中心性...")
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# 计算度中心性
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degree_centrality = nx.degree_centrality(G)
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# 计算加权度中心性（考虑边权重）
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weighted_degree_centrality = {}
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for node in G.nodes():
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total_weight = sum(G[node][neighbor]['weight'] for neighbor in G.neighbors(node))
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max_possible_weight = sum(data['weight'] for _, _, data in G.edges(data=True))
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weighted_degree_centrality[node] = total_weight / max_possible_weight if max_possible_weight > 0 else 0
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print(f"度中心性计算完成")
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return degree_centrality, weighted_degree_centrality
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def calculate_betweenness_centrality(G):
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"""
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计算介数中心性
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Args:
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G (nx.Graph): 网络图对象
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Returns:
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dict: 节点介数中心性字典
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"""
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print("计算介数中心性...")
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# 检查图是否连通
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if not nx.is_connected(G):
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print("警告: 图不连通，将使用最大连通分量计算介数中心性")
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# 找到最大连通分量
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largest_cc = max(nx.connected_components(G), key=len)
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G_largest = G.subgraph(largest_cc)
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print(f"最大连通分量包含 {len(largest_cc)} 个节点")
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else:
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G_largest = G
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# 计算介数中心性
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betweenness_centrality = nx.betweenness_centrality(G_largest, weight='weight')
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# 为不在最大连通分量中的节点设置介数中心性为0
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full_betweenness_centrality = {}
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for node in G.nodes():
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if node in betweenness_centrality:
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full_betweenness_centrality[node] = betweenness_centrality[node]
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else:
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full_betweenness_centrality[node] = 0.0
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print(f"介数中心性计算完成")
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return full_betweenness_centrality
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def calculate_additional_centralities(G):
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"""
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计算其他重要的中心性指标
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Args:
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G (nx.Graph): 网络图对象
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Returns:
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dict: 包含各种中心性的字典
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"""
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print("计算其他中心性指标...")
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centralities = {}
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# 特征向量中心性
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try:
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eigenvector_centrality = nx.eigenvector_centrality(G, max_iter=1000, weight='weight')
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centralities['eigenvector'] = eigenvector_centrality
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print("特征向量中心性计算完成")
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except Exception as e:
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print(f"特征向量中心性计算失败: {e}")
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centralities['eigenvector'] = {node: 0.0 for node in G.nodes()}
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# 接近中心性（仅在连通分量内计算）
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try:
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if nx.is_connected(G):
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closeness_centrality = nx.closeness_centrality(G, distance='weight')
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centralities['closeness'] = closeness_centrality
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print("接近中心性计算完成")
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else:
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# 对每个连通分量分别计算
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closeness_centrality = {}
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for component in nx.connected_components(G):
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subgraph = G.subgraph(component)
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if len(component) > 1: # 至少需要2个节点
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sub_closeness = nx.closeness_centrality(subgraph, distance='weight')
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closeness_centrality.update(sub_closeness)
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else:
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# 孤立节点的接近中心性为0
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for node in component:
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closeness_centrality[node] = 0.0
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centralities['closeness'] = closeness_centrality
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print("接近中心性计算完成（分连通分量）")
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except Exception as e:
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print(f"接近中心性计算失败: {e}")
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centralities['closeness'] = {node: 0.0 for node in G.nodes()}
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# PageRank中心性
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try:
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pagerank = nx.pagerank(G, weight='weight')
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centralities['pagerank'] = pagerank
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print("PageRank中心性计算完成")
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except Exception as e:
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print(f"PageRank中心性计算失败: {e}")
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centralities['pagerank'] = {node: 0.0 for node in G.nodes()}
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return centralities
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def analyze_centrality_results(degree_cent, weighted_degree_cent, betweenness_cent, additional_cent):
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"""
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分析中心性结果
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Args:
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degree_cent (dict): 度中心性
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weighted_degree_cent (dict): 加权度中心性
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betweenness_cent (dict): 介数中心性
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additional_cent (dict): 其他中心性
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Returns:
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dict: 分析结果
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"""
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print("\n=== 中心性分析结果 ===")
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# 基本统计
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centrality_stats = {}
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for name, centrality in [
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('degree', degree_cent),
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('weighted_degree', weighted_degree_cent),
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('betweenness', betweenness_cent),
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('eigenvector', additional_cent.get('eigenvector', {})),
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('closeness', additional_cent.get('closeness', {})),
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('pagerank', additional_cent.get('pagerank', {}))
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]:
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values = list(centrality.values())
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centrality_stats[name] = {
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'mean': np.mean(values),
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'std': np.std(values),
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'min': np.min(values),
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'max': np.max(values),
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'median': np.median(values)
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}
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print(f"\n{name.upper()}中心性统计:")
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print(f" 平均值: {centrality_stats[name]['mean']:.6f}")
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print(f" 标准差: {centrality_stats[name]['std']:.6f}")
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print(f" 最小值: {centrality_stats[name]['min']:.6f}")
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print(f" 最大值: {centrality_stats[name]['max']:.6f}")
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print(f" 中位数: {centrality_stats[name]['median']:.6f}")
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# 找出关键节点
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top_nodes = {}
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for name, centrality in [
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('degree', degree_cent),
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('weighted_degree', weighted_degree_cent),
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('betweenness', betweenness_cent),
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('eigenvector', additional_cent.get('eigenvector', {})),
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('closeness', additional_cent.get('closeness', {})),
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('pagerank', additional_cent.get('pagerank', {}))
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]:
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top_nodes[name] = sorted(centrality.items(), key=lambda x: x[1], reverse=True)[:10]
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print(f"\n{name.upper()}中心性前10节点:")
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for i, (node, value) in enumerate(top_nodes[name], 1):
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print(f" {i:2d}. {node}: {value:.6f}")
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return {
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'centrality_stats': centrality_stats,
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'top_nodes': top_nodes
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}
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def visualize_centrality_results(degree_cent, weighted_degree_cent, betweenness_cent, additional_cent, analysis_results, output_dir="output"):
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"""
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可视化中心性结果
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Args:
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degree_cent (dict): 度中心性
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weighted_degree_cent (dict): 加权度中心性
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betweenness_cent (dict): 介数中心性
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additional_cent (dict): 其他中心性
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analysis_results (dict): 分析结果
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output_dir (str): 输出目录
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"""
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print("生成中心性可视化图表...")
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# 设置中文字体
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plt.rcParams['font.sans-serif'] = ['SimHei', 'DejaVu Sans']
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plt.rcParams['axes.unicode_minus'] = False
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# 1. 中心性分布直方图
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fig, axes = plt.subplots(2, 3, figsize=(18, 12))
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fig.suptitle('各种中心性分布', fontsize=16)
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centralities = [
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('degree', degree_cent, '度中心性'),
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('weighted_degree', weighted_degree_cent, '加权度中心性'),
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('betweenness', betweenness_cent, '介数中心性'),
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('eigenvector', additional_cent.get('eigenvector', {}), '特征向量中心性'),
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('closeness', additional_cent.get('closeness', {}), '接近中心性'),
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('pagerank', additional_cent.get('pagerank', {}), 'PageRank中心性')
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]
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for i, (name, centrality, title) in enumerate(centralities):
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row, col = i // 3, i % 3
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values = list(centrality.values())
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axes[row, col].hist(values, bins=50, alpha=0.7, edgecolor='black')
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axes[row, col].set_title(title)
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axes[row, col].set_xlabel('中心性值')
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axes[row, col].set_ylabel('频次')
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axes[row, col].grid(True, alpha=0.3)
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# 添加统计信息
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mean_val = np.mean(values)
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axes[row, col].axvline(mean_val, color='red', linestyle='--', alpha=0.7, label=f'平均值: {mean_val:.4f}')
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axes[row, col].legend()
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plt.tight_layout()
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plt.savefig(os.path.join(output_dir, 'centrality_distributions.png'), dpi=300, bbox_inches='tight')
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plt.close()
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# 2. 前10节点对比图
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top_nodes = analysis_results['top_nodes']
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fig, axes = plt.subplots(2, 3, figsize=(18, 12))
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fig.suptitle('各种中心性前10节点', fontsize=16)
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for i, (name, title) in enumerate([
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('degree', '度中心性'),
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('weighted_degree', '加权度中心性'),
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('betweenness', '介数中心性'),
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('eigenvector', '特征向量中心性'),
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('closeness', '接近中心性'),
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('pagerank', 'PageRank中心性')
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]):
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row, col = i // 3, i % 3
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if name in top_nodes and top_nodes[name]:
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nodes = [item[0][:15] + '...' if len(item[0]) > 15 else item[0] for item in top_nodes[name]]
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values = [item[1] for item in top_nodes[name]]
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bars = axes[row, col].bar(range(len(nodes)), values, alpha=0.7, color='lightblue', edgecolor='black')
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axes[row, col].set_title(title)
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axes[row, col].set_xlabel('节点')
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axes[row, col].set_ylabel('中心性值')
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axes[row, col].set_xticks(range(len(nodes)))
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axes[row, col].set_xticklabels(nodes, rotation=45, ha='right')
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axes[row, col].grid(True, alpha=0.3)
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# 在柱状图上添加数值标签
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for bar, value in zip(bars, values):
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axes[row, col].text(bar.get_x() + bar.get_width()/2, bar.get_height() + max(values)*0.01,
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f'{value:.3f}', ha='center', va='bottom', fontsize=8)
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plt.tight_layout()
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plt.savefig(os.path.join(output_dir, 'top_nodes_comparison.png'), dpi=300, bbox_inches='tight')
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plt.close()
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# 3. 中心性相关性热力图
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centrality_data = {
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'Degree': degree_cent,
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'Weighted_Degree': weighted_degree_cent,
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'Betweenness': betweenness_cent,
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'Eigenvector': additional_cent.get('eigenvector', {}),
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'Closeness': additional_cent.get('closeness', {}),
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'PageRank': additional_cent.get('pagerank', {})
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}
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# 创建DataFrame
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df_centrality = pd.DataFrame(centrality_data)
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correlation_matrix = df_centrality.corr()
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plt.figure(figsize=(10, 8))
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sns.heatmap(correlation_matrix, annot=True, cmap='coolwarm', center=0,
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square=True, fmt='.3f', cbar_kws={'label': '相关系数'})
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plt.title('中心性指标相关性热力图')
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plt.tight_layout()
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plt.savefig(os.path.join(output_dir, 'centrality_correlation.png'), dpi=300, bbox_inches='tight')
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plt.close()
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print("中心性可视化图表已保存")
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def save_centrality_results(degree_cent, weighted_degree_cent, betweenness_cent, additional_cent, analysis_results, output_dir="output"):
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"""
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保存中心性分析结果
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Args:
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degree_cent (dict): 度中心性
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weighted_degree_cent (dict): 加权度中心性
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betweenness_cent (dict): 介数中心性
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additional_cent (dict): 其他中心性
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analysis_results (dict): 分析结果
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output_dir (str): 输出目录
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"""
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if not os.path.exists(output_dir):
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os.makedirs(output_dir)
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# 1. 保存所有中心性结果
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centrality_file = os.path.join(output_dir, "centrality_analysis.csv")
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# 创建DataFrame
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all_nodes = set(degree_cent.keys())
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centrality_data = []
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for node in all_nodes:
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row = {
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'node': node,
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'degree_centrality': degree_cent.get(node, 0),
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'weighted_degree_centrality': weighted_degree_cent.get(node, 0),
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'betweenness_centrality': betweenness_cent.get(node, 0),
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'eigenvector_centrality': additional_cent.get('eigenvector', {}).get(node, 0),
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'closeness_centrality': additional_cent.get('closeness', {}).get(node, 0),
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'pagerank_centrality': additional_cent.get('pagerank', {}).get(node, 0)
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}
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centrality_data.append(row)
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df_centrality = pd.DataFrame(centrality_data)
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df_centrality.to_csv(centrality_file, index=False, encoding='utf-8')
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print(f"中心性分析结果已保存到: {centrality_file}")
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# 2. 保存统计信息
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stats_file = os.path.join(output_dir, "centrality_statistics.txt")
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with open(stats_file, 'w', encoding='utf-8') as f:
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f.write("中心性分析统计结果\n")
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f.write("="*60 + "\n")
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centrality_stats = analysis_results['centrality_stats']
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for name, stats in centrality_stats.items():
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f.write(f"\n{name.upper()}中心性统计:\n")
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f.write(f" 平均值: {stats['mean']:.6f}\n")
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f.write(f" 标准差: {stats['std']:.6f}\n")
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f.write(f" 最小值: {stats['min']:.6f}\n")
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f.write(f" 最大值: {stats['max']:.6f}\n")
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f.write(f" 中位数: {stats['median']:.6f}\n")
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f.write("\n关键节点识别:\n")
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top_nodes = analysis_results['top_nodes']
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for name, top_list in top_nodes.items():
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f.write(f"\n{name.upper()}中心性前10节点:\n")
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for i, (node, value) in enumerate(top_list, 1):
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f.write(f" {i:2d}. {node}: {value:.6f}\n")
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print(f"中心性统计信息已保存到: {stats_file}")
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# 3. 保存为pickle格式
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pickle_file = os.path.join(output_dir, "centrality_results.pkl")
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results = {
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'degree_centrality': degree_cent,
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'weighted_degree_centrality': weighted_degree_cent,
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'betweenness_centrality': betweenness_cent,
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'additional_centralities': additional_cent,
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'analysis_results': analysis_results
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}
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with open(pickle_file, 'wb') as f:
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pickle.dump(results, f)
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print(f"完整中心性结果已保存到: {pickle_file}")
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def main():
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"""主函数"""
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# 配置文件路径
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graph_file = "output/network_graph.pkl"
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output_dir = "output"
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try:
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# 1. 加载图结构
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G = load_graph(graph_file)
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# 2. 计算度中心性
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degree_cent, weighted_degree_cent = calculate_degree_centrality(G)
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# 3. 计算介数中心性
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betweenness_cent = calculate_betweenness_centrality(G)
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# 4. 计算其他中心性
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additional_cent = calculate_additional_centralities(G)
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# 5. 分析结果
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analysis_results = analyze_centrality_results(degree_cent, weighted_degree_cent, betweenness_cent, additional_cent)
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# 6. 可视化结果
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visualize_centrality_results(degree_cent, weighted_degree_cent, betweenness_cent, additional_cent, analysis_results, output_dir)
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# 7. 保存结果
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save_centrality_results(degree_cent, weighted_degree_cent, betweenness_cent, additional_cent, analysis_results, output_dir)
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print("\n✅ 中心性分析完成！")
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except FileNotFoundError:
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print(f"❌ 错误: 找不到图文件 {graph_file}")
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print("请先运行 1_build_graph.py 构建图结构")
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except Exception as e:
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print(f"❌ 发生错误: {str(e)}")
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if __name__ == "__main__":
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main()
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