社会网络分析原理及 Python 实战应用

import networkx as nx# 计算度中心度def calculate_degree_centrality(G):    return nx.degree_centrality(G)# 计算介数中心度def calculate_betweenness_centrality(G):    return nx.betweenness_centrality(G, normalized=True)# 计算接近中心度def calculate_closeness_centrality(G):    return nx.closeness_centrality(G)# 生成测试网络G = nx.barabasi_albert_graph(100, 2)# 执行计算degree_centrality = calculate_degree_centrality(G)betweenness_centrality = calculate_betweenness_centrality(G)closeness_centrality = calculate_closeness_centrality(G)# 输出结果print("度中心度:", degree_centrality)print("介数中心度:", betweenness_centrality)print("接近中心度:", closeness_centrality)

import networkx as nx# 计算度数中心势def calculate_degree_centrality_potential(G):    degree_centrality = nx.degree_centrality(G)    degree_centrality_potential = {}    for node in G.nodes():        neighbors = set(G.neighbors(node))        node_potential = sum(degree_centrality[n] for n in neighbors)        degree_centrality_potential[node] = node_potential    return degree_centrality_potential# 计算接近中心势def calculate_closeness_centrality_potential(G):    closeness_centrality = nx.closeness_centrality(G)    closeness_centrality_potential = {}    for node in G.nodes():        neighbors = set(G.neighbors(node))        node_potential = sum(closeness_centrality[n] for n in neighbors)        closeness_centrality_potential[node] = 1 / node_potential    return closeness_centrality_potential# 计算中介中心势def calculate_betweenness_centrality_potential(G):    betweenness_centrality = nx.betweenness_centrality(G, normalized=True)    betweenness_centrality_potential = {}    for node in G.nodes():        neighbors = set(G.neighbors(node))        node_potential = sum(betweenness_centrality[n] for n in neighbors)        betweenness_centrality_potential[node] = node_potential    return betweenness_centrality_potential# 测试网络G = nx.barabasi_albert_graph(100, 2)# 计算并输出degree_centrality_potential = calculate_degree_centrality_potential(G)closeness_centrality_potential = calculate_closeness_centrality_potential(G)betweenness_centrality_potential = calculate_betweenness_centrality_potential(G)print("度数中心势:", degree_centrality_potential)print("接近中心势:", closeness_centrality_potential)print("中介中心势:", betweenness_centrality_potential)

import networkx as nx# 构建自定义网络G = nx.Graph()G.add_edges_from([(1, 2), (1, 3), (2, 3), (2, 4)])# 计算网络密度density = nx.density(G)print("网络密度:", density)# 计算同配性系数assortativity = nx.degree_assortativity_coefficient(G)print("同配性:", assortativity)

import networkx as nx# 构建网络G = nx.Graph()G.add_edges_from([(1, 2), (1, 3), (2, 3), (2, 4)])# 网络直径diameter = nx.diameter(G)print("直径:", diameter)# 节点偏心率eccentricity = nx.eccentricity(G)print("节点偏心率:", eccentricity)# 网络半径radius = nx.radius(G)print("半径:", radius)# 维纳指数wiener_index = nx.wiener_index(G)print("维纳指数:", wiener_index)# 网络全局效率global_efficiency = nx.global_efficiency(G)print("网络全局效率:", global_efficiency)# 网络平均一致估计mean_nodal_efficiency = 1 / global_efficiencyprint("网络平均一致估计:", mean_nodal_efficiency)# 平均路径长度average_path_length = nx.average_shortest_path_length(G)print("平均路径长度:", average_path_length)

import networkx as nx# 构建网络G = nx.Graph()G.add_edges_from([(1, 2), (1, 3), (2, 3), (2, 4)])# 整体网络聚类系数clustering_coefficient = nx.average_clustering(G)print("网络聚类系数:", clustering_coefficient)# 局部聚类系数均值local_clustering_coefficient = nx.clustering(G)average_local_clustering_coefficient = sum(local_clustering_coefficient.values()) / len(local_clustering_coefficient)print("局部聚类系数:", average_local_clustering_coefficient)# 模块化系数（社区划分质量）modularity_coefficient = nx.algorithms.community.quality.modularity(G, nx.algorithms.community.greedy_modularity_communities(G))print("模块化系数:", modularity_coefficient)

import networkx as nx# 构建网络G = nx.Graph()G.add_edges_from([('A', 'B'), ('A', 'D'), ('B', 'C'), ('B', 'D'), ('D', 'E'), ('E', 'D')])# 计算互惠性reciprocity = nx.reciprocity(G)print("互惠性:", reciprocity)

import networkx as nxG = nx.Graph()G.add_edges_from([('A', 'B'), ('A', 'D'), ('B', 'C'), ('B', 'D'), ('D', 'E'), ('E', 'D')])betweenness_centrality = nx.betweenness_centrality(G)print("介数中心性:", betweenness_centrality)

import networkx as nximport matplotlib.pyplot as pltG = nx.Graph()G.add_edges_from([('A', 'B'), ('A', 'D'), ('B', 'C'), ('B', 'D'), ('D', 'E'), ('E', 'D')])# 提取度序列并统计degree_sequence = [d for n, d in G.degree()]degree_count = nx.degree_histogram(G)degrees = range(len(degree_count))# 绘图plt.bar(degrees, degree_count, width=0.80, color='b')plt.title("Degree Distribution")plt.ylabel("Frequency")plt.xlabel("Degree")plt.show()

import networkx as nxG = nx.Graph()G.add_edges_from([('A', 'B'), ('A', 'D'), ('B', 'C'), ('B', 'D'), ('D', 'E'), ('E', 'D')])# 提取K-核节点k_core = nx.k_core(G)print("K-Core子图节点:", k_core.nodes())

import networkx as nximport numpy as npdef calculate_small_world_effect(G):    # 原始网络平均最短路径    L_real = nx.average_shortest_path_length(G)    # 生成同结构随机网络    G_random = nx.double_edge_swap(G, nswap=len(G.edges())*5, max_tries=len(G.edges())*10)    # 随机网络平均最短路径    L_random = nx.average_shortest_path_length(G_random)    # 小世界指数    small_world_effect = L_real / L_random    return small_world_effect# 生成小世界模型网络G = nx.watts_strogatz_graph(100, 6, 0.1)small_world_effect = calculate_small_world_effect(G)print("小世界效应指数:", small_world_effect)

import networkx as nximport matplotlib.pyplot as pltfrom networkx.algorithms.community import greedy_modularity_communities# 加载经典测试网络G = nx.karate_club_graph()# 挖掘社区communities = list(greedy_modularity_communities(G))# 绘图展示fig, ax = plt.subplots()pos = nx.spring_layout(G)nx.draw(G, pos, with_labels=True, node_color='lightblue', node_size=500, ax=ax)ax.set_title('Karate Club Network with Agglomerative Hierarchical Clustering')plt.show()# 输出社区分组print("识别出的社区：")for idx, community in enumerate(communities):    print(f"社区 {idx + 1}: {community}")

import networkx as nximport matplotlib.pyplot as pltdef core_and_periphery_partition(G, threshold):    core_nodes = [node for node, degree in G.degree() if degree >= threshold]    periphery_nodes = [node for node, degree in G.degree() if degree < threshold]    core_subgraph = G.subgraph(core_nodes)    periphery_subgraph = G.subgraph(periphery_nodes)    return core_subgraph, periphery_subgraph# 构建随机网络G = nx.erdos_renyi_graph(n=20, p=0.2)# 设置度数阈值degree_threshold = 5# 划分核心与边缘core_subgraph, periphery_subgraph = core_and_periphery_partition(G, degree_threshold)# 双栏绘图fig, axs = plt.subplots(1, 2, figsize=(12, 5))# 绘制核心节点if core_subgraph.number_of_nodes() > 0:    nx.draw(core_subgraph, ax=axs[0], with_labels=True, node_color='lightblue', node_size=500)    axs[0].set_title('Core Nodes')else:    axs[0].set_title('No Core Nodes to Display')    axs[0].axis('off')# 绘制边缘节点if periphery_subgraph.number_of_nodes() > 0:    nx.draw(periphery_subgraph, ax=axs[1], with_labels=True, node_color='lightgreen', node_size=500)    axs[1].set_title('Periphery Nodes')else:    axs[1].set_title('No Periphery Nodes to Display')    axs[1].axis('off')plt.tight_layout()plt.show()

import networkx as nx# 构建网络G = nx.Graph()G.add_edges_from([(1, 2), (1, 3), (2, 3), (2, 4)])# 全局效率global_efficiency = nx.global_efficiency(G)print("全局效率:", global_efficiency)# 局部效率local_efficiency = nx.local_efficiency(G)print("每个节点的局部效率:", local_efficiency)