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浙江大学学报(工学版)
浙江大学学报(工学版)  2023, Vol. 57 Issue (4): 719-725    DOI: 10.3785/j.issn.1008-973X.2023.04.009
自动化技术、计算机技术     
时序多层网络熵值结构洞节点重要性建模
胡钢1,2(),牛琼1,2,王琴2,许丽鹏1,2,任勇军3
1. 安徽工业大学 复杂系统多学科管理与控制安徽普通高校重点实验室，安徽 马鞍山 243032
2. 安徽工业大学 管理科学与工程学院，安徽 马鞍山 243032
3. 南京信息工程大学 计算机与软件学院，江苏 南京 210044
Modeling of node importance in entropy-value structured hole of temporal multilayer network
Gang HU1,2(),Qiong NIU1,2,Qin WANG2,Li-peng XU1,2,Yong-jun REN3
1. Key Laboratory of Multidisciplinary Management and Control of Complex Systems of Anhui Higher Education Institutes, Anhui University of Technology, Maanshan 243032, China
2. School of Management Science and Engineering, Anhui University of Technology, Maanshan 243032, China
3. School of Computer Science, Nanjing University of Information Science and Technology, Nanjing 210044, China
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摘要：

分析动态多层复杂网络时空演化过程中的网络节点重要性序结构，提出时序多层网络熵值结构洞节点重要性辨识模型. 分析时序网络节点局部信息熵的属性与节点全局K-shell信息集结偏好信息熵. 依据复杂网络结构洞系数，提出节点熵值结构洞节点重要性辨识模型. 时序化处理节点演化信息，提出节点重要性时序网络计算模型. 通过SIR模型检验节点传播效率，开展实证网络仿真. 本文的时序多层网络节点演化重要性排序结果与经典时序网络模型相比，Kendall值有了显著的提高.
关键词： 熵值;  结构洞;  K壳;  时序网络;  节点重要性    
Abstract:

The importance ranking structure of network nodes in the temporal and spatial evolution process of temporal multilayer network was analyzed. A model for identifying the importance of network nodes in the temporal evolution process of temporal multilayer networks based on entropy-value structured holes was proposed. The attributes of local information entropy of nodes in the temporal network and their global K-shell information aggregation preference entropy were analyzed. A model for identifying the importance of nodes of their entropy and structural hole was proposed based on the complex network structural hole coefficient. A temporal network calculation model was developed for analyzing the temporal evolution of node importance. The efficiency of node propagation was tested by using the SIR model, and empirical network simulations were conducted. The simulation results showed a significant improvement in the Kendall value of the temporal evolution ranking of network nodes compared to classic temporal network models.
Key words: entropy    structural hole    K-shell    temporal network    node importance
收稿日期: 2022-04-21 出版日期: 2023-04-21
CLC:  TP 393  
基金资助: 国家自然科学基金资助项目（71772002）；安徽省自然科学基金资助项目（2108085MG236）；安徽省高校自然科学研究资助项目（KJ2021A0385）；安徽省高校研究生科学研究资助项目（YJS20210356）；安徽普通高校重点实验室开放基金资助项目（GS2021-05）
作者简介: 胡钢（1970—），男，副教授，从事复杂网络、决策分析的研究. orcid.org/0000-0003-4952-4940. E-mail： hug_2004@126.com
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引用本文:

胡钢,牛琼,王琴,许丽鹏,任勇军. 时序多层网络熵值结构洞节点重要性建模[J]. 浙江大学学报(工学版), 2023, 57(4): 719-725.

Gang HU,Qiong NIU,Qin WANG,Li-peng XU,Yong-jun REN. Modeling of node importance in entropy-value structured hole of temporal multilayer network. Journal of ZheJiang University (Engineering Science), 2023, 57(4): 719-725.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2023.04.009    或    https://www.zjujournals.com/eng/CN/Y2023/V57/I4/719

图 1  时序多层网络节点信息演化图
图 2  K-shell分解
图 3  结构洞网络
图 4  结构洞约束系数计算的示意图
T N Na E 时间段 $\left\langle k \right\rangle $ $\left\langle {{k^2}} \right\rangle $ $\;{\beta _{{\rm{th}}}}$
1 92 72 188 第1~10天 4.09 28.41 0.14
2 92 70 152 第11~20天 3.30 18.83 0.18
3 92 59 123 第21~30天 2.67 15.39 0.17
4 92 70 186 第31~40天 4.04 28.61 0.14
5 92 62 103 第41~50天 2.24 10.46 0.21
6 92 68 147 第51~60天 3.20 17.93 0.18
7 92 69 151 第61~70天 3.28 19.83 0.17
8 92 69 160 第71~80天 3.48 23.65 0.15
9 92 68 158 第81~90天 3.43 21.54 0.16
10 92 62 94 第91~100天 2.04 8.30 0.25
表 1  Workspace网络的基本特征统计
T N Na E 时间段 $\left\langle k \right\rangle $ $\left\langle {{k^2}} \right\rangle $ $\;{\beta _{{\rm{th}}}}$
1 851 664 2863 第1~30天 62.24 1206.43 0.05
2 851 646 2505 第31~60天 54.46 903.61 0.06
3 851 607 1770 第61~90天 38.48 493.30 0.08
4 851 633 2170 第91~120天 47.17 688.20 0.07
5 851 665 3053 第121~150天 66.37 1300.28 0.05
6 851 676 3110 第151~180天 67.61 1364.50 0.05
7 851 689 3236 第181~210天 70.35 1537.57 0.05
8 851 648 2602 第211~240天 56.57 976.17 0.06
9 851 675 2822 第241~270天 61.35 1115.15 0.06
10 851 671 2590 第271~300天 56.30 1008.50 0.06
11 851 696 3198 第301~330天 69.52 1483.78 0.05
12 851 694 3290 第331~360天 71.52 1493.76 0.05
表 2  Email-Eu-core网络的基本特征统计
图 5  Workspace数据节点使用ESHT方法与SAM方法排序结果的Kendall相关性系数分析对比
图 6  Workspace数据节点使用ESHT方法与OSAM方法排序结果的Kendall相关性系数分析对比
图 7  Email-Eu-core数据节点使用ESHT方法与SAM方法排序结果的Kendall相关性系数分析对比
图 8  Email-Eu-core数据节点使用ESHT方法与OSAM方法排序结果的Kendall相关性系数分析对比
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