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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (4): 719-725    DOI: 10.3785/j.issn.1008-973X.2023.04.009
    
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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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     
Received: 21 April 2022      Published: 21 April 2023
CLC:  TP 393  
Fund:  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）
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Gang HU
Qiong NIU
Qin WANG
Li-peng XU
Yong-jun REN
Cite this article:

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.

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


时序多层网络熵值结构洞节点重要性建模

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 
Fig.1 Evolution diagram of temporal multilayer network node information
Fig.2 K-shell decomposition
Fig.3 Structural hole network
Fig.4 Schematic diagram of structural hole constraint coefficient calculation
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
Tab.1 Basic characteristics statistics of Workspace network
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
Tab.2 Basic characteristics statistics of Email-Eu-core network
Fig.5 Comparative analysis of Kendall correlation coefficients between sorting results of ESHT and SAM methods for Workspace data nodes
Fig.6 Comparative analysis of Kendall correlation coefficients between sorting results of ESHT and OSAM methods for Workspace data nodes
Fig.7 Comparative analysis of Kendall correlation coefficients between sorting results of ESHT and SAM methods for Email-Eu-core data nodes
Fig.8 Comparative analysis of Kendall correlation coefficients between sorting results of ESHT and OSAM methods for Email-Eu-core data nodes
[1]   AGHAALIZADEH S, AFSHORD S T, BOUYER A, et al. A three-stage algorithm for local community detection based on the high node importance ranking in social networks [J]. Physica A: Statistical Mechanics and its Applications. 2021, 563: 125420.
[2]   LI H, ZHANG R, ZHAO Z, et al LPA-MNI: an improved label propagation algorithm based on modularity and node importance for community detection[J]. Entropy (Basel, Switzerland), 2021, 23 (5): 497
doi: 10.3390/e23050497
[3]   纪秋磊, 梁伟, 傅伯杰, 等 基于Google Earth Engine与复杂网络的黄河流域土地利用/覆被变化分析[J]. 生态学报, 2021, 42 (6): 1- 14
JI Qiu-lei, LIANG Wei, FU Bo-jie, et al Land ues/cover change in the Tellow River Basin based on Google Earth Engine and complex network[J]. Acta Ecologica Sinica, 2021, 42 (6): 1- 14
[4]   CHENFENG X, SONGHUA H, MOFENG Y, et al Mobile device data reveal the dynamics in a positive relationship between human mobility and COVID-19 infections[J]. Proceedings of the National Academy of Sciences, 2020, 117 (44): 27087- 27089
doi: 10.1073/pnas.2010836117
[5]   YABE T, TSUBOUCHI K, FUJIWARA N, et al Non-compulsory measures sufficiently reduced human mobility in Tokyo during the COVID-19 epidemic[J]. Scientific Reports, 2020, 10 (1): 1- 9
doi: 10.1038/s41598-019-56847-4
[6]   BONACICH P Factoring and weighting approaches to status scores and clique identification[J]. Journal of Mathematical Sociology, 2010, 2 (1): 113
[7]   LORRAIN F, WHITE H C Structural equivalence of individuals in social networks[J]. Social Networks, 1977, 1 (1): 67- 98
[8]   BORGATTI S P Centrality and network flow[J]. Social Networks, 2005, 27 (1): 55- 71
doi: 10.1016/j.socnet.2004.11.008
[9]   ZELEN S M Rethinking centrality: methods and examples[J]. Social Networks, 1989, 11 (1): 1- 37
doi: 10.1016/0378-8733(89)90016-6
[10]   杨松青, 蒋沅, 童天驰, 等 基于Tsallis熵的复杂网络节点重要性评估方法[J]. 物理学报, 2021, 70 (21): 273- 284
YANG Song-qing, JIANG Yuan, TONG Tian-chi, et al A method for evaluating the importance of nodes in complex network based on Tsallis entropy[J]. Chinese Journal of Physics, 2021, 70 (21): 273- 284
[11]   LU M Node importance evaluation based on neighborhood structure hole and improved TOPSIS[J]. Computer Networks, 2020, 178 (9): 107336- 107349
[12]   苏晓萍, 宋玉蓉. 利用邻域“结构洞”寻找社会网络中最具影响力节点[J]. 物理学报, 2015, 64(2): 5-15.
SU Xiao-ping, SONG Yu-rong. Leveraging neighborhood “structural holes” to identifying key spreaders in social networks [J] Chinese Journal of Physics, 2015, 64(2): 5-15.
[13]   ZENG A, ZHANG C J Ranking spreaders by decomposing complex networks[J]. Physics Letters A, 2013, 377 (14): 1031- 1035
doi: 10.1016/j.physleta.2013.02.039
[14]   SUN Q, YANG G Y, ZHOU A, et al An entropy-based self-adaptive node importance evaluation method for complex networks[J]. Complexity, 2020, 2020 (10): 1- 13
[15]   杨杰, 张名扬, 芮晓彬, 等 融合节点覆盖范围和结构洞的影响力最大化算法[J]. 计算机应用, 2021, 42 (4): 1- 8
YANG Jie, ZHANG Ming-yang, RUI Xiao-bin, et al Influence maximization algorithm based on node coverage and structural holes[J]. Journal of Computer Applications, 2021, 42 (4): 1- 8
[16]   KIM H, ANDERSON R Temporal node centrality in complex networks[J]. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 2012, 85 (2): 1- 8
[17]   TAYLOR D, MYERS S A, CLAUSET A, et al Eigenvector-based centrality measures for temporal networks[J]. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2017, 15 (1): 537- 574
doi: 10.1137/16M1066142
[18]   杨剑楠, 刘建国, 郭强 基于层间相似性的时序网络节点重要性研究[J]. 物理学报, 2018, 67 (4): 279- 286
YANG Jian-nan, LIU Jian-guo, GUO Qiang Node importance idenfication for temporal network based on inter-layer similarity[J]. Chinese Journal of Physics, 2018, 67 (4): 279- 286
doi: 10.7498/aps.67.20172255
[19]   胡钢, 许丽鹏, 徐翔 基于时序网络层间同构率动态演化的重要节点辨识[J]. 物理学报, 2021, 70 (10): 355- 366
HU Gang, XU Li-peng, XU Xiang Identification of important nodes based on dynamic evolution of inter-layer isomorphism rate in temporal networks[J]. Chinese Journal of Physics, 2021, 70 (10): 355- 366
[20]   曹连谦, 王立夫, 孔芝, 等. 多层异质复杂网络系统的能控性[EB/OL]. [2022-04-01]. https://doi.org/10.16383/j.aas.c210654.
CAO Lian-qian, WANG Li-fu, KONG Zhi, et al. Controllability of multi-layer heterogeneous complex network systems[EB/OL]. [2022-04-01]. https://doi.org/10.16383/j.aas.c210654.
[21]   穆俊芳, 郑文萍, 王杰, 等 基于重连机制的复杂网络鲁棒性分析[J]. 计算机科学, 2021, 48 (7): 130- 136
MU Jun-fang, ZHENG Wen-ping, WANG Jie, et al Robustness analysis of complex network based on rewiring mechanism[J]. Computer Science, 2021, 48 (7): 130- 136
[22]   BURT R S Structural holes: the social structure of competition[J]. The Economic Journal, 1994, 40 (2): 685- 686
[23]   GÉNOIS M, BARRAT A Can co-location be used as a proxy for face-to-face contacts?[J]. Epj Data Science, 2018, 7 (1): 11
doi: 10.1140/epjds/s13688-018-0140-1
[24]   PARANJAPE A, BENSON A R, LESKOVEC J. Motifs in temporal networks [M]. New York: ACM, 2017: 601-610.
[25]   CASTELLANO C, PASTOR-SATORRAS R Thresholds for epidemic spreading in networks[J]. Physical Review Letters, 2010, 105 (21): 218701
doi: 10.1103/PhysRevLett.105.218701
[26]   BORRONI C G A new rank correlation measure[J]. Statistical Papers, 2013, 54 (2): 255- 270
doi: 10.1007/s00362-011-0423-0
[27]   胡钢, 牛琼, 许丽鹏, 等 基于网络超链接信息熵的节点重要性序结构演化建模分析[J]. 电子学报, 2022, 50 (11): 2638- 2644
HU Gang, NIU Qiong, XU Li-peng, et al The model to analyses of node importance order structure evolution based on network hyperlink information entropy[J]. Acta Electronica Sinica, 2022, 50 (11): 2638- 2644
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