Supply chain research based on complex network theory

Cui Jun-Ying; Xu Shu-Qi; Na Xu; Pan Li-Ming; Lü Lin-Yuan

doi:10.7498/aps.73.20240702

Abstract

Supply chain is a chain structure formed by the sequential processes of production and distribution, spanning from raw material suppliers to end customers. An efficient and reliable supply chain is of great significance in enhancing enterprise’s market competitiveness and promoting sustainable social and economic development. The supply chain includes the interconnected flows of materials, resources, capital, and information across various stages, including procurement, production, warehousing, distribution, customer service, information management, and financial management. By representing the various participants in the supply chain as nodes and their interactions—such as the logistics, capital flow, information flow, and other interactions—as edges, the supply chain can be described and characterized as a complex network. In recent years, using complex network theory and methods to model and analyze supply chains has attracted increasing attention from researchers. This paper systematically reviews the supply chain research based on complex network theory, providing an in-depth analysis of supply chain networks in terms of network construction, structural properties, and management characteristics. First, this paper reviews two kinds of approaches to constructing supply chain network: empirical data-based approach and network model-based approach. In the empirical data-based research, scholars use common supply chain databases or integrate multiple data sources to identify the supply chain participants and clarify their attributes, behaviors, and interactions. Alternatively, the research based on network models employs the Barabási–Albert (BA) model, incorporating factors such as node distance, fitness, and edge weights, or uses hypergraph models to construct supply chain networks. Next, this paper summarizes the research on the structural properties of supply chain networks, focusing on their topological structure, key node identification, community detection, and vulnerability analysis. Relevant studies explore the topological structure of supply chain networks, uncovering the connections between nodes, hierarchical structures, and information flow paths between nodes. By analyzing factors such as node centrality, connection strength, and flow paths, the key nodes within the supply chain network are identified. Community detection algorithms are used to investigate the relationships between different structural parts and to analyze the positional structure, cooperative relationships, and interaction modes. Furthermore, quantitative evaluation indicators and management strategies are proposed for the robustness and resilience of supply chain networks. Further research has explored the management characteristics of supply chain networks, including risk propagation and competition game. Relevant studies have employed three main methods—epidemic model, cascading failure model, and agent-based model—to construct risk propagation models, simulate the spread of disruption risks, and analyze the mechanisms, paths, and extent of risk propagation within supply chain networks. These studies provide valuable insights for developing risk prevention and mitigation strategies. In addition, the game theory has been used to investigate the cooperative competition, resource allocation, and strategy selection among enterprises within the supply chain network. This paper reviews the research contents and emerging trends in supply chain studies based on complex network methods. It demonstrates the effectiveness and applicability of complex network theory in supply chain network research, discusses key challenges, such as how to obtain accurate, comprehensive, and timely supply chain network data, proposes standardized data processing methods, and determines the attributes of supply chain network nodes and the strength of their relationships. Furthermore, research on the structure of supply chain network has not yet fully captured the unique characteristics of supply chain networks. Existing models and methods for vulnerability assessment often fail to consider the dynamic and nonlinear characteristics of supply chain networks. Research on risk propagation in supply chains has not sufficiently integrated empirical data, overlooking the diversity of risk sources and the complexity of propagation paths. The asymmetry and incompleteness of information in supply chain networks, as well as multiple sources of uncertainty, make the prediction and analysis of multi-party decision-making behavior more complex. This paper also outlines several key directions for future research. One direction involves using high-order network theory to model interactions among multiple nodes and to describe the dynamics of multi-agent interactions within supply chain networks. Furthermore, integrating long short-term memory (LSTM) methods to process long-term dependence in time-series data can enhance the analysis of network structure evolution and improve the prediction of future states. The application of reinforcement learning algorithms can also adaptively adjust network structures and strategies according to changing conditions and demands, thereby improving the adaptability and response speed of supply chain networks in emergency situations. This paper aims to provide valuable insights for supplying chain research and promoting the development and application of complex network methods in this field.

Keywords:

Authors and contacts

1.
Department of Physics, University of Fribourg, Fribourg CH-1700, Switzerland
2.
Institute of Dataspace, Hefei Comprehensive National Science Center, Hefei 230088, China
3.
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
4.
School of Cyber Science and Technology, University of Science and Technology of China, Hefei 230026, China

Corresponding author: Lü Lin-Yuan, linyuan.lv@ustc.edu.cn

Funds: Project supported by the Major Program of the National Natural Science Foundation of China (Grant No. T2293771), the National Science Fund for Distinguished Young Scholars of China (Grant No. 62306191), and the China Scholarship Council of China (Grant No. 202108410127).

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References

[1]	Choi T Y, Dooley K J, Rungtusanatham M 2001 J. Oper. Manag. 19 351 Google Scholar
[2]	Surana A, Kumara S, Greaves M, Raghavan U N 2005 Int. J. Prod. Res. 43 4235 Google Scholar
[3]	Helbing D, Armbruster D, Mikhailov A S, Lefeber E 2006 Physica A 363 xi Google Scholar
[4]	Cao W G, Xie S L, Qiao X D 2008 Eighth International Conference of Chinese Logistics and Transportation Professionals Chengdu, China, July 31–August 3, 2008 p1949
[5]	Zhang H M, Feng T T, Yang Y S 2022 Resour. Policy 75 102492 Google Scholar
[6]	Dolgui A, Ivanov D, Sokolov B 2018 Int. J. Prod. Res. 56 414 Google Scholar
[7]	Cruz J M 2008 Eur. J. Oper. Res. 184 1005 Google Scholar
[8]	Hearnshaw E J, Wilson M M 2013 Int. J. Oper. Prod. Man. 33 442 Google Scholar
[9]	Pathak S D, Day J M, Nair A, Sawaya W J, Kristal M M 2007 Decision Sci. 38 547 Google Scholar
[10]	Borgatti S P, Li X 2009 J. Supply Chain Manag. 45 5 Google Scholar
[11]	Ledwoch A, Yasarcan H, Brintrup A 2018 Int. J. Prod. Econ. 197 13 Google Scholar
[12]	Wang K Q, Zeng Z F, Sun D C 2008 Fourth International Conference on Semantics, Knowledge and Grid Beijing, China, December 3–5, 2008 p493
[13]	Ou C Y, Pan F B, Lin S J 2024 Sustainability 16 5514 Google Scholar
[14]	Xu M J, Wang X P, Zhao L D 2014 Int. J. Syst. Sci. Oper. Logist. 1 105 Google Scholar
[15]	Liang D, Bhamra R, Liu Z Y, Pan Y C 2022 Mathematics 10 3008 Google Scholar
[16]	Chan C K, Zhou Y, Wong K H 2019 Eur. J. Oper. Res. 275 514 Google Scholar
[17]	Gedik R, Medal H, Rainwater C, Pohl E A, Mason S J 2014 Transp. Res. E Logist. Transp. Rev. 71 45 Google Scholar
[18]	Carvalho H, Naghshineh B, Govindan K, Cruz-Machado V 2022 Comput. Ind. Eng. 171 108375 Google Scholar
[19]	Carnovale S, Rogers D S, Yeniyurt S 2019 J. Purch. Supply Manag. 25 134 Google Scholar
[20]	Wuttke D A, Blome C, Henke M 2013 Int. J. Prod. Econ. 145 773 Google Scholar
[21]	Yu H, Li H R 2023 Resour. Policy 85 104055 Google Scholar
[22]	Rezapour S, Farahani R Z, Pourakbar M 2017 Eur. J. Oper. Res. 259 1017 Google Scholar
[23]	Ivanov D 2023 Int. J. Prod. Res. 61 1683 Google Scholar
[24]	Van den Brink S, Kleijn R, Sprecher B, Tukker A 2020 Resour. Conserv. Recycl. 156 104743 Google Scholar
[25]	Sloane A, O’reilly S 2013 Prod. Plan. Control 24 621 Google Scholar
[26]	Wang J P, Zhou H, Jin X D 2021 Chaos Soliton. Fract. 143 110259 Google Scholar
[27]	Brintrup A, Ledwoch A, Barros J 2016 Logist. Res. 9 1 Google Scholar
[28]	Kim Y, Choi T Y, Yan T, Dooley K 2011 J. Oper. Manag. 29 194 Google Scholar
[29]	史金艳, 杨健亨, 李延喜, 张启望 2019 中国工业经济 9 136 Google Scholar Shi J Y, Yang J H, Li Y X, Zhang Q W 2019 Chin. Ind. Econ. 9 136 Google Scholar
[30]	Zhao K, Zuo Z, Blackhurst J V 2019 J. Oper. Manag. 65 190 Google Scholar
[31]	D’Ignazio A, Giovannetti E 2014 Int. J. Prod. Econ. 147 486 Google Scholar
[32]	Tang L B, Wang P, Ma Z J, Pauliuk S, Chen W Q, Dai T, Lin Z P 2023 J. Ind. Ecol. 27 323 Google Scholar
[33]	Bellamy M A, Ghosh S, Hora M 2014 J. Oper. Manag. 32 357 Google Scholar
[34]	Mu D, Ren H Y, Wang C, Yue X P, Du J B, Ghadimi P 2023 Resour. Policy 80 103225 Google Scholar
[35]	Hu X Q, Wang C, Lim M K, Chen W Q, Teng L M, Wang P, Wang H M, Zhang C, Yao C Y, Ghadimi P 2023 Renew. Sust. Energ. Rev. 173 113083 Google Scholar
[36]	Basole R C, Bellamy M A 2014 Decision Sci. 45 753 Google Scholar
[37]	Barabási A L, Albert R 1999 Science 286 509 Google Scholar
[38]	Albert R, Barabási A L 2002 Rev. Mod. Phys. 74 47 Google Scholar
[39]	Bell M, Perera S, Piraveenan M, Bliemer M, Latty T, Reid C 2017 Sci. Rep. 7 42431 Google Scholar
[40]	Chen H W, Chen G P, Zhang Q N, Zhang X X 2023 PLoS One 18 e0278697 Google Scholar
[41]	Wang J P, Zhou H, Sun X L, Yuan Y F 2023 Chaos Soliton. Fract. 170 113371 Google Scholar
[42]	于海生, 赵林度, 来向红 2009 管理学报 6 187 Google Scholar Yu H S, Zhao L D, Lai X H 2009 Chin. J. Manag. 6 187 Google Scholar
[43]	Tian Y Z, Shi Y Q, Shi X Q, Li M H, Zhang M 2021 IEEE Access 9 91265 Google Scholar
[44]	Suo Q, Guo J L, Sun S W, Liu H 2018 Physica A 489 141 Google Scholar
[45]	汪小帆, 李翔, 陈关荣 2012 网络科学导论 (北京: 高等教育出版社) p397 Wang X F, Li X, Chen G R 2012 Network Science: An Introduction (Beijing: High Education Press) p397
[46]	赵晴 2021 硕士学位论文 (北京: 北京邮电大学) Zhao Q 2021 M. S. Thesis (Beijing: Beijing University of Posts and Telecommunications
[47]	石海佳, 石磊 2009 化工学报 60 1500 Google Scholar Shi H J, Shi L 2009 CIESC J. 60 1500 Google Scholar
[48]	李季明, 张宁 2008 复杂系统与复杂性科学 5 72 Google Scholar Li J M, Zhang N 2008 Cmplx. Syst. Complex. Sci. 5 72 Google Scholar
[49]	Orenstein P 2016 Second International Symposium on Stochastic Models in Reliability Engineering, Life Science and Operations Management Beer Sheva, Israel, February 15–18, 2016 p562
[50]	Yang Y, Poon J P, Liu Y, Bagchi-Sen S 2015 Energy 93 534 Google Scholar
[51]	Kang L, Wu W Z, Yu H, Su F Z 2022 Sensors 22 5889 Google Scholar
[52]	孙军艳, 傅卫平, 王雯 2015 西安理工大学学报 31 391 Google Scholar Sun J Y, Wei P F, Wang W 2015 J. Xi’an Univ. Technol. 31 391 Google Scholar
[53]	Bombelli A, Santos B F, Tavasszy L 2020 Transp. Res. E Logist. Transp. Rev. 138 101959 Google Scholar
[54]	Yang J L, Chen W 2023 Resour. Policy 86 104277 Google Scholar
[55]	Yue X P, Mu D, Wang C, Ren H Y, Ghadimi P 2023 Int. J. Prod. Res. 61 2758 Google Scholar
[56]	Li Z F, Li H W, Zhang Q Q, Qi X L 2024 Ocean Coast. Manag. 248 106969 Google Scholar
[57]	Yuan X J, Ge C B, Liu Y P, Li N, Wang Y 2022 Sustainability 14 16059 Google Scholar
[58]	Xia Q F, Du D B, Cao W P, Li X Y 2023 Resour. Policy 82 103532 Google Scholar
[59]	Zhao G M, Li W X, Geng Y, Bleischwitz R 2023 Resour. Policy 85 103815 Google Scholar
[60]	谭丹, 马顺甜 2022 经济地理 42 110 Google Scholar Tan D, Ma S T 2022 Econ. Geography 42 110 Google Scholar
[61]	Zuo Z L, McLellan B C, Li Y L, Guo H X, Cheng J H 2022 Resour. Policy 78 102912 Google Scholar
[62]	Xu M Q, Pan Q, Muscoloni A, Xia H X, Cannistraci C V 2020 Nat. Commun. 11 2849 Google Scholar
[63]	Lü L Y, Chen D B, Ren X L, Zhang Q M, Zhang Y C, Zhou T 2016 Phys. Rep. 650 1 Google Scholar
[64]	任晓龙, 吕琳媛 2014 科学通报 59 1175 Google Scholar Ren X L, Lü L Y 2014 Chin. Sci. Bull. 59 1175 Google Scholar
[65]	于明洋, 吕可夫, 阮永平 2022 系统工程理论与实践 42 1796 Google Scholar Yu M Y, Lü K F, Ruan Y P 2022 System Eng. Theor. Prac. 42 1796 Google Scholar
[66]	Perera S, Bell M G, Bliemer M C 2017 Appl. Netw. Sci. 2 1 Google Scholar
[67]	Guo Y Q, Zhao B Y, Zhang H W 2023 Energy 263 125912 Google Scholar
[68]	Zhu J F, Liu W, Yang Y B 2023 J. Mar. Sci. Eng. 11 724 Google Scholar
[69]	Mizgier K J, Jüttner M P, Wagner S M 2013 Int. J. Prod. Res. 51 1477 Google Scholar
[70]	Basole R C, Ghosh S, Hora M S 2017 IEEE T. Eng. Manage. 65 141 Google Scholar
[71]	Bonacich P 1987 Am. J. Sociol. 92 1170 Google Scholar
[72]	Shi J Y, Liu X, Li Y X, Yu C H, Han Y S 2022 Int. Rev. Financ. Anal. 80 102040 Google Scholar
[73]	Liu R X 2022 M. S. Thesis (Chengdu: Southwestern University of Finance and Economics) (in Chinese)[刘若曦 2022 硕士学位论文 (成都: 西南财经大学)]
[74]	Lavassani K M, Movahedi B 2021 Int. J. Glob. Bus. 16 86 Google Scholar
[75]	Shi J Y, Yang J H, Li Y X 2019 J. Bus. Econ. Manag. 20 1258 Google Scholar
[76]	Huang H S, Zhang J P, Yan J, Gong Y, Wang L K 2024 Eur. J. Innov. Manag. 27 551 Google Scholar
[77]	Lou P, Chen Y T, Yan J W 2020 IEEE Access 8 148827 Google Scholar
[78]	Blondel V D, Guillaume J L, Lambiotte R, Lefebvre E 2008 J. Stat. Mech. : Theory Exp. 2008 P10008 Google Scholar
[79]	Newman M E, Girvan M 2004 Phys. Rev. E 69 026113 Google Scholar
[80]	Ng A, Jordan M, Weiss Y 2001 Advances in Neural Information Processing Systems Vancouver, British Columbia, Canada, December 3–8, 2001 p849
[81]	Rosvall M, Bergstrom C T 2007 arXiv: 0707.0609 [physics. soc-ph]
[82]	Zhang Q, Pu S H, Yin M 2023 J. Mar. Sci. Eng. 11 1585 Google Scholar
[83]	Kito T, Brintrup A, New S, Reed-Tsochas F 2014 Saïd Business School WP 3 Google Scholar
[84]	Leicht E A, Newman M E 2008 Phys. Rev. Lett. 100 118703 Google Scholar
[85]	Wiedmer R, Griffis S E 2021 J. Bus. Logist. 42 264 Google Scholar
[86]	Shi D Y, Shang F, Chen B S, Expert P, Lü L Y, Stanley H E, Lambiotte R, Evans T S, Li R Q 2024 Commun. Phys. 7 170 Google Scholar
[87]	Ma'arif M R 2016 Sixth International Annual Engineering Seminar Yogyakarta, Indonesia, August 1–3, 2016 p206
[88]	Chakraborty T, Chauhan S S, Ouhimmou M 2020 Int. J. Prod. Res. 58 3618 Google Scholar
[89]	Hu X Q, Wang C, Zhu X Y, Yao C Y, Ghadimi P 2021 Resour. , Conserv. Recycl. 170 105591 Google Scholar
[90]	Wang W Y, Fan L W, Zhou P 2022 Energy 238 121924 Google Scholar
[91]	Chen G, Kong R, Wang Y X 2020 Physica A 540 123002 Google Scholar
[92]	Zhong W Q, An H Z, Gao X Y, Sun X Q 2014 Physica A 413 42 Google Scholar
[93]	Zhong W Q, An H Z, Shen L, Dai T, Fang W, Gao X Y, Dong D 2017 Energy 123 260 Google Scholar
[94]	Zheng S X, Zhou X R, Xing W L, Zhao P 2022 Resour. Policy 77 102783 Google Scholar
[95]	Li Y H, Zobel C W, Seref O, Chatfield D 2020 Int. J. Prod. Econ. 223 107529 Google Scholar
[96]	Shi X Q, Long W, Li Y Y, Deng D S 2022 Physica A 586 126518 Google Scholar
[97]	Li Y H, Zobel C W 2020 Int. J. Prod. Econ. 228 107693 Google Scholar
[98]	赵志刚, 周根贵, 李虎雄 2019 计算机科学 46 138 Google Scholar Zhao Z G, Zhou G G, Li H X 2019 Comput. Sci. 46 138 Google Scholar
[99]	Wang J P, Zhou H, Zhao Z, Sun X L 2023 Fourth International Conference on Computer Engineering and Application Hangzhou, China, April 7–9, 2023 p61
[100]	谢廷宇, 康凯, 王军进, 张学龙 2018 数学的实践与认识 48 40 Google Scholar Xie T Y, Kang K, Wang J J, Zhang X L 2018 J. Math. Prac. Theor. 48 40 Google Scholar
[101]	Zhao K, Scheibe K, Blackhurst J, Kumar A 2018 IEEE T. Eng. Manage. 66 127 Google Scholar
[102]	徐翔斌, 李恒 2015 系统工程 33 17 Google Scholar Xu X B, Li H 2015 Syst. Eng. 33 17 Google Scholar
[103]	Nair A, Vidal J M 2011 Int. J. Prod. Res. 49 1391 Google Scholar
[104]	Wei N, Xie W J, Zhou W X 2022 Energy 251 123939 Google Scholar
[105]	Sun J Y, Tang J M, Fu W P, Chen Z R, Niu Y R 2020 Comput. Ind. Eng. 144 106457 Google Scholar
[106]	Shahnazi R, Sajedianfard N, Melatos M 2023 Energy Rep. 10 2017 Google Scholar
[107]	Wen T, Gao Q Y, Chen Y W, Cheong K H 2022 Reliab. Eng. Syst. Safe. 226 108578 Google Scholar
[108]	Tan W J, Zhang A N, Cai W 2019 Int. J. Prod. Res. 57 6385 Google Scholar
[109]	Xu M Q, Deng W H, Zhu Y F, Linyuan L 2023 Reliab. Eng. Syst. Safe. 240 109576 Google Scholar
[110]	Xu X J, Zhu Y F, Xu M Q, Deng W H, Zuo Y Q 2022 Ocean Coast. Manag. 229 106325 Google Scholar
[111]	Xu M Q, Zhu Y F, Deng W H, Shen Y H, Li T 2024 Global Netw. 24 e12445 Google Scholar
[112]	Vugrin E D, Warren D E, Ehlen M A 2011 Process Saf. Prog. 30 280 Google Scholar
[113]	Turnquist M, Vugrin E 2013 Environ. Syst. Decis. 33 104 Google Scholar
[114]	Yildiz H, Yoon J, Talluri S, Ho W 2016 Decision Sci. 47 661 Google Scholar
[115]	Hosseini S, Barker K 2016 Comput. Ind. Eng. 93 252 Google Scholar
[116]	Hosseini S, Barker K 2016 Int. J. Prod. Econ. 180 68 Google Scholar
[117]	Bai X W, Ma Z J, Zhou Y M 2023 Transp. Res. E Logist. Transp. Rev. 170 103016 Google Scholar
[118]	Jin P F, Wang S G, Meng Z, Chen B 2023 Resour. Policy 87 104339 Google Scholar
[119]	Yu Y, Ma D P, Zhu W W 2023 Resour. Policy 83 103636 Google Scholar
[120]	Yu Y, Ma D P, Qian Y M 2023 Resour. Policy 86 104296 Google Scholar
[121]	Kim Y, Chen Y S, Linderman K 2015 J. Oper. Manag. 33 43 Google Scholar
[122]	Azad N, Hassini E 2019 Eur. J. Oper. Res. 275 481 Google Scholar
[123]	Li Z Y, Zhao P X, Han X 2022 Physica A 589 126611 Google Scholar
[124]	Ponomarov S Y, Holcomb M C 2009 Int. J. Logist. Manag. 20 124 Google Scholar
[125]	Hethcote H W 2000 SIAM Rev. 42 599 Google Scholar
[126]	杨康, 张仲义 2013 系统科学与数学 33 1224 Google Scholar Yang K, Zhang Z Y 2013 J. Syst. Sci. Math. Sci. 33 1224 Google Scholar
[127]	易慧妮 2015 硕士学位论文 (成都: 西南交通大学) Yi H N 2015 M. S. Thesis (Chengdu: Southwest Jiaotong University
[128]	Berger N, Schulze-Schwering S, Long E, Spinler S 2023 Eur. J. Oper. Res. 304 1036 Google Scholar
[129]	Wang C, Huang X, Hu X Q, Zhao L F, Liu C, Ghadimi P 2021 Appl. Energy 290 116744 Google Scholar
[130]	Guo H Y, Cheng Y Y 2019 Physica A 529 121400 Google Scholar
[131]	Guo H Y, Cheng Y Y, Xie X X 2020 Physica A 545 123506 Google Scholar
[132]	Kang X Y, Wang M X, Chen L, Li X 2023 Resour. Policy 85 103797 Google Scholar
[133]	Zheng S X, Zhou X R, Tan Z L, Zhang H, Liu C, Hao H C, Hu H, Cai X M, Yang H S, Luo W B 2022 Energy Sustain. Dev. 71 517 Google Scholar
[134]	Tang L, Jing K, He J, Stanley H E 2016 Physica A 443 58 Google Scholar
[135]	马靖莲 2016 博士学位论文 (西安: 长安大学) Ma J L 2016 Ph. D. Dissertation (Sian: Chang’an University
[136]	Yue X P, Mu D, Wang C, Ren H Y, Peng R, Du J B 2024 Reliab. Eng. Syst. Safe. 242 109728 Google Scholar
[137]	Wang Y, Zhang F 2018 Nonlinear Dynam. 92 1403 Google Scholar
[138]	Liu H, Han Y Y, Ni J L, Zhu A D 2022 Math. Probl. Eng. 2022 1 Google Scholar
[139]	Proselkov Y, Zhang J, Xu L, Hofmann E, Choi T Y, Rogers D, Brintrup A 2024 Int. J. Prod. Res. 62 823 Google Scholar
[140]	Inoue H, Todo Y 2019 Nat. Sustain. 2 841 Google Scholar
[141]	石霞虹 2012 硕士学位论文 (杭州: 杭州电子科技大学) Shi X H 2012 M. S. Thesis (Hangzhou: Hangzhou Dianzi University
[142]	Sytch M, Kim Y, Page S 2022 Calif. Manage. Rev. 64 119 Google Scholar
[143]	Li Y H, Chen K D, Collignon S, Ivanov D 2021 Eur. J. Oper. Res. 291 1117 Google Scholar
[144]	Nash Jr J F 1950 Proc. Natl. Acad. Sci. U. S. A. 36 48 Google Scholar
[145]	Peng Y T, Xu D, Veglianti E, Magnaghi E 2023 J. Ind. Manag. Optim. 19 3459 Google Scholar
[146]	Chen Z B, Tian C Y, Zhang D, Chen D Y 2020 Oper. Res. 20 649 Google Scholar
[147]	Nagurney A, Loo J, Dong J, Zhang D 2002 Netnomics 4 187 Google Scholar
[148]	Nagurney A, Dong J, Zhang D 2002 Transp. Res. E Logist. Transp. Rev. 38 281 Google Scholar
[149]	Dong J, Zhang D 2002 Transportation and Traffic Theory in the 21st Century Adelaide, Australia, July 16–18, 2002 p179
[150]	Dong J, Zhang D, Nagurney A 2004 Eur. J. Oper. Res. 156 194 Google Scholar
[151]	Dong J, Zhang D, Yan H, Nagurney A 2005 Ann. Oper. Res. 135 155 Google Scholar
[152]	Feyzian-Tary I, Razmi J, Sangari M S 2018 Ann. Oper. Res. 264 89 Google Scholar
[153]	He S X, Cui Y T 2023 Supply Chain Anal. 4 100039 Google Scholar
[154]	Von Stackelberg H, Peacock A T, Schneider E, Hutchison T W 1953 Economica 20 384 Google Scholar
[155]	Wang D P, Du G, Jiao R J, Wu R, Yu J P, Yang D 2016 Int. J. Prod. Econ. 172 1 Google Scholar
[156]	房艳君, 吴梦娜 2016 统计与决策 17 49 Google Scholar Fang Y J, Wu M N 2016 Stat. Decis. 17 49 Google Scholar
[157]	Tan J, Jiang G Q, Wang Z G 2019 Int. J. Intell. Inf. Technol. 15 54 Google Scholar
[158]	Daniele P 2010 Transp. Res. E Logist. Transp. Rev. 46 855 Google Scholar
[159]	Nagurney A 2021 Eur. J. Oper. Res. 293 880 Google Scholar

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图 1 供应链网络的典型结构^[26]

Figure 1. Typical structure of supply chain networks^[26].

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图 2 (a) 供应商网络; (b) 产品网络, 节点颜色代表节点所属社团^[27]

Figure 2. (a) Supplier network; (b) product network, nodes are colour-coded according to communities^[27].

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图 3 全球电动汽车锂电池供应链网络, 粉色节点代表供应核心部件的公司, 绿色节点代表供应关键矿物的公司, 橙色节点代表供应汽车的公司, 蓝色节点代表电池制造商, 节点大小与企业规模成正比^[34]

Figure 3. Visualization of the Electric Vehicle Lithium-ion Battery supply chain network, pink nodes represent supplying core components of firms, green nodes represent supplying critical minerals of firms, orange nodes represent supplying auto of firms, blue nodes represent battery manufacturer, where node size is proportional to company volume^[34].

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图 4 全球电动汽车锂离子电池上下游产业链相关的供应链网络^[35]

Figure 4. Supply chain network related to the upstream and downstream industrial chain of global electric vehicle lithium-ion batteries^[35]

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图 5 基于超图模型构建的供应链网络的演化机制　(a)玫红色圆代表现存节点, 绿色实线代表初始超边; (b) 添加新超边, 在现存节点之间添加新超边, 橙色虚线代表新超边; (c) 重组超边, 删除初始超边, 添加新超边, 蓝色虚线代表重组之后的新超边; (d) 链接新节点, 新增节点根据超边优先链接机制与现存节点连接形成新超边, 天蓝色圆代表新节点, 紫色虚线代表链接新节点的超边^[44]

Figure 5. Evolution mechanisms of supply chain networks constructed based on hypergraph models: (a) Magenta circles represent existing nodes and green solid lines represent original hyperedges; (b) add new hyperedges, add new hyperedges between existing nodes, orange dashed lines represent new hyperedges; (c) rewire hyperedges, delete original hyperedges and add new hyperedges, blue dashed lines represent new hyperedges by rewired; (d) link new nodes, link newly-added nodes with previously existing nodes according to their hyperedge preferential mechanism, sky blue circles represent new nodes, purple dashed lines represent hyperedges linking the new nodes^[44].

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Figure 6. Global crude oil trade network exhibits a core-edge structure in representative years, where dark red and light red nodes represent core and sub-core countries, respectively, and white nodes represent marginal countries, the larger node and darker color illustrate the greater the trade influence^[57]: (a) 2007; (b) 2010; (c) 2020.

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图 7 2000, 2002, 2004, 2009, 2018和2020年全球高岭土贸易网络的社团演变, 不同的颜色代表不同的社团, 节点的大小代表贸易国家的加权度^[94]

Figure 7. Evolution of communities in the global kaolin trade network in 2000, 2002, 2004, 2009, 2018, and 2020, different colours represent different associations, size of the nodes in the network represents the weighted degree of the trading country^[94].

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图 8 供应链网络的脆弱性随时间的状态转换^[95], 其中TIME =0 时, y₀表示中断事件的初始影响, TIME = t^max时, yt^max表示中断事件的全部影响, T表示网络从中断中恢复的时间速度. y₀和yt^max 刻画了网络的鲁棒性, 而T则描述了网络的可恢复能力

Figure 8. State transitions of supply chain network vulnerability over time^[95], where TIME = 0, y₀ represents the initial impact of the disruption event, TIME = t^max, yt^max represents the complete impact of the disruption event, and T denotes the speed at which the network recovers from the disruption. y₀ and yt^max characterize the robustness of the network, while T describes the network's recoverability.

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图 9 节点中断条件下铜贸易多层网络风险传播模型, 网络中的节点代表国家, 边代表贸易关系, 红色节点代表受风险冲击影响的国家, 红色边代表受风险冲击的边, 虚线表示产业链的层间关系^[132]

Figure 9. Risk propagation model of copper trade multilayer networks under node interruption conditions, nodes in the network represent countries, the edges represent trade relations, red nodes represent countries affected by the shock, the red edge indicates the edge affected by the shock, the dotted line represents the inter-layer relationship of the industrial chain^[132].

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表 1 常见的供应链网络类型

Table 1. Common types of supply chain networks.

供应链网络类型	内容
物流网络^[17]	实际货物的运输、仓储、配送等
信息流网络^[18]	订单、库存信息、生产计划等的传递和共享
资金流网络^[19,20]	货币和财务信息的流动, 包括支付、结算、融资和资金管理等.
价值链网络^[21]	价值在供应链中的创造和传递, 涉及生产、分销、销售等环节
合作网络^[22]	各参与方之间的合作和协同关系, 包括供应商、制造商、分销商等
数字化网络^[23]	数字技术在供应链中的应用, 如物联网、大数据、人工智能等
全球供应链网络^[24]	跨国和全球范围内的供应链关系, 包括国际贸易、全球物流等
生态系统网络^[25]	将供应链视为生态系统, 关注各组成部分之间的相互关系和可持续性

DownLoad: CSV

[1]	Choi T Y, Dooley K J, Rungtusanatham M 2001 J. Oper. Manag. 19 351 Google Scholar
[2]	Surana A, Kumara S, Greaves M, Raghavan U N 2005 Int. J. Prod. Res. 43 4235 Google Scholar
[3]	Helbing D, Armbruster D, Mikhailov A S, Lefeber E 2006 Physica A 363 xi Google Scholar
[4]	Cao W G, Xie S L, Qiao X D 2008 Eighth International Conference of Chinese Logistics and Transportation Professionals Chengdu, China, July 31–August 3, 2008 p1949
[5]	Zhang H M, Feng T T, Yang Y S 2022 Resour. Policy 75 102492 Google Scholar
[6]	Dolgui A, Ivanov D, Sokolov B 2018 Int. J. Prod. Res. 56 414 Google Scholar
[7]	Cruz J M 2008 Eur. J. Oper. Res. 184 1005 Google Scholar
[8]	Hearnshaw E J, Wilson M M 2013 Int. J. Oper. Prod. Man. 33 442 Google Scholar
[9]	Pathak S D, Day J M, Nair A, Sawaya W J, Kristal M M 2007 Decision Sci. 38 547 Google Scholar
[10]	Borgatti S P, Li X 2009 J. Supply Chain Manag. 45 5 Google Scholar
[11]	Ledwoch A, Yasarcan H, Brintrup A 2018 Int. J. Prod. Econ. 197 13 Google Scholar
[12]	Wang K Q, Zeng Z F, Sun D C 2008 Fourth International Conference on Semantics, Knowledge and Grid Beijing, China, December 3–5, 2008 p493
[13]	Ou C Y, Pan F B, Lin S J 2024 Sustainability 16 5514 Google Scholar
[14]	Xu M J, Wang X P, Zhao L D 2014 Int. J. Syst. Sci. Oper. Logist. 1 105 Google Scholar
[15]	Liang D, Bhamra R, Liu Z Y, Pan Y C 2022 Mathematics 10 3008 Google Scholar
[16]	Chan C K, Zhou Y, Wong K H 2019 Eur. J. Oper. Res. 275 514 Google Scholar
[17]	Gedik R, Medal H, Rainwater C, Pohl E A, Mason S J 2014 Transp. Res. E Logist. Transp. Rev. 71 45 Google Scholar
[18]	Carvalho H, Naghshineh B, Govindan K, Cruz-Machado V 2022 Comput. Ind. Eng. 171 108375 Google Scholar
[19]	Carnovale S, Rogers D S, Yeniyurt S 2019 J. Purch. Supply Manag. 25 134 Google Scholar
[20]	Wuttke D A, Blome C, Henke M 2013 Int. J. Prod. Econ. 145 773 Google Scholar
[21]	Yu H, Li H R 2023 Resour. Policy 85 104055 Google Scholar
[22]	Rezapour S, Farahani R Z, Pourakbar M 2017 Eur. J. Oper. Res. 259 1017 Google Scholar
[23]	Ivanov D 2023 Int. J. Prod. Res. 61 1683 Google Scholar
[24]	Van den Brink S, Kleijn R, Sprecher B, Tukker A 2020 Resour. Conserv. Recycl. 156 104743 Google Scholar
[25]	Sloane A, O’reilly S 2013 Prod. Plan. Control 24 621 Google Scholar
[26]	Wang J P, Zhou H, Jin X D 2021 Chaos Soliton. Fract. 143 110259 Google Scholar
[27]	Brintrup A, Ledwoch A, Barros J 2016 Logist. Res. 9 1 Google Scholar
[28]	Kim Y, Choi T Y, Yan T, Dooley K 2011 J. Oper. Manag. 29 194 Google Scholar
[29]	史金艳, 杨健亨, 李延喜, 张启望 2019 中国工业经济 9 136 Google Scholar Shi J Y, Yang J H, Li Y X, Zhang Q W 2019 Chin. Ind. Econ. 9 136 Google Scholar
[30]	Zhao K, Zuo Z, Blackhurst J V 2019 J. Oper. Manag. 65 190 Google Scholar
[31]	D’Ignazio A, Giovannetti E 2014 Int. J. Prod. Econ. 147 486 Google Scholar
[32]	Tang L B, Wang P, Ma Z J, Pauliuk S, Chen W Q, Dai T, Lin Z P 2023 J. Ind. Ecol. 27 323 Google Scholar
[33]	Bellamy M A, Ghosh S, Hora M 2014 J. Oper. Manag. 32 357 Google Scholar
[34]	Mu D, Ren H Y, Wang C, Yue X P, Du J B, Ghadimi P 2023 Resour. Policy 80 103225 Google Scholar
[35]	Hu X Q, Wang C, Lim M K, Chen W Q, Teng L M, Wang P, Wang H M, Zhang C, Yao C Y, Ghadimi P 2023 Renew. Sust. Energ. Rev. 173 113083 Google Scholar
[36]	Basole R C, Bellamy M A 2014 Decision Sci. 45 753 Google Scholar
[37]	Barabási A L, Albert R 1999 Science 286 509 Google Scholar
[38]	Albert R, Barabási A L 2002 Rev. Mod. Phys. 74 47 Google Scholar
[39]	Bell M, Perera S, Piraveenan M, Bliemer M, Latty T, Reid C 2017 Sci. Rep. 7 42431 Google Scholar
[40]	Chen H W, Chen G P, Zhang Q N, Zhang X X 2023 PLoS One 18 e0278697 Google Scholar
[41]	Wang J P, Zhou H, Sun X L, Yuan Y F 2023 Chaos Soliton. Fract. 170 113371 Google Scholar
[42]	于海生, 赵林度, 来向红 2009 管理学报 6 187 Google Scholar Yu H S, Zhao L D, Lai X H 2009 Chin. J. Manag. 6 187 Google Scholar
[43]	Tian Y Z, Shi Y Q, Shi X Q, Li M H, Zhang M 2021 IEEE Access 9 91265 Google Scholar
[44]	Suo Q, Guo J L, Sun S W, Liu H 2018 Physica A 489 141 Google Scholar
[45]	汪小帆, 李翔, 陈关荣 2012 网络科学导论 (北京: 高等教育出版社) p397 Wang X F, Li X, Chen G R 2012 Network Science: An Introduction (Beijing: High Education Press) p397
[46]	赵晴 2021 硕士学位论文 (北京: 北京邮电大学) Zhao Q 2021 M. S. Thesis (Beijing: Beijing University of Posts and Telecommunications
[47]	石海佳, 石磊 2009 化工学报 60 1500 Google Scholar Shi H J, Shi L 2009 CIESC J. 60 1500 Google Scholar
[48]	李季明, 张宁 2008 复杂系统与复杂性科学 5 72 Google Scholar Li J M, Zhang N 2008 Cmplx. Syst. Complex. Sci. 5 72 Google Scholar
[49]	Orenstein P 2016 Second International Symposium on Stochastic Models in Reliability Engineering, Life Science and Operations Management Beer Sheva, Israel, February 15–18, 2016 p562
[50]	Yang Y, Poon J P, Liu Y, Bagchi-Sen S 2015 Energy 93 534 Google Scholar
[51]	Kang L, Wu W Z, Yu H, Su F Z 2022 Sensors 22 5889 Google Scholar
[52]	孙军艳, 傅卫平, 王雯 2015 西安理工大学学报 31 391 Google Scholar Sun J Y, Wei P F, Wang W 2015 J. Xi’an Univ. Technol. 31 391 Google Scholar
[53]	Bombelli A, Santos B F, Tavasszy L 2020 Transp. Res. E Logist. Transp. Rev. 138 101959 Google Scholar
[54]	Yang J L, Chen W 2023 Resour. Policy 86 104277 Google Scholar
[55]	Yue X P, Mu D, Wang C, Ren H Y, Ghadimi P 2023 Int. J. Prod. Res. 61 2758 Google Scholar
[56]	Li Z F, Li H W, Zhang Q Q, Qi X L 2024 Ocean Coast. Manag. 248 106969 Google Scholar
[57]	Yuan X J, Ge C B, Liu Y P, Li N, Wang Y 2022 Sustainability 14 16059 Google Scholar
[58]	Xia Q F, Du D B, Cao W P, Li X Y 2023 Resour. Policy 82 103532 Google Scholar
[59]	Zhao G M, Li W X, Geng Y, Bleischwitz R 2023 Resour. Policy 85 103815 Google Scholar
[60]	谭丹, 马顺甜 2022 经济地理 42 110 Google Scholar Tan D, Ma S T 2022 Econ. Geography 42 110 Google Scholar
[61]	Zuo Z L, McLellan B C, Li Y L, Guo H X, Cheng J H 2022 Resour. Policy 78 102912 Google Scholar
[62]	Xu M Q, Pan Q, Muscoloni A, Xia H X, Cannistraci C V 2020 Nat. Commun. 11 2849 Google Scholar
[63]	Lü L Y, Chen D B, Ren X L, Zhang Q M, Zhang Y C, Zhou T 2016 Phys. Rep. 650 1 Google Scholar
[64]	任晓龙, 吕琳媛 2014 科学通报 59 1175 Google Scholar Ren X L, Lü L Y 2014 Chin. Sci. Bull. 59 1175 Google Scholar
[65]	于明洋, 吕可夫, 阮永平 2022 系统工程理论与实践 42 1796 Google Scholar Yu M Y, Lü K F, Ruan Y P 2022 System Eng. Theor. Prac. 42 1796 Google Scholar
[66]	Perera S, Bell M G, Bliemer M C 2017 Appl. Netw. Sci. 2 1 Google Scholar
[67]	Guo Y Q, Zhao B Y, Zhang H W 2023 Energy 263 125912 Google Scholar
[68]	Zhu J F, Liu W, Yang Y B 2023 J. Mar. Sci. Eng. 11 724 Google Scholar
[69]	Mizgier K J, Jüttner M P, Wagner S M 2013 Int. J. Prod. Res. 51 1477 Google Scholar
[70]	Basole R C, Ghosh S, Hora M S 2017 IEEE T. Eng. Manage. 65 141 Google Scholar
[71]	Bonacich P 1987 Am. J. Sociol. 92 1170 Google Scholar
[72]	Shi J Y, Liu X, Li Y X, Yu C H, Han Y S 2022 Int. Rev. Financ. Anal. 80 102040 Google Scholar
[73]	Liu R X 2022 M. S. Thesis (Chengdu: Southwestern University of Finance and Economics) (in Chinese)[刘若曦 2022 硕士学位论文 (成都: 西南财经大学)]
[74]	Lavassani K M, Movahedi B 2021 Int. J. Glob. Bus. 16 86 Google Scholar
[75]	Shi J Y, Yang J H, Li Y X 2019 J. Bus. Econ. Manag. 20 1258 Google Scholar
[76]	Huang H S, Zhang J P, Yan J, Gong Y, Wang L K 2024 Eur. J. Innov. Manag. 27 551 Google Scholar
[77]	Lou P, Chen Y T, Yan J W 2020 IEEE Access 8 148827 Google Scholar
[78]	Blondel V D, Guillaume J L, Lambiotte R, Lefebvre E 2008 J. Stat. Mech. : Theory Exp. 2008 P10008 Google Scholar
[79]	Newman M E, Girvan M 2004 Phys. Rev. E 69 026113 Google Scholar
[80]	Ng A, Jordan M, Weiss Y 2001 Advances in Neural Information Processing Systems Vancouver, British Columbia, Canada, December 3–8, 2001 p849
[81]	Rosvall M, Bergstrom C T 2007 arXiv: 0707.0609 [physics. soc-ph]
[82]	Zhang Q, Pu S H, Yin M 2023 J. Mar. Sci. Eng. 11 1585 Google Scholar
[83]	Kito T, Brintrup A, New S, Reed-Tsochas F 2014 Saïd Business School WP 3 Google Scholar
[84]	Leicht E A, Newman M E 2008 Phys. Rev. Lett. 100 118703 Google Scholar
[85]	Wiedmer R, Griffis S E 2021 J. Bus. Logist. 42 264 Google Scholar
[86]	Shi D Y, Shang F, Chen B S, Expert P, Lü L Y, Stanley H E, Lambiotte R, Evans T S, Li R Q 2024 Commun. Phys. 7 170 Google Scholar
[87]	Ma'arif M R 2016 Sixth International Annual Engineering Seminar Yogyakarta, Indonesia, August 1–3, 2016 p206
[88]	Chakraborty T, Chauhan S S, Ouhimmou M 2020 Int. J. Prod. Res. 58 3618 Google Scholar
[89]	Hu X Q, Wang C, Zhu X Y, Yao C Y, Ghadimi P 2021 Resour. , Conserv. Recycl. 170 105591 Google Scholar
[90]	Wang W Y, Fan L W, Zhou P 2022 Energy 238 121924 Google Scholar
[91]	Chen G, Kong R, Wang Y X 2020 Physica A 540 123002 Google Scholar
[92]	Zhong W Q, An H Z, Gao X Y, Sun X Q 2014 Physica A 413 42 Google Scholar
[93]	Zhong W Q, An H Z, Shen L, Dai T, Fang W, Gao X Y, Dong D 2017 Energy 123 260 Google Scholar
[94]	Zheng S X, Zhou X R, Xing W L, Zhao P 2022 Resour. Policy 77 102783 Google Scholar
[95]	Li Y H, Zobel C W, Seref O, Chatfield D 2020 Int. J. Prod. Econ. 223 107529 Google Scholar
[96]	Shi X Q, Long W, Li Y Y, Deng D S 2022 Physica A 586 126518 Google Scholar
[97]	Li Y H, Zobel C W 2020 Int. J. Prod. Econ. 228 107693 Google Scholar
[98]	赵志刚, 周根贵, 李虎雄 2019 计算机科学 46 138 Google Scholar Zhao Z G, Zhou G G, Li H X 2019 Comput. Sci. 46 138 Google Scholar
[99]	Wang J P, Zhou H, Zhao Z, Sun X L 2023 Fourth International Conference on Computer Engineering and Application Hangzhou, China, April 7–9, 2023 p61
[100]	谢廷宇, 康凯, 王军进, 张学龙 2018 数学的实践与认识 48 40 Google Scholar Xie T Y, Kang K, Wang J J, Zhang X L 2018 J. Math. Prac. Theor. 48 40 Google Scholar
[101]	Zhao K, Scheibe K, Blackhurst J, Kumar A 2018 IEEE T. Eng. Manage. 66 127 Google Scholar
[102]	徐翔斌, 李恒 2015 系统工程 33 17 Google Scholar Xu X B, Li H 2015 Syst. Eng. 33 17 Google Scholar
[103]	Nair A, Vidal J M 2011 Int. J. Prod. Res. 49 1391 Google Scholar
[104]	Wei N, Xie W J, Zhou W X 2022 Energy 251 123939 Google Scholar
[105]	Sun J Y, Tang J M, Fu W P, Chen Z R, Niu Y R 2020 Comput. Ind. Eng. 144 106457 Google Scholar
[106]	Shahnazi R, Sajedianfard N, Melatos M 2023 Energy Rep. 10 2017 Google Scholar
[107]	Wen T, Gao Q Y, Chen Y W, Cheong K H 2022 Reliab. Eng. Syst. Safe. 226 108578 Google Scholar
[108]	Tan W J, Zhang A N, Cai W 2019 Int. J. Prod. Res. 57 6385 Google Scholar
[109]	Xu M Q, Deng W H, Zhu Y F, Linyuan L 2023 Reliab. Eng. Syst. Safe. 240 109576 Google Scholar
[110]	Xu X J, Zhu Y F, Xu M Q, Deng W H, Zuo Y Q 2022 Ocean Coast. Manag. 229 106325 Google Scholar
[111]	Xu M Q, Zhu Y F, Deng W H, Shen Y H, Li T 2024 Global Netw. 24 e12445 Google Scholar
[112]	Vugrin E D, Warren D E, Ehlen M A 2011 Process Saf. Prog. 30 280 Google Scholar
[113]	Turnquist M, Vugrin E 2013 Environ. Syst. Decis. 33 104 Google Scholar
[114]	Yildiz H, Yoon J, Talluri S, Ho W 2016 Decision Sci. 47 661 Google Scholar
[115]	Hosseini S, Barker K 2016 Comput. Ind. Eng. 93 252 Google Scholar
[116]	Hosseini S, Barker K 2016 Int. J. Prod. Econ. 180 68 Google Scholar
[117]	Bai X W, Ma Z J, Zhou Y M 2023 Transp. Res. E Logist. Transp. Rev. 170 103016 Google Scholar
[118]	Jin P F, Wang S G, Meng Z, Chen B 2023 Resour. Policy 87 104339 Google Scholar
[119]	Yu Y, Ma D P, Zhu W W 2023 Resour. Policy 83 103636 Google Scholar
[120]	Yu Y, Ma D P, Qian Y M 2023 Resour. Policy 86 104296 Google Scholar
[121]	Kim Y, Chen Y S, Linderman K 2015 J. Oper. Manag. 33 43 Google Scholar
[122]	Azad N, Hassini E 2019 Eur. J. Oper. Res. 275 481 Google Scholar
[123]	Li Z Y, Zhao P X, Han X 2022 Physica A 589 126611 Google Scholar
[124]	Ponomarov S Y, Holcomb M C 2009 Int. J. Logist. Manag. 20 124 Google Scholar
[125]	Hethcote H W 2000 SIAM Rev. 42 599 Google Scholar
[126]	杨康, 张仲义 2013 系统科学与数学 33 1224 Google Scholar Yang K, Zhang Z Y 2013 J. Syst. Sci. Math. Sci. 33 1224 Google Scholar
[127]	易慧妮 2015 硕士学位论文 (成都: 西南交通大学) Yi H N 2015 M. S. Thesis (Chengdu: Southwest Jiaotong University
[128]	Berger N, Schulze-Schwering S, Long E, Spinler S 2023 Eur. J. Oper. Res. 304 1036 Google Scholar
[129]	Wang C, Huang X, Hu X Q, Zhao L F, Liu C, Ghadimi P 2021 Appl. Energy 290 116744 Google Scholar
[130]	Guo H Y, Cheng Y Y 2019 Physica A 529 121400 Google Scholar
[131]	Guo H Y, Cheng Y Y, Xie X X 2020 Physica A 545 123506 Google Scholar
[132]	Kang X Y, Wang M X, Chen L, Li X 2023 Resour. Policy 85 103797 Google Scholar
[133]	Zheng S X, Zhou X R, Tan Z L, Zhang H, Liu C, Hao H C, Hu H, Cai X M, Yang H S, Luo W B 2022 Energy Sustain. Dev. 71 517 Google Scholar
[134]	Tang L, Jing K, He J, Stanley H E 2016 Physica A 443 58 Google Scholar
[135]	马靖莲 2016 博士学位论文 (西安: 长安大学) Ma J L 2016 Ph. D. Dissertation (Sian: Chang’an University
[136]	Yue X P, Mu D, Wang C, Ren H Y, Peng R, Du J B 2024 Reliab. Eng. Syst. Safe. 242 109728 Google Scholar
[137]	Wang Y, Zhang F 2018 Nonlinear Dynam. 92 1403 Google Scholar
[138]	Liu H, Han Y Y, Ni J L, Zhu A D 2022 Math. Probl. Eng. 2022 1 Google Scholar
[139]	Proselkov Y, Zhang J, Xu L, Hofmann E, Choi T Y, Rogers D, Brintrup A 2024 Int. J. Prod. Res. 62 823 Google Scholar
[140]	Inoue H, Todo Y 2019 Nat. Sustain. 2 841 Google Scholar
[141]	石霞虹 2012 硕士学位论文 (杭州: 杭州电子科技大学) Shi X H 2012 M. S. Thesis (Hangzhou: Hangzhou Dianzi University
[142]	Sytch M, Kim Y, Page S 2022 Calif. Manage. Rev. 64 119 Google Scholar
[143]	Li Y H, Chen K D, Collignon S, Ivanov D 2021 Eur. J. Oper. Res. 291 1117 Google Scholar
[144]	Nash Jr J F 1950 Proc. Natl. Acad. Sci. U. S. A. 36 48 Google Scholar
[145]	Peng Y T, Xu D, Veglianti E, Magnaghi E 2023 J. Ind. Manag. Optim. 19 3459 Google Scholar
[146]	Chen Z B, Tian C Y, Zhang D, Chen D Y 2020 Oper. Res. 20 649 Google Scholar
[147]	Nagurney A, Loo J, Dong J, Zhang D 2002 Netnomics 4 187 Google Scholar
[148]	Nagurney A, Dong J, Zhang D 2002 Transp. Res. E Logist. Transp. Rev. 38 281 Google Scholar
[149]	Dong J, Zhang D 2002 Transportation and Traffic Theory in the 21st Century Adelaide, Australia, July 16–18, 2002 p179
[150]	Dong J, Zhang D, Nagurney A 2004 Eur. J. Oper. Res. 156 194 Google Scholar
[151]	Dong J, Zhang D, Yan H, Nagurney A 2005 Ann. Oper. Res. 135 155 Google Scholar
[152]	Feyzian-Tary I, Razmi J, Sangari M S 2018 Ann. Oper. Res. 264 89 Google Scholar
[153]	He S X, Cui Y T 2023 Supply Chain Anal. 4 100039 Google Scholar
[154]	Von Stackelberg H, Peacock A T, Schneider E, Hutchison T W 1953 Economica 20 384 Google Scholar
[155]	Wang D P, Du G, Jiao R J, Wu R, Yu J P, Yang D 2016 Int. J. Prod. Econ. 172 1 Google Scholar
[156]	房艳君, 吴梦娜 2016 统计与决策 17 49 Google Scholar Fang Y J, Wu M N 2016 Stat. Decis. 17 49 Google Scholar
[157]	Tan J, Jiang G Q, Wang Z G 2019 Int. J. Intell. Inf. Technol. 15 54 Google Scholar
[158]	Daniele P 2010 Transp. Res. E Logist. Transp. Rev. 46 855 Google Scholar
[159]	Nagurney A 2021 Eur. J. Oper. Res. 293 880 Google Scholar

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[19]	Lü Ling, Zhang Chao. Chaos synchronization of a complex network with different nodes. Acta Physica Sinica, 2009, 58(3): 1462-1466. doi: 10.7498/aps.58.1462
[20]	Gao Zhong-Ke, Jin Ning-De. Complex network community structure of two-phase flow pattern and its statistical characteristics. Acta Physica Sinica, 2008, 57(11): 6909-6920. doi: 10.7498/aps.57.6909

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Vol. 73, Issue 19 - 2024-10-05

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