{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T05:34:23Z","timestamp":1776922463874,"version":"3.51.2"},"reference-count":39,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,6,30]],"date-time":"2024-06-30T00:00:00Z","timestamp":1719705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Pre-research Project of Hebei GEO University","award":["KY2024YB21"],"award-info":[{"award-number":["KY2024YB21"]}]},{"name":"The National Pre-research Project of Hebei GEO University","award":["SD201060"],"award-info":[{"award-number":["SD201060"]}]},{"name":"The National Pre-research Project of Hebei GEO University","award":["20230202015"],"award-info":[{"award-number":["20230202015"]}]},{"name":"Key Project of Humanities and Social Sciences Research in Colleges and Universities in Hebei Province","award":["KY2024YB21"],"award-info":[{"award-number":["KY2024YB21"]}]},{"name":"Key Project of Humanities and Social Sciences Research in Colleges and Universities in Hebei Province","award":["SD201060"],"award-info":[{"award-number":["SD201060"]}]},{"name":"Key Project of Humanities and Social Sciences Research in Colleges and Universities in Hebei Province","award":["20230202015"],"award-info":[{"award-number":["20230202015"]}]},{"name":"Research Topic of Social Science Development in Hebei Province","award":["KY2024YB21"],"award-info":[{"award-number":["KY2024YB21"]}]},{"name":"Research Topic of Social Science Development in Hebei Province","award":["SD201060"],"award-info":[{"award-number":["SD201060"]}]},{"name":"Research Topic of Social Science Development in Hebei Province","award":["20230202015"],"award-info":[{"award-number":["20230202015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Investigating the significant \u201croles\u201d within financial complex networks and their stability is of great importance for preventing financial risks. On one hand, this paper initially constructs a complex network model of the stock market based on mutual information theory and threshold methods, combined with the closing price returns of stocks. It then analyzes the basic topological characteristics of this network and examines its stability under random and targeted attacks by varying the threshold values. On the other hand, using systemic risk entropy as a metric to quantify the stability of the stock market, this paper validates the impact of the COVID-19 pandemic as a widespread, unexpected event on network stability. The research results indicate that this complex network exhibits small-world characteristics but cannot be strictly classified as a scale-free network. In this network, key roles are played by the industrial sector, media and information services, pharmaceuticals and healthcare, transportation, and utilities. Upon reducing the threshold, the network\u2019s resilience to random attacks is correspondingly strengthened. Dynamically, from 2000 to 2022, systemic risk in significant industrial share markets significantly increased. From a static perspective, the period around 2019, affected by the COVID-19 pandemic, experienced the most drastic fluctuations. Compared to the year 2000, systemic risk entropy in 2022 increased nearly sixtyfold, further indicating an increasing instability within this complex network.<\/jats:p>","DOI":"10.3390\/e26070569","type":"journal-article","created":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T09:01:39Z","timestamp":1719910899000},"page":"569","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Study on the Stability of Complex Networks in the Stock Markets of Key Industries in China"],"prefix":"10.3390","volume":"26","author":[{"given":"Zinuoqi","family":"Wang","sequence":"first","affiliation":[{"name":"School of Economics, Hebei GEO University, Shijiazhuang 050031, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-9473-7807","authenticated-orcid":false,"given":"Guofeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Economics, Hebei GEO University, Shijiazhuang 050031, China"},{"name":"Research Base for Scientific-Technological Innovation and Regional Economic Sustainable Development of Hebei Province, Hebei GEO University, Shijiazhuang 050031, China"},{"name":"Natural Resource Asset Capital Research Center, Hebei GEO University, Shijiazhuang 050031, China"}]},{"given":"Xiaojing","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Earth Sciences, Hebei GEO University, Shijiazhuang 050031, China"}]},{"given":"Ruixian","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Economics, Hebei GEO University, Shijiazhuang 050031, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1093\/rfs\/3.1.5","article-title":"Transmission of volatility between stock markets","volume":"3","author":"King","year":"1990","journal-title":"Rev. Financ. Stud."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"167","DOI":"10.2307\/3867666","article-title":"Financial market contagion in the Asian crisis","volume":"46","author":"Baig","year":"1999","journal-title":"IMF Econ. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.chieco.2009.11.001","article-title":"The co-movement of stock markets in East Asia: Did the 1997\u20131998 Asian financial crisis really strengthen stock market integration?","volume":"21","author":"Huyghebaert","year":"2010","journal-title":"China Econ. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1072","DOI":"10.1111\/j.1465-7295.2009.00249.x","article-title":"Financial contagion on the international trade network","volume":"48","author":"Kali","year":"2010","journal-title":"Econ. Inq."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.physa.2018.02.153","article-title":"Dynamics of financial crises in the world trade network","volume":"501","author":"Askari","year":"2018","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/S1057-5219(01)00052-7","article-title":"What drives contagion: Trade, neighborhood, or financial links?","volume":"10","year":"2001","journal-title":"Int. Rev. Financ. Anal."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"101702","DOI":"10.1016\/j.irfa.2021.101702","article-title":"Crude oil market and stock markets during the COVID-19 pandemic: Evidence from the US, Japan, and Germany","volume":"74","author":"Zhang","year":"2021","journal-title":"Int. Rev. Financ. Anal."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Diebold, F.X., and Yilmaz, K. (2008). Macroeconomic Volatility and Stock Market Volatility, Worldwide, National Bureau of Economic Research.","DOI":"10.3386\/w14269"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"983","DOI":"10.3233\/IDA-2009-0404","article-title":"Stock market stability index: An intelligent approach","volume":"13","author":"Son","year":"2009","journal-title":"Intell. Data Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1002\/fut.21573","article-title":"Does index futures trading reduce volatility in the Chinese stock market? A panel data evaluation approach","volume":"33","author":"Chen","year":"2013","journal-title":"J. Futures Mark."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Johnsson, M. (2012). Graph mining based SOM: A tool to analyze economic stability. Applications of Self-Organizing Maps, InTech.","DOI":"10.5772\/3464"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1707","DOI":"10.1038\/s41467-020-15356-z","article-title":"A behavioral approach to instability pathways in financial markets","volume":"11","author":"Spelta","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.gfj.2010.03.005","article-title":"Empirical investigation of herding behavior in Chinese stock markets: Evidence from quantile regression analysis","volume":"21","author":"Chiang","year":"2010","journal-title":"Global Financ. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1911","DOI":"10.1016\/j.jbankfin.2009.12.014","article-title":"An empirical analysis of herd behavior in global stock markets","volume":"34","author":"Chiang","year":"2010","journal-title":"J. Bank. Financ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/j.jebo.2022.06.009","article-title":"Causes of fragile stock market stability","volume":"200","author":"Gardini","year":"2022","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1238\/Physica.Topical.106a00048","article-title":"Asset trees and asset graphs in financial markets","volume":"2003","author":"Onnela","year":"2003","journal-title":"Phys. Scr."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"013117","DOI":"10.1063\/1.3683467","article-title":"The structure and resilience of financial market networks","volume":"22","author":"Peron","year":"2012","journal-title":"Chaos"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/j.jfineco.2011.12.010","article-title":"Econometric measures of connectedness and systemic risk in the finance and insurance sectors","volume":"104","author":"Billio","year":"2012","journal-title":"J. Financ. Econ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.physa.2013.08.053","article-title":"Stock network stability in times of crisis","volume":"393","author":"Heiberger","year":"2014","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s100510050929","article-title":"Hierarchical structure in financial markets","volume":"11","author":"Mantegna","year":"1999","journal-title":"Eur. Phys. J. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1016\/j.physa.2018.09.140","article-title":"The stability of Chinese stock network and its mechanism","volume":"515","author":"Zhang","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2956","DOI":"10.1016\/j.physa.2009.03.028","article-title":"A network analysis of the Chinese stock market","volume":"388","author":"Huang","year":"2009","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"012033","DOI":"10.1088\/1742-6596\/394\/1\/012033","article-title":"Entropy: A new measure of stock market volatility?","volume":"394","author":"Bentes","year":"2012","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1002\/for.2411","article-title":"Predicting systemic risk with entropic indicators","volume":"36","author":"Gradojevic","year":"2017","journal-title":"J. Forecast."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Guo, X., Zhang, H., and Tian, T. (2018). Development of stock correlation networks using mutual information and financial big data. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0195941"},{"key":"ref_26","unstructured":"Sharma, C., and Habib, A. (2019). Uncovering networks amongst stocks returns by studying nonlinear interactions in high frequency data of the Indian Stock Market using mutual information. arXiv."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of \u2018small-world\u2019 networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/MCAS.2003.1228503","article-title":"Complex networks: Small-world, scale-free and beyond","volume":"3","author":"Wang","year":"2003","journal-title":"IEEE Circuits Syst. Mag."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1350005","DOI":"10.1142\/S0129183113500058","article-title":"Dynamic evolution of financial network and its relation to economic crises","volume":"24","author":"Gao","year":"2013","journal-title":"Int. J. Mod. Phys. C"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.physa.2015.10.108","article-title":"Topology of the South African stock market network across the 2008 financial crisis","volume":"445","author":"Majapa","year":"2016","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1016\/j.jempfin.2010.04.008","article-title":"A network perspective of the stock market","volume":"17","author":"Chi","year":"2010","journal-title":"J. Empir. Financ."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"123448","DOI":"10.1016\/j.physa.2019.123448","article-title":"Systemic importance of financial institutions: A complex network perspective","volume":"545","author":"Yang","year":"2020","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.physrep.2012.01.007","article-title":"Physical approach to complex systems","volume":"515","year":"2012","journal-title":"Phys. Rep."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"6105872","DOI":"10.1155\/2020\/6105872","article-title":"An introduction to complex systems science and its applications","volume":"2020","author":"Siegenfeld","year":"2020","journal-title":"Complexity"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s13194-012-0056-8","article-title":"What is a complex system?","volume":"3","author":"Ladyman","year":"2013","journal-title":"Eur. J. Philos. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Dro\u017cd\u017c, S., Kwapie\u0144, J., O\u015bwi\u0119cimka, P., Stanisz, T., and W\u0105torek, M. (2020). Complexity in economic and social systems: Cryptocurrency market at around COVID-19. Entropy, 22.","DOI":"10.3390\/e22091043"},{"key":"ref_37","first-page":"116","article-title":"Local government officials\u2019 environmental assessment incentives with ESG performance of listed companies","volume":"10","author":"Shi","year":"2023","journal-title":"Res. Financ. Econ. Issues"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Hu, C., and Guo, R. (2024). Research on risk contagion in ESG industries: An information entropy-based network approach. Entropy, 26.","DOI":"10.3390\/e26030206"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Yang, M., Ren, F., and Li, S. (2020). Stock network stability after crashes based on entropy method. Front. Phys., 8.","DOI":"10.3389\/fphy.2020.00163"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/7\/569\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:08:24Z","timestamp":1760108904000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/7\/569"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,30]]},"references-count":39,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2024,7]]}},"alternative-id":["e26070569"],"URL":"https:\/\/doi.org\/10.3390\/e26070569","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,30]]}}}