{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T02:23:32Z","timestamp":1775096612653,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,10,31]],"date-time":"2024-10-31T00:00:00Z","timestamp":1730332800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62066048"],"award-info":[{"award-number":["62066048"]}]},{"name":"National Natural Science Foundation of China","award":["62366057"],"award-info":[{"award-number":["62366057"]}]},{"name":"National Natural Science Foundation of China","award":["202101AT070167"],"award-info":[{"award-number":["202101AT070167"]}]},{"name":"Science Foundation of Yunnan Province","award":["62066048"],"award-info":[{"award-number":["62066048"]}]},{"name":"Science Foundation of Yunnan Province","award":["62366057"],"award-info":[{"award-number":["62366057"]}]},{"name":"Science Foundation of Yunnan Province","award":["202101AT070167"],"award-info":[{"award-number":["202101AT070167"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Identifying critical edges in complex networks is a fundamental challenge in the study of complex networks. Traditional approaches tend to rely solely on either global information or local information. However, this dependence on a single information source fails to capture the multi-layered complexity of critical edges, often resulting in incomplete or inaccurate identification. Therefore, it is essential to develop a method that integrates multiple sources of information to enhance critical edge identification and provide a deeper understanding and optimization of the structure and function of complex networks. In this paper, we introduce a Global\u2013Local Hybrid Centrality method which integrates a second-order neighborhood index, a first-order neighborhood index, and an edge betweenness index, thus combining both local and global perspectives. We further employ the edge percolation process to evaluate the significance of edges in maintaining network connectivity. Experimental results on various real-world complex network datasets demonstrate that the proposed method significantly improves the accuracy of critical edge identification, providing theoretical and methodological support for the analysis and optimization of complex networks.<\/jats:p>","DOI":"10.3390\/e26110933","type":"journal-article","created":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T13:09:27Z","timestamp":1730466567000},"page":"933","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Synergistic Integration of Local and Global Information for Critical Edge Identification"],"prefix":"10.3390","volume":"26","author":[{"given":"Na","family":"Zhao","sequence":"first","affiliation":[{"name":"Key Laboratory in Software Engineering of Yunnan Province, Yunnan University, Kunming 650091, China"},{"name":"Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 610056, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-7004-7504","authenticated-orcid":false,"given":"Ting","family":"Luo","sequence":"additional","affiliation":[{"name":"Key Laboratory in Software Engineering of Yunnan Province, Yunnan University, Kunming 650091, China"}]},{"given":"Hao","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory in Software Engineering of Yunnan Province, Yunnan University, Kunming 650091, China"}]},{"given":"Shuang-Ping","family":"Yang","sequence":"additional","affiliation":[{"name":"Key Laboratory in Software Engineering of Yunnan Province, Yunnan University, Kunming 650091, China"}]},{"given":"Ni-Fei","family":"Xiong","sequence":"additional","affiliation":[{"name":"Key Laboratory in Software Engineering of Yunnan Province, Yunnan University, Kunming 650091, China"}]},{"given":"Ming","family":"Jing","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence & Information Engineering, West Yunnan University, Lincang 677000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1281-2287","authenticated-orcid":false,"given":"Jian","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650504, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Lei, M., and Wei, D. (2018, January 9\u201311). Identifying influence for community in complex networks. Proceedings of the 2018 Chinese Control and Decision Conference (CCDC), Shenyang, China.","DOI":"10.1109\/CCDC.2018.8408061"},{"key":"ref_2","first-page":"2380909","article-title":"Evaluating the robustness of attributed dynamic bus-metro networks based on community reconstruction","volume":"12","author":"Chen","year":"2024","journal-title":"Transp. B Transp. Dyn."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"107307","DOI":"10.1016\/j.ress.2020.107307","article-title":"Estimation and improvement of transportation network robustness by exploiting communities","volume":"206","author":"Wandelt","year":"2021","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"128848","DOI":"10.1016\/j.physa.2023.128848","article-title":"Effect of transfer costs on traffic dynamics of multimodal transportation networks","volume":"623","author":"Zhang","year":"2023","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ji, Y., He, W., Cheng, S., Kurths, J., and Zhan, M. (2020). Dynamic network characteristics of power-electronics-based power systems. Sci. Rep., 10.","DOI":"10.1038\/s41598-020-66635-0"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"125540","DOI":"10.1016\/j.physa.2020.125540","article-title":"Power network robustness analysis based on electrical engineering and complex network theory","volume":"564","author":"Zhou","year":"2021","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2297860","DOI":"10.1080\/19490976.2023.2297860","article-title":"Multi-omic approaches for host-microbiome data integration","volume":"16","author":"Chetty","year":"2024","journal-title":"Gut Microbes"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1038\/nature14604","article-title":"Influence maximization in complex networks through optimal percolation","volume":"524","author":"Morone","year":"2015","journal-title":"Nature"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"7821","DOI":"10.1073\/pnas.122653799","article-title":"Community structure in social and biological networks","volume":"99","author":"Girvan","year":"2002","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"056109","DOI":"10.1103\/PhysRevE.65.056109","article-title":"Attack vulnerability of complex networks","volume":"65","author":"Holme","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Liu, Y., Tang, M., Zhou, T., and Do, Y. (2015). Improving the accuracy of the k-shell method by removing redundant links: From a perspective of spreading dynamics. Sci. Rep., 5.","DOI":"10.1038\/srep13172"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7332","DOI":"10.1073\/pnas.0610245104","article-title":"Structure and tie strengths in mobile communication networks","volume":"104","author":"Onnela","year":"2007","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"P10011","DOI":"10.1088\/1742-5468\/2010\/10\/P10011","article-title":"Bridgeness: A local index on edge significance in maintaining global connectivity","volume":"2010","author":"Cheng","year":"2010","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"123877","DOI":"10.1016\/j.physa.2019.123877","article-title":"Identifying significant edges via neighborhood information","volume":"548","author":"Zhao","year":"2020","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Yu, E.Y., Chen, D.B., and Zhao, J.Y. (2018). Identifying critical edges in complex networks. Sci. Rep., 8.","DOI":"10.1038\/s41598-018-32631-8"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1109\/JSYST.2023.3327089","article-title":"Novel Approach to Edge Importance Ranking: Balancing Network Structure and Transmission Performance","volume":"18","author":"Chen","year":"2023","journal-title":"IEEE Syst. J."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"L\u00fc, L., Zhang, Y.-C., Yeung, C.H., and Zhou, T. (2011). Leaders in social networks, the delicious case. PLoS ONE, 6.","DOI":"10.1371\/journal.pone.0021202"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.knosys.2012.01.007","article-title":"A novel measure of edge centrality in social networks","volume":"30","author":"Ferrara","year":"2012","journal-title":"Knowl. Based Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1140\/epjds\/s13688-018-0162-8","article-title":"Link transmission centrality in large-scale social networks","volume":"7","author":"Zhang","year":"2018","journal-title":"EPJ Data Sci."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Hu, Q., Gao, Y., Ma, P., Yin, Y., Zhang, Y., and Xing, C. (2013, January 14\u201316). A new approach to identify influential spreaders in complex networks. Proceedings of the International Conference on Web-Age Information Management, Beidaihe, China.","DOI":"10.1007\/978-3-642-38562-9_10"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"195701","DOI":"10.1103\/PhysRevLett.107.195701","article-title":"Robustness of a network of networks","volume":"107","author":"Gao","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"098901","DOI":"10.1088\/1674-1056\/aca6d8","article-title":"Important edge identification in complex networks based on local and global features","volume":"32","author":"Song","year":"2023","journal-title":"Chin. Phys. B"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Rossi, R.A., and Ahmed, N.K. (2015, January 25\u201330). The Network Data Repository with Interactive Graph Analytics and Visualization. Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, Austin, TX, USA. Available online: http:\/\/networkrepository.com.","DOI":"10.1609\/aaai.v29i1.9277"},{"key":"ref_24","first-page":"539","article-title":"Learning to discover social circles in ego networks","volume":"25","author":"Leskovec","year":"2012","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"e57443","DOI":"10.7554\/eLife.57443","article-title":"A connectome and analysis of the adult Drosophila central brain","volume":"9","author":"Scheffer","year":"2020","journal-title":"eLife"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2443","DOI":"10.1093\/nar\/gkg340","article-title":"Topological structure analysis of the protein\u2013protein interaction network in budding yeast","volume":"31","author":"Bu","year":"2003","journal-title":"Nucleic Acids Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2-es","DOI":"10.1145\/1217299.1217301","article-title":"Graph evolution: Densification and shrinking diameters","volume":"Volume 1","author":"Leskovec","year":"2007","journal-title":"ACM Transactions on Knowledge Discovery from Data (TKDD)"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Leskovec, J., Kleinberg, J., and Faloutsos, C. (2005, January 21\u201324). Graphs over time: Densification laws, shrinking diameters and possible explanations. Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining, Chicago, IL, USA.","DOI":"10.1145\/1081870.1081893"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Rozemberczki, B., Davies, R., Sarkar, R., and Sutton, C. (2019, January 27\u201330). Gemsec: Graph embedding with self clustering. Proceedings of the 2019 IEEE\/ACM International Conference on Advances in Social Networks Analysis and Mining, Vancouver, BC, Canada.","DOI":"10.1145\/3341161.3342890"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1038\/35019019","article-title":"Error and attack tolerance of complex networks","volume":"406","author":"Albert","year":"2000","journal-title":"Nature"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5468","DOI":"10.1103\/PhysRevLett.85.5468","article-title":"Network robustness and fragility: Percolation on random graphs","volume":"85","author":"Callaway","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"110163","DOI":"10.1016\/j.knosys.2022.110163","article-title":"Ranking influential spreaders based on both node k-shell and structural hole","volume":"260","author":"Zhao","year":"2023","journal-title":"Knowl.-Based Syst."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Liu, Y., Wang, X., Wang, X., Wang, Z., and Kurths, J. (2023). Diffusion source inference for large-scale complex networks based on network percolation. IEEE Trans. Neural Netw. Learn. Syst.","DOI":"10.1109\/TNNLS.2023.3321767"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3111","DOI":"10.1109\/TNET.2024.3382546","article-title":"Fast Outbreak Sense and Effective Source Inference via Minimum Observer Set","volume":"32","author":"Liu","year":"2024","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1510","DOI":"10.1109\/TIFS.2023.3338423","article-title":"Diffusion containment in complex networks through collective influence of connections","volume":"19","author":"Liu","year":"2023","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"107753","DOI":"10.1016\/j.cnsns.2023.107753","article-title":"Efficient approaches for attaining epidemic-free networks with minimum edge removal set","volume":"130","author":"Liu","year":"2024","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"20230625","DOI":"10.1098\/rsif.2023.0625","article-title":"Individual-centralized seeding strategy for influence maximization in information-limited networks","volume":"21","author":"Liu","year":"2024","journal-title":"J. R. Soc. Interface"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/11\/933\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:25:18Z","timestamp":1760113518000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/11\/933"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,31]]},"references-count":37,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["e26110933"],"URL":"https:\/\/doi.org\/10.3390\/e26110933","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,31]]}}}