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Moreover, their generalization capability across different network types is often weak, leading to low accuracy in identifying key nodes. To solve these limitations, this paper has proposed an adaptive multi-scale hierarchical method for key nodes identification in complex networks, called AdaMH. First, a hierarchical structural influence framework is constructed by integrating local, semi-local, and global topological scales. Second, an adaptive entropy weight allocation strategy based on information entropy is employed to achieve robust fusion of multi-scale structural features. Finally, extensive comparative analysis experiments are conducted on nine real-world datasets against five well-known baseline methods. Experimental results under the SIR spreading model prove that the top-10 nodes identified by AdaMH increase the final infection range by 1% to 156% compared with baseline methods. These results indicate that AdaMH effectively captures synergistic relations among multi-scale structural features, thereby providing an efficient identification of key nodes. In addition, the proposed method can also be applied in the field of fraudulent node mining.<\/jats:p>","DOI":"10.1063\/5.0348978","type":"journal-article","created":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T12:49:59Z","timestamp":1791377399000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Adaptive multi-scale hierarchical method for complex network key nodes identification"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8619-0356","authenticated-orcid":false,"given":"Xiaoyang","family":"Liu","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, Chongqing University of Technology 1 , Chongqing 400054,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-8087-5174","authenticated-orcid":false,"given":"Wanqian","family":"Zhang","sequence":"additional","affiliation":[{"name":"Faculty of Computer Engineering and Information Technology, Azarbaijan Shahid Madani University 2 , Tabriz,","place":["Iran"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4808-2856","authenticated-orcid":false,"given":"Asgarali","family":"Bouyer","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and Natural Science, Istinye University 3 , Istanbul,","place":["Turkey"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6166-2118","authenticated-orcid":false,"given":"Na","family":"Zhao","sequence":"additional","affiliation":[{"name":"National Pilot School of Software, Yunnan University 4 , Kunming 650500,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2953-2313","authenticated-orcid":false,"given":"Xiaofang","family":"Xia","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Xidian University 5 , Xi'an 710126,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9124-4921","authenticated-orcid":false,"given":"Hocine","family":"Cherifi","sequence":"additional","affiliation":[{"name":"Lab of Interdisciplinary Carnot de Bourgogne, University of Burgundy 6 , Dijon,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,7]]},"reference":[{"key":"2026100708495369200_c1","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1038\/nature14604","volume":"524","year":"2015","journal-title":"Nature"},{"key":"2026100708495369200_c2","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1038\/s41586-022-05543-x","volume":"613","year":"2023","journal-title":"Nature"},{"key":"2026100708495369200_c3","doi-asserted-by":"publisher","first-page":"110054","DOI":"10.1016\/j.ress.2024.110054","volume":"246","year":"2024","journal-title":"Reliab. 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