{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T18:01:45Z","timestamp":1767895305619,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T00:00:00Z","timestamp":1720396800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62002249"],"award-info":[{"award-number":["62002249"]}]},{"name":"National Natural Science Foundation of China","award":["A2112"],"award-info":[{"award-number":["A2112"]}]},{"name":"Open Project Program of the State Key Lab of CADCG","award":["62002249"],"award-info":[{"award-number":["62002249"]}]},{"name":"Open Project Program of the State Key Lab of CADCG","award":["A2112"],"award-info":[{"award-number":["A2112"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The controllability of complex networks is a core issue in network research. Assessing the controllability robustness of networks under destructive attacks holds significant practical importance. This paper studies the controllability of networks from the perspective of malicious attacks. A novel attack model is proposed to evaluate and challenge network controllability. This method disrupts network controllability with high precision by identifying and targeting critical candidate nodes. The model is compared with traditional attack methods, including degree-based, betweenness-based, closeness-based, pagerank-based, and hierarchical attacks. Results show that the model outperforms these methods in both disruption effectiveness and computational efficiency. Extensive experiments on both synthetic and real-world networks validate the superior performance of this approach. This study provides valuable insights for identifying key nodes crucial for maintaining network controllability. It also offers a solid framework for enhancing network resilience against malicious attacks.<\/jats:p>","DOI":"10.3390\/e26070580","type":"journal-article","created":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T11:30:02Z","timestamp":1720438202000},"page":"580","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Critical Candidate Node-Based Attack Model of Network Controllability"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-2747-7288","authenticated-orcid":false,"given":"Wenli","family":"Huang","sequence":"first","affiliation":[{"name":"School of Computer Science, Sichuan Normal University, Chengdu 610101, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-6141-6629","authenticated-orcid":false,"given":"Liang","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Computer Science, Sichuan Normal University, Chengdu 610101, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5323-858X","authenticated-orcid":false,"given":"Junli","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Science, Sichuan Normal University, Chengdu 610101, China"},{"name":"Visual Computing and Virtual Reality Key Laboratory of Sichuan, Sichuan Normal University, Chengdu 610068, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,8]]},"reference":[{"key":"ref_1","unstructured":"Barab\u00e1si, A. 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