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Driver nodes are typically selected sequentially, and greedy optimization serves as the standard benchmark for such sequential methods since it produces near-optimal node sets. However, this level of accuracy comes at a computational cost that becomes prohibitive for large networks. In this work, we propose a second-order perturbation framework that overcomes this limitation by estimating the shift in the smallest eigenvalue of the network Laplacian, the quantity that governs the stability of the pinned network, using second-order perturbation theory. Consequently, the proposed method reduces the computational complexity of driver-node selection from O(N5) in conventional greedy schemes to O(N4), enabling efficient and scalable selection in large-scale networks. Extensive simulations across diverse network topologies, including small-world, scale-free, and random networks, demonstrate that the proposed method consistently outperforms standard centrality-based heuristics. It achieves performance comparable to optimal greedy benchmarks, while offering substantially higher computational efficiency. The proposed framework thus provides a practical and scalable solution for the control of large complex networks, and more broadly, demonstrates the utility of higher-order perturbation analysis for node-ranking problems in network controllability.<\/jats:p>","DOI":"10.1063\/5.0351619","type":"journal-article","created":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T12:58:38Z","timestamp":1790600318000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Efficient driver-node selection for pinning control via second-order perturbations"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-9083-5966","authenticated-orcid":false,"given":"Fatemeh","family":"Ghoreishian Amiri","sequence":"first","affiliation":[{"name":"Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic) 1 , Tehran,","place":["Iran"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2664-9006","authenticated-orcid":false,"given":"Fahimeh","family":"Nazarimehr","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic) 1 , Tehran,","place":["Iran"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6845-7539","authenticated-orcid":false,"given":"Sajad","family":"Jafari","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic) 1 , Tehran,","place":["Iran"]},{"name":"Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic) 2 , Tehran,","place":["Iran"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3087-541X","authenticated-orcid":false,"given":"Matja\u017e","family":"Perc","sequence":"additional","affiliation":[{"name":"Faculty of Natural Sciences and Mathematics, University of Maribor 3 , Koro\u0161ka cesta 160, 2000 Maribor,","place":["Slovenia"]},{"name":"Community Healthcare Center Dr. Adolf Drolc Maribor 4 , Ulica talcev 9, 2000 Maribor,","place":["Slovenia"]},{"name":"Department of Physics, Kyung Hee University 5 , 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447,","place":["Republic of Korea"]},{"name":"University College, Korea University 6 , 145 Anam-ro, Seongbuk-gu, Seoul 02841,","place":["Republic of Korea"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,28]]},"reference":[{"key":"2026092808583322600_c1","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1038\/nature10011","article-title":"Controllability of complex networks","volume":"473","year":"2011","journal-title":"Nature"},{"key":"2026092808583322600_c2","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1038\/nphys3422","article-title":"Spectrum of controlling and observing complex networks","volume":"11","year":"2015","journal-title":"Nat. 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