{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,4]],"date-time":"2025-10-04T08:02:36Z","timestamp":1759564956151,"version":"3.37.3"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,1,19]],"date-time":"2024-01-19T00:00:00Z","timestamp":1705622400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,19]],"date-time":"2024-01-19T00:00:00Z","timestamp":1705622400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[2024,3]]},"DOI":"10.1007\/s00607-023-01244-z","type":"journal-article","created":{"date-parts":[[2024,1,19]],"date-time":"2024-01-19T13:02:19Z","timestamp":1705669339000},"page":"821-864","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quantifying influential nodes in complex networks using optimization and particle dynamics: a comparative study"],"prefix":"10.1007","volume":"106","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8594-7006","authenticated-orcid":false,"given":"Edwin","family":"Montes-Orozco","sequence":"first","affiliation":[]},{"given":"Roman-Anselmo","family":"Mora-Guti\u00e9rrez","sequence":"additional","affiliation":[]},{"given":"Sergio-Gerardo","family":"de-los-Cobos-Silva","sequence":"additional","affiliation":[]},{"given":"Eric-Alfredo","family":"Rinc\u00f3n-Garc\u00eda","sequence":"additional","affiliation":[]},{"given":"Miguel-\u00c1ngel","family":"Guti\u00e9rrez-Andrade","sequence":"additional","affiliation":[]},{"given":"Pedro","family":"Lara-Vel\u00e1zquez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,1,19]]},"reference":[{"key":"1244_CR1","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1016\/j.physa.2016.08.067","volume":"465","author":"W-B Du","year":"2017","unstructured":"Du W-B, Liang B-Y, Hong C, Lordan O (2017) Analysis of the chinese provincial air transportation network. Phys A Statist Mechan Appl 465:579\u2013586","journal-title":"Phys A Statist Mechan Appl"},{"key":"1244_CR2","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1016\/j.physa.2016.03.033","volume":"457","author":"J-H Liu","year":"2016","unstructured":"Liu J-H, Wang J, Shao J, Zhou T (2016) Online social activity reflects economic status. Phys A Statist Mechan Appl 457:581\u2013589","journal-title":"Phys A Statist Mechan Appl"},{"issue":"4","key":"1244_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12043-019-1748-9","volume":"92","author":"Y Wang","year":"2019","unstructured":"Wang Y, Wang S, Deng Y (2019) A modified efficiency centrality to identify influential nodes in weighted networks. Pramana 92(4):1\u201311","journal-title":"Pramana"},{"issue":"10","key":"1244_CR4","doi-asserted-by":"publisher","first-page":"2196","DOI":"10.1109\/TIFS.2015.2451073","volume":"10","author":"M Alzaabi","year":"2015","unstructured":"Alzaabi M, Taha K, Martin TA (2015) Cisri: a crime investigation system using the relative importance of information spreaders in networks depicting criminals communications. IEEE Trans Informat Forens Secu 10(10):2196\u20132211","journal-title":"IEEE Trans Informat Forens Secu"},{"issue":"2","key":"1244_CR5","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1109\/TCBB.2014.2361350","volume":"12","author":"M Li","year":"2015","unstructured":"Li M, Lu Y, Wang J, Wu F-X, Pan Y (2015) A topology potential-based method for identifying essential proteins from ppi networks. IEEE\/ACM Trans Computat Biol Bioinform (TCBB) 12(2):372\u2013383","journal-title":"IEEE\/ACM Trans Computat Biol Bioinform (TCBB)"},{"issue":"6","key":"1244_CR6","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0131418","volume":"10","author":"J Luo","year":"2015","unstructured":"Luo J, Qi Y (2015) Identification of essential proteins based on a new combination of local interaction density and protein complexes. PloS one 10(6):e0131418","journal-title":"PloS one"},{"key":"1244_CR7","first-page":"1","volume":"5","author":"Y Liu","year":"2015","unstructured":"Liu Y, Tang M, Zhou T, Do Y (2015) Core-like groups result in invalidation of identifying super-spreader by k-shell decomposition. Sci Rep 5:1\u201321","journal-title":"Sci Rep"},{"key":"1244_CR8","first-page":"1","volume":"650","author":"L Lu","year":"2016","unstructured":"Lu L, Chen D, Ren X-L, Zhang Q-M, Zhang Y-C, Zhou T (2016) Vital nodes identification in complex networks. Phys Rep Rev Sect Phys Lett 650:1\u201363","journal-title":"Phys Rep Rev Sect Phys Lett"},{"issue":"2","key":"1244_CR9","first-page":"1","volume":"64","author":"S Xiao-Ping","year":"2015","unstructured":"Xiao-Ping S, Yu-Rong S (2015) Leveraging neighborhood \u201cstructural holes\u2019\u2019 to identifying key spreaders in social networks. Acta phys Sin 64(2):1\u201312","journal-title":"Acta phys Sin"},{"issue":"5","key":"1244_CR10","first-page":"1","volume":"64","author":"H Zhong-Ming","year":"2015","unstructured":"Zhong-Ming H, Yang W, Xu-Sheng T, Da-Gao D, Wei-Jie Y (2015) Ranking key nodes in complex networks by considering structural holes. Acta Phys Sin 64(5):1\u201310","journal-title":"Acta Phys Sin"},{"key":"1244_CR11","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.physa.2014.02.041","volume":"404","author":"Q Li","year":"2014","unstructured":"Li Q, Zhou T, L\u00fc L, Chen D (2014) Identifying influential spreaders by weighted leaderrank. Phys A Statist Mechan Appl 404:47\u201355","journal-title":"Phys A Statist Mechan Appl"},{"key":"1244_CR12","doi-asserted-by":"crossref","unstructured":"Wahid-Ul-Ashraf A, Budka M, Musial-Gabrys K (2017) Newton\u2019s gravitational law for link prediction in social networks, in International Workshop on Complex Networks and their Applications, pp.\u00a093\u2013104, Springer","DOI":"10.1007\/978-3-319-72150-7_8"},{"key":"1244_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2019.105464","volume":"193","author":"F Liu","year":"2020","unstructured":"Liu F, Wang Z, Deng Y (2020) Gmm: a generalized mechanics model for identifying the importance of nodes in complex networks. Knowl Based Syst 193:105464","journal-title":"Knowl Based Syst"},{"key":"1244_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2020.105717","volume":"195","author":"T Wen","year":"2020","unstructured":"Wen T, Pelusi D, Deng Y (2020) Vital spreaders identification in complex networks with multi-local dimension. Knowl Based Syst 195:105717","journal-title":"Knowl Based Syst"},{"issue":"2","key":"1244_CR15","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1080\/09540091.2020.1806203","volume":"33","author":"J Zhao","year":"2021","unstructured":"Zhao J, Song Y, Liu F, Deng Y (2021) The identification of influential nodes based on structure similarity. Connect Sci 33(2):201\u2013218","journal-title":"Connect Sci"},{"issue":"2","key":"1244_CR16","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1007\/s00500-016-2335-3","volume":"22","author":"L Yang","year":"2018","unstructured":"Yang L, Qiao Y, Liu Z, Ma J, Li X (2018) Identifying opinion leader nodes in online social networks with a new closeness evaluation algorithm. Soft Comput 22(2):453\u2013464","journal-title":"Soft Comput"},{"key":"1244_CR17","doi-asserted-by":"publisher","first-page":"122874","DOI":"10.1109\/ACCESS.2020.3007726","volume":"8","author":"E Montes-Orozco","year":"2020","unstructured":"Montes-Orozco E, Mora-Gutierrez R-A, De-Los-Cobos-Silva S-G, Rinc\u00f3n-Garc\u00eda E-A, Torres-Cockrell G-S, Ju\u00e1rez-G\u00f3mez J, Obreg\u00f3n-Quintana B, Lara-Vel\u00e1zquez P, Gutierrez-Andrade M-A (2020) Identification of covid-19 spreaders using multiplex networks approach. IEEE Access 8:122874\u2013122883","journal-title":"IEEE Access"},{"issue":"6","key":"1244_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRevE.93.062314","volume":"93","author":"F Radicchi","year":"2016","unstructured":"Radicchi F, Castellano C (2016) Leveraging percolation theory to single out influential spreaders in networks. Phys Rev E 93(6):1\u201318","journal-title":"Phys Rev E"},{"key":"1244_CR19","doi-asserted-by":"publisher","first-page":"1044","DOI":"10.1016\/j.physa.2018.08.135","volume":"512","author":"L Fei","year":"2018","unstructured":"Fei L, Zhang Q, Deng Y (2018) Identifying influential nodes in complex networks based on the inverse-square law. Phys A Statist Mechan Appl 512:1044\u20131059","journal-title":"Phys A Statist Mechan Appl"},{"issue":"7563","key":"1244_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/nature14604","volume":"524","author":"F Morone","year":"2015","unstructured":"Morone F, Makse HA (2015) Influence maximization in complex networks through optimal percolation. Nature 524(7563):1\u201365","journal-title":"Nature"},{"key":"1244_CR21","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/j.ins.2021.01.053","volume":"577","author":"Q Shang","year":"2021","unstructured":"Shang Q, Deng Y, Cheong KH (2021) Identifying influential nodes in complex networks: effective distance gravity model. Informat Sci 577:162\u2013179","journal-title":"Informat Sci"},{"key":"1244_CR22","doi-asserted-by":"crossref","unstructured":"Chen W, Lin T, Tan Z, Zhao M, Zhou X (2016) Robust influence maximization. In: proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, pp.\u00a0795\u2013804","DOI":"10.1145\/2939672.2939745"},{"issue":"12","key":"1244_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pone.0145283","volume":"10","author":"J-L He","year":"2015","unstructured":"He J-L, Fu Y, Chen D-B (2015) A novel top-k strategy for influence maximization in complex networks with community structure. PloS one 10(12):1\u201310","journal-title":"PloS one"},{"issue":"6","key":"1244_CR24","first-page":"1","volume":"108","author":"X-Y Zhao","year":"2015","unstructured":"Zhao X-Y, Huang B, Tang M, Zhang H-F, Chen D-B (2015) Identifying effective multiple spreaders by coloring complex networks. EPL (Europhys Lett) 108(6):1\u20136","journal-title":"EPL (Europhys Lett)"},{"key":"1244_CR25","first-page":"1","volume":"1","author":"W Lin","year":"2021","unstructured":"Lin W, Wandelt S, Sun X (2021) Efficient network dismantling through genetic algorithms. Soft Comput 1:1\u201319","journal-title":"Soft Comput"},{"issue":"13","key":"1244_CR26","doi-asserted-by":"publisher","first-page":"8223","DOI":"10.1007\/s00500-021-05749-7","volume":"25","author":"L Han","year":"2021","unstructured":"Han L, Li K-C, Castiglione A, Tang J, Huang H, Zhou Q (2021) A clique-based discrete bat algorithm for influence maximization in identifying top-k influential nodes of social networks. Soft Comput 25(13):8223\u20138240","journal-title":"Soft Comput"},{"issue":"1","key":"1244_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1088\/0022-3719\/12\/1\/008","volume":"12","author":"J Chalupa","year":"1979","unstructured":"Chalupa J, Leath PL, Reich GR (1979) Bootstrap percolation on a bethe lattice. J Phys C Solid State Phys 12(1):1\u201331","journal-title":"J Phys C Solid State Phys"},{"key":"1244_CR28","first-page":"1","volume":"5","author":"J Gao","year":"2015","unstructured":"Gao J, Zhou T, Hu Y (2015) Bootstrap percolation on spatial networks. Sci Rep 5:1\u201310","journal-title":"Sci Rep"},{"key":"1244_CR29","doi-asserted-by":"crossref","unstructured":"Montes-Orozco E, Mora-Guti\u00e9rrez RA, Obreg\u00f3n-Quintana B, de-los Cobos-Silva SG, Rinc\u00f3n-Garc\u00eda EA, Guti\u00e9rrez-Andrade MA, Lara-Vel\u00e1zquez P (2020) Methodology to quantify the robustness in complex networks, Computing, vol.\u00a0Acepted, no.\u00a0\u2013, pp.\u00a01\u201325","DOI":"10.1155\/2020\/8796360"},{"key":"1244_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2020.113681","volume":"161","author":"G Maji","year":"2020","unstructured":"Maji G, Mandal S, Sen S (2020) A systematic survey on influential spreaders identification in complex networks with a focus on k-shell based techniques. Expert Syst Appl 161:113681","journal-title":"Expert Syst Appl"},{"issue":"27","key":"1244_CR31","doi-asserted-by":"publisher","first-page":"11150","DOI":"10.1073\/pnas.0701175104","volume":"104","author":"S Carmi","year":"2007","unstructured":"Carmi S, Havlin S, Kirkpatrick S, Shavitt Y, Shir E (2007) A model of internet topology using k-shell decomposition. Proc National Acad Sci 104(27):11150\u201311154","journal-title":"Proc National Acad Sci"},{"issue":"7\u20138","key":"1244_CR32","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1016\/j.physleta.2015.12.031","volume":"380","author":"L Guo","year":"2016","unstructured":"Guo L, Lin J-H, Guo Q, Liu J-G (2016) Identifying multiple influential spreaders in term of the distance-based coloring. Phys Lett A 380(7\u20138):837\u2013842","journal-title":"Phys Lett A"},{"issue":"12","key":"1244_CR33","doi-asserted-by":"publisher","first-page":"1850142","DOI":"10.1142\/S0217979218501424","volume":"32","author":"K Berahmand","year":"2018","unstructured":"Berahmand K, Samadi N, Sheikholeslami SM (2018) Effect of rich-club on diffusion in complex networks. Int J Modern Phys B 32(12):1850142","journal-title":"Int J Modern Phys B"},{"key":"1244_CR34","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/j.chaos.2018.03.014","volume":"110","author":"K Berahmand","year":"2018","unstructured":"Berahmand K, Bouyer A, Samadi N (2018) A new centrality measure based on the negative and positive effects of clustering coefficient for identifying influential spreaders in complex networks. Chaos Solitons Fractals 110:41\u201354","journal-title":"Chaos Solitons Fractals"},{"key":"1244_CR35","doi-asserted-by":"publisher","first-page":"1711","DOI":"10.1007\/s00607-018-0684-8","volume":"101","author":"K Berahmand","year":"2019","unstructured":"Berahmand K, Bouyer A, Samadi N (2019) A new local and multidimensional ranking measure to detect spreaders in social networks. Computing 101:1711\u20131733","journal-title":"Computing"},{"issue":"4","key":"1244_CR36","doi-asserted-by":"publisher","DOI":"10.1063\/1.5030894","volume":"28","author":"T Bian","year":"2018","unstructured":"Bian T, Deng Y (2018) Identifying influential nodes in complex networks: a node information dimension approach. Chaos Interdiscipl J Nonlinear Sci 28(4):043109","journal-title":"Chaos Interdiscipl J Nonlinear Sci"},{"key":"1244_CR37","unstructured":"Freeman SC, Freeman LC (1979) The networkers network: A study of the impact of a new communications medium on sociometric structure. School of Social Sciences University of Calif.,"},{"issue":"04","key":"1244_CR38","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1142\/S0219525903001067","volume":"6","author":"PM Gleiser","year":"2003","unstructured":"Gleiser PM, Danon L (2003) Community structure in jazz. Adv Complex Syst 6(04):565\u2013573","journal-title":"Adv Complex Syst"},{"issue":"4","key":"1244_CR39","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1038\/nphys560","volume":"3","author":"V Colizza","year":"2007","unstructured":"Colizza V, Pastor-Satorras R, Vespignani A (2007) Reaction-diffusion processes and metapopulation models in heterogeneous networks. Nature Phys 3(4):276\u2013282","journal-title":"Nature Phys"},{"key":"1244_CR40","doi-asserted-by":"crossref","unstructured":"Montes-Orozco E, Mora-Guti\u00e9rrez R-A, De-los Cobos-Silva S-G, Rinc\u00f3n-Garc\u00eda EA, Guti\u00e9rrez-Andrade MA, Lara-Vel\u00e1zquez P (2022) Analysis and characterization of the spread of covid-19 in mexico through complex networks and optimization approaches, Complexity, vol.\u00a02022","DOI":"10.1155\/2022\/2951744"},{"issue":"3","key":"1244_CR41","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1103\/PhysRevE.69.036103","volume":"69","author":"M Kaiser","year":"2004","unstructured":"Kaiser M, Hilgetag CC (2004) Spatial growth of real-world networks. Phys Rev E 69(3):36\u2013103","journal-title":"Phys Rev E"},{"issue":"6684","key":"1244_CR42","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1038\/30918","volume":"393","author":"DJ Watts","year":"1998","unstructured":"Watts DJ, Strogatz SH (1998) Collective dynamics of \u2018small-world\u2019 networks. Nature 393(6684):440","journal-title":"Nature"},{"issue":"1","key":"1244_CR43","first-page":"17","volume":"5","author":"P Erdos","year":"1960","unstructured":"Erdos P, R\u00e9nyi A (1960) On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5(1):17\u201360","journal-title":"Publ Math Inst Hung Acad Sci"},{"issue":"1","key":"1244_CR44","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1103\/RevModPhys.74.47","volume":"74","author":"R Albert","year":"2002","unstructured":"Albert R, Barab\u00e1si A-L (2002) Statistical mechanics of complex networks. Rev Modern Phys 74(1):47","journal-title":"Rev Modern Phys"},{"issue":"5","key":"1244_CR45","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1038\/scientificamerican0503-60","volume":"288","author":"A-L Barab\u00e1si","year":"2003","unstructured":"Barab\u00e1si A-L, Bonabeau E (2003) Scale-free networks. Sci Am 288(5):60\u201369","journal-title":"Sci Am"},{"key":"1244_CR46","unstructured":"U.\u00a0ExECUM-Estudio Comparativo\u00a0de Universidades., \u201cDirecci\u00f3n general de evaluaci\u00f3n institucional,\u201d UNAM: http:\/\/www.execum.unam.mx, (2020)"},{"key":"1244_CR47","unstructured":"Unit QI (2020) Qs university rankings. international indicators.,"},{"key":"1244_CR48","unstructured":"Optimization G (2017) Gurobi optimizer version 7.0. 2,"},{"issue":"4","key":"1244_CR49","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1023\/A:1008202821328","volume":"11","author":"R Storn","year":"1997","unstructured":"Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Global Opt 11(4):341\u2013359","journal-title":"J Global Opt"},{"key":"1244_CR50","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/j.jocs.2017.08.014","volume":"22","author":"FD Sahneh","year":"2017","unstructured":"Sahneh FD, Vajdi A, Shakeri H, Fan F, Scoglio C (2017) Gemfsim: a stochastic simulator for the generalized epidemic modeling framework. J Computat Sci 22:36\u201344","journal-title":"J Computat Sci"}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00607-023-01244-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00607-023-01244-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00607-023-01244-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,2]],"date-time":"2024-03-02T14:07:21Z","timestamp":1709388441000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00607-023-01244-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,19]]},"references-count":50,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["1244"],"URL":"https:\/\/doi.org\/10.1007\/s00607-023-01244-z","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"type":"print","value":"0010-485X"},{"type":"electronic","value":"1436-5057"}],"subject":[],"published":{"date-parts":[[2024,1,19]]},"assertion":[{"value":"24 April 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 December 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have not conflicts of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}