{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T08:40:44Z","timestamp":1780476044997,"version":"3.54.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2020,5,25]],"date-time":"2020-05-25T00:00:00Z","timestamp":1590364800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2020,5,25]],"date-time":"2020-05-25T00:00:00Z","timestamp":1590364800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100000002","name":"U.S. Department of Health & Human Services | National Institutes of Health","doi-asserted-by":"publisher","award":["R01AI141529"],"award-info":[{"award-number":["R01AI141529"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"U.S. Department of Health & Human Services | National Institutes of Health","doi-asserted-by":"publisher","award":["R01HD093761"],"award-info":[{"award-number":["R01HD093761"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"U.S. Department of Health & Human Services | National Institutes of Health","doi-asserted-by":"publisher","award":["UH3OD023268"],"award-info":[{"award-number":["UH3OD023268"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"U.S. Department of Health & Human Services | National Institutes of Health","doi-asserted-by":"publisher","award":["U19AI095219"],"award-info":[{"award-number":["U19AI095219"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"name":"U.S. Department of Health & Human Services | National Institutes of Health"},{"name":"U.S. Department of Health & Human Services | National Institutes of Health"},{"name":"U.S. Department of Health & Human Services | National Institutes of Health"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Mach Intell"],"DOI":"10.1038\/s42256-020-0177-2","type":"journal-article","created":{"date-parts":[[2020,5,25]],"date-time":"2020-05-25T16:02:35Z","timestamp":1590422555000},"page":"317-324","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":370,"title":["Finding key players in complex networks through deep reinforcement learning"],"prefix":"10.1038","volume":"2","author":[{"given":"Changjun","family":"Fan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1812-6843","authenticated-orcid":false,"given":"Yizhou","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2728-4907","authenticated-orcid":false,"given":"Yang-Yu","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,5,25]]},"reference":[{"key":"177_CR1","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. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47 (2002).","journal-title":"Rev. Mod. Phys."},{"key":"177_CR2","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1137\/S003614450342480","volume":"45","author":"ME Newman","year":"2003","unstructured":"Newman, M. E. The structure and function of complex networks. SIAM Rev. 45, 167\u2013256 (2003).","journal-title":"SIAM Rev."},{"key":"177_CR3","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1038\/nature14604","volume":"524","author":"F Morone","year":"2015","unstructured":"Morone, F. & Makse, H. A. Influence maximization in complex networks through optimal percolation. Nature 524, 65\u201368 (2015).","journal-title":"Nature"},{"key":"177_CR4","doi-asserted-by":"crossref","unstructured":"Kempe, D., Kleinberg, J. & Tardos, \u00c9. Influential nodes in a diffusion model for social networks. In International Colloquium on Automata, Languages and Programming 1127\u20131138 (Springer, 2005).","DOI":"10.1007\/11523468_91"},{"key":"177_CR5","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/0167-6377(82)90020-7","volume":"1","author":"H Corley","year":"1982","unstructured":"Corley, H. & David, Y. S. Most vital links and nodes in weighted networks. Oper. Res. Lett. 1, 157\u2013160 (1982).","journal-title":"Oper. Res. Lett."},{"key":"177_CR6","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s10588-006-7084-x","volume":"12","author":"SP Borgatti","year":"2006","unstructured":"Borgatti, S. P. Identifying sets of key players in a social network. Comput. Math. Org. Theory 12, 21\u201334 (2006).","journal-title":"Comput. Math. Org. Theory"},{"key":"177_CR7","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.cosrev.2018.02.002","volume":"28","author":"M Lalou","year":"2018","unstructured":"Lalou, M., Tahraoui, M. A. & Kheddouci, H. The critical node detection problem in networks: a survey. Comput. Sci. Rev. 28, 92\u2013117 (2018).","journal-title":"Comput. Sci. Rev."},{"key":"177_CR8","doi-asserted-by":"publisher","first-page":"2193","DOI":"10.1016\/j.cor.2008.08.016","volume":"36","author":"A Arulselvan","year":"2009","unstructured":"Arulselvan, A., Commander, C. W., Elefteriadou, L. & Pardalos, P. M. Detecting critical nodes in sparse graphs. Comput. Oper. Res. 36, 2193\u20132200 (2009).","journal-title":"Comput. Oper. Res."},{"key":"177_CR9","doi-asserted-by":"publisher","first-page":"1078","DOI":"10.1126\/science.257.5073.1078","volume":"257","author":"ID Kuntz","year":"1992","unstructured":"Kuntz, I. D. Structure-based strategies for drug design and discovery. Science 257, 1078\u20131082 (1992).","journal-title":"Science"},{"key":"177_CR10","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s10898-010-9603-z","volume":"51","author":"B Vitoriano","year":"2011","unstructured":"Vitoriano, B., Ortu\u00f1o, M. T., Tirado, G. & Montero, J. A multi-criteria optimization model for humanitarian aid distribution. J. Global Optim. 51, 189\u2013208 (2011).","journal-title":"J. Global Optim."},{"key":"177_CR11","doi-asserted-by":"crossref","unstructured":"Kempe, D., Kleinberg, J. & Tardos, \u00c9. Maximizing the spread of influence through a social network. In Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 137\u2013146 (ACM, 2003).","DOI":"10.1145\/956750.956769"},{"key":"177_CR12","doi-asserted-by":"publisher","first-page":"3200","DOI":"10.1103\/PhysRevLett.86.3200","volume":"86","author":"R Pastor-Satorras","year":"2001","unstructured":"Pastor-Satorras, R. & Vespignani, A. Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200 (2001).","journal-title":"Phys. Rev. Lett."},{"key":"177_CR13","doi-asserted-by":"publisher","first-page":"3682","DOI":"10.1103\/PhysRevLett.86.3682","volume":"86","author":"R Cohen","year":"2001","unstructured":"Cohen, R., Erez, K., Ben-Avraham, D. & Havlin, S. Breakdown of the internet under intentional attack. Phys. Rev. Lett. 86, 3682 (2001).","journal-title":"Phys. Rev. Lett."},{"key":"177_CR14","doi-asserted-by":"publisher","first-page":"12368","DOI":"10.1073\/pnas.1605083113","volume":"113","author":"A Braunstein","year":"2016","unstructured":"Braunstein, A., Dall\u2019Asta, L., Semerjian, G. & Zdeborov\u00e1, L. Network dismantling. Proc. Natl Acad. Sci. USA 113, 12368\u201312373 (2016).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"177_CR15","doi-asserted-by":"publisher","first-page":"963","DOI":"10.1109\/TNET.2012.2215882","volume":"21","author":"Y Shen","year":"2013","unstructured":"Shen, Y., Nguyen, N. P., Xuan, Y. & Thai, M. T. On the discovery of critical links and nodes for assessing network vulnerability. IEEE\/ACM Trans. Netw. 21, 963\u2013973 (2013).","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"177_CR16","doi-asserted-by":"publisher","first-page":"012305","DOI":"10.1103\/PhysRevE.94.012305","volume":"94","author":"S Mugisha","year":"2016","unstructured":"Mugisha, S. & Zhou, H.-J. Identifying optimal targets of network attack by belief propagation. Phys. Rev. E 94, 012305 (2016).","journal-title":"Phys. Rev. E"},{"key":"177_CR17","doi-asserted-by":"publisher","DOI":"10.1038\/srep37954","volume":"6","author":"L Zdeborov\u00e1","year":"2016","unstructured":"Zdeborov\u00e1, L., Zhang, P. & Zhou, H.-J. Fast and simple decycling and dismantling of networks. Sci. Rep. 6, 37954 (2016).","journal-title":"Sci. Rep."},{"key":"177_CR18","doi-asserted-by":"publisher","first-page":"6554","DOI":"10.1073\/pnas.1806108116","volume":"116","author":"X-L Ren","year":"2019","unstructured":"Ren, X.-L., Gleinig, N., Helbing, D. & Antulov-Fantulin, N. Generalized network dismantling. Proc. Natl Acad. Sci. USA 116, 6554\u20136559 (2019).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"177_CR19","unstructured":"Khalil, E., Dai, H., Zhang, Y., Dilkina, B. & Song, L. Learning combinatorial optimization algorithms over graphs. In Advances in Neural Information Processing Systems 6348\u20136358 (NIPS, 2017)."},{"key":"177_CR20","unstructured":"Nazari, M., Oroojlooy, A., Snyder, L. & Tak\u00e1c, M. Reinforcement learning for solving the vehicle routing problem. In Advances in Neural Information Processing Systems 9839\u20139849 (NIPS, 2018)."},{"key":"177_CR21","unstructured":"Bello, I., Pham, H., Le, Q. V., Norouzi, M. & Bengio, S. Neural combinatorial optimization with reinforcement learning. Preprint at https:\/\/arxiv.org\/abs\/1611.09940 (2016)."},{"key":"177_CR22","unstructured":"Bengio, Y., Lodi, A. & Prouvost, A. Machine learning for combinatorial optimization: a methodological tour d\u2019horizon. Preprint at https:\/\/arxiv.org\/abs\/1811.06128 (2018)."},{"key":"177_CR23","unstructured":"James, J., Yu, W. & Gu, J. Online vehicle routing with neural combinatorial optimization and deep reinforcement learning. In IEEE Transactions on Intelligent Transportation Systems 1\u201312 (IEEE, 2019)."},{"key":"177_CR24","unstructured":"Li, Z., Chen, Q. & Koltun, V. Combinatorial optimization with graph convolutional networks and guided tree search. In Advances in Neural Information Processing Systems 539\u2013548 (NIPS, 2018)."},{"key":"177_CR25","unstructured":"Hamilton, W., Ying, Z. & Leskovec, J. Inductive representation learning on large graphs. In Advances in Neural Information Processing Systems 1024\u20131034 (NIPS, 2017)."},{"key":"177_CR26","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1126\/science.aao1733","volume":"359","author":"N Brown","year":"2018","unstructured":"Brown, N. & Sandholm, T. Superhuman AI for heads-up no-limit poker: Libratus beats top professionals. Science 359, 418\u2013424 (2018).","journal-title":"Science"},{"key":"177_CR27","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1038\/nature24270","volume":"550","author":"D Silver","year":"2017","unstructured":"Silver, D. et al. Mastering the game of go without human knowledge. Nature 550, 354\u2013359 (2017).","journal-title":"Nature"},{"key":"177_CR28","doi-asserted-by":"publisher","first-page":"508","DOI":"10.1126\/science.aam6960","volume":"356","author":"M Morav\u010d\u00edk","year":"2017","unstructured":"Morav\u010d\u00edk, M. et al. Deepstack: expert-level artificial intelligence in heads-up no-limit poker. Science 356, 508\u2013513 (2017).","journal-title":"Science"},{"key":"177_CR29","doi-asserted-by":"publisher","first-page":"3838","DOI":"10.1073\/pnas.1009440108","volume":"108","author":"CM Schneider","year":"2011","unstructured":"Schneider, C. M., Moreira, A. A., Andrade, J. S., Havlin, S. & Herrmann, H. J. Mitigation of malicious attacks on networks. Proc. Natl Acad. Sci. USA 108, 3838\u20133841 (2011).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"177_CR30","doi-asserted-by":"crossref","unstructured":"Henderson, K. et al. Rolx: structural role extraction & mining in large graphs. In Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 1231\u20131239 (ACM, 2012).","DOI":"10.1145\/2339530.2339723"},{"key":"177_CR31","unstructured":"Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks. In Proceedings of the International Conference on Learning Representations (ICLR, 2017)."},{"key":"177_CR32","doi-asserted-by":"publisher","first-page":"e21202","DOI":"10.1371\/journal.pone.0021202","volume":"6","author":"L L\u00fc","year":"2011","unstructured":"L\u00fc, L., Zhang, Y.-C., Yeung, C. H. & Zhou, T. Leaders in social networks, the delicious case. PLoS ONE 6, e21202 (2011).","journal-title":"PLoS ONE"},{"key":"177_CR33","doi-asserted-by":"crossref","unstructured":"Wang, D., Cui, P. & Zhu, W. Structural deep network embedding. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 1225\u20131234 (ACM, 2016).","DOI":"10.1145\/2939672.2939753"},{"key":"177_CR34","doi-asserted-by":"crossref","first-page":"290","DOI":"10.5486\/PMD.1959.6.3-4.12","volume":"6","author":"P Erd\u00f6s","year":"1959","unstructured":"Erd\u00f6s, P. & R\u00e9nyi, A. On random graphs. Publ. Math. Debrecen 6, 290\u2013297 (1959).","journal-title":"Publ. Math. Debrecen"},{"key":"177_CR35","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1038\/30918","volume":"393","author":"DJ Watts","year":"1998","unstructured":"Watts, D. J. & Strogatz, S. H. Collective dynamics of \u2018small-world\u2019 networks. Nature 393, 440\u2013442 (1998).","journal-title":"Nature"},{"key":"177_CR36","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1126\/science.286.5439.509","volume":"286","author":"A-L Barab\u00e1si","year":"1999","unstructured":"Barab\u00e1si, A.-L. & Albert, R. Emergence of scaling in random networks. Science 286, 509\u2013512 (1999).","journal-title":"Science"},{"key":"177_CR37","unstructured":"Barab\u00e1si, A.-L. Network Science (Cambridge Univ. Press, 2016)."},{"key":"177_CR38","doi-asserted-by":"publisher","first-page":"208301","DOI":"10.1103\/PhysRevLett.117.208301","volume":"117","author":"P Clusella","year":"2016","unstructured":"Clusella, P., Grassberger, P., P\u00e9rez-Reche, F. J. & Politi, A. Immunization and targeted destruction of networks using explosive percolation. Phys. Rev. Lett. 117, 208301 (2016).","journal-title":"Phys. Rev. Lett."},{"key":"177_CR39","doi-asserted-by":"crossref","unstructured":"Rossi, R. A. & Ahmed, N. K. The network data repository with interactive graph analytics and visualization. In Proceedings of 29th AAAI Conference on Artificial Intelligence 4292\u20134293 (ACM, 2015).","DOI":"10.1609\/aaai.v29i1.9277"}],"container-title":["Nature Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s42256-020-0177-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s42256-020-0177-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s42256-020-0177-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T03:43:49Z","timestamp":1670384629000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s42256-020-0177-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,25]]},"references-count":39,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["177"],"URL":"https:\/\/doi.org\/10.1038\/s42256-020-0177-2","relation":{},"ISSN":["2522-5839"],"issn-type":[{"value":"2522-5839","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,25]]},"assertion":[{"value":"6 October 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 April 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 May 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}