{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T01:19:39Z","timestamp":1778462379511,"version":"3.51.4"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T00:00:00Z","timestamp":1624838400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T00:00:00Z","timestamp":1624838400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s11424-021-0111-7","type":"journal-article","created":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T09:05:09Z","timestamp":1624871109000},"page":"2168-2181","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Identifying Influential Spreaders in Complex Networks by Considering the Impact of the Number of Shortest Paths"],"prefix":"10.1007","volume":"34","author":[{"given":"Yangyang","family":"Luan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongkui","family":"Bao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haifeng","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,6,28]]},"reference":[{"issue":"4","key":"111_CR1","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1109\/MC.2013.75","volume":"46","author":"P Basaras","year":"2013","unstructured":"Basaras P, Katsaros D, and Tassiulas L, Detecting influential spreaders in complex, dynamic networks, Computer, 2013, 46(4): 24\u201329.","journal-title":"Computer"},{"issue":"6","key":"111_CR2","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, et al., Leaders in social networks, the delicious case, PLoS One, 2011, 6(6): e21202.","journal-title":"PLoS One"},{"issue":"2","key":"111_CR3","doi-asserted-by":"publisher","first-page":"026116","DOI":"10.1103\/PhysRevE.85.026116","volume":"85","author":"J Borge-Holthoefer","year":"2012","unstructured":"Borge-Holthoefer J and Moreno Y, Absence of influential spreaders in rumor dynamics, Physical Review E, 2012, 85(2): 026116.","journal-title":"Physical Review E"},{"issue":"4","key":"111_CR4","doi-asserted-by":"publisher","first-page":"650","DOI":"10.1007\/s11424-014-2236-4","volume":"27","author":"P Wang","year":"2014","unstructured":"Wang P, Tian C, and Lu J, Identifying influential spreaders in artificial complex networks, Journal of Systems Science and Complexity, 2014, 27(4): 650\u2013665.","journal-title":"Journal of Systems Science and Complexity"},{"issue":"6","key":"111_CR5","doi-asserted-by":"publisher","first-page":"68006","DOI":"10.1209\/0295-5075\/104\/68006","volume":"104","author":"D B Chen","year":"2013","unstructured":"Chen D B, Xiao R, Zeng A, et al., Path diversity improves the identification of influential spreaders, EPL (Europhysics Letters), 2013, 104(6): 68006.","journal-title":"EPL (Europhysics Letters)"},{"issue":"4","key":"111_CR6","doi-asserted-by":"publisher","first-page":"48805","DOI":"10.1209\/0295-5075\/106\/48005","volume":"106","author":"Z M Ren","year":"2014","unstructured":"Ren Z M, Zeng A, Chen D B, et al., Iterative resource allocation for ranking spreaders in complex networks, EPL (Europhysics Letters), 2014, 106(4): 48805.","journal-title":"EPL (Europhysics Letters)"},{"key":"111_CR7","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1016\/j.eswa.2017.10.018","volume":"93","author":"Z Ahmad","year":"2018","unstructured":"Ahmad Z and Amir S, A hierarchical approach for influential node ranking in complex social networks, Expert Systems with Applications, 2018, 93: 200\u2013211.","journal-title":"Expert Systems with Applications"},{"issue":"5","key":"111_CR8","doi-asserted-by":"publisher","first-page":"1306","DOI":"10.1007\/s11424-018-7331-5","volume":"32","author":"H Sotoodeh","year":"2019","unstructured":"Sotoodeh H and Falahrad M, Relative degree structural hole centrality, CRD-SH: A new centrality measure in complex networks, Journal of Systems Science and Complexity, 2019, 32(5): 1306\u20131323.","journal-title":"Journal of Systems Science and Complexity"},{"key":"111_CR9","doi-asserted-by":"publisher","first-page":"104833","DOI":"10.1016\/j.knosys.2019.07.004","volume":"187","author":"J Tang","year":"2020","unstructured":"Tang J, Zhang R, Wang P, et al., A discrete shuffled frog-leaping algorithm to identify influential nodes for influence maximization in social networks, Knowledge-Based Systems, 2020, 187: 104833.","journal-title":"Knowledge-Based Systems"},{"issue":"1","key":"111_CR10","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1080\/0022250X.1972.9989806","volume":"2","author":"P Bonacich","year":"1972","unstructured":"Bonacich P, Factoring and weighting approaches to status scores and clique identification, Journal of Mathematical Sociology, 1972, 2(1): 113\u2013120.","journal-title":"Journal of Mathematical Sociology"},{"issue":"11","key":"111_CR11","doi-asserted-by":"publisher","first-page":"888","DOI":"10.1038\/nphys1746","volume":"6","author":"M Kitsak","year":"2010","unstructured":"Kitsak M, Gallos L K, Havlin S, et al. A, Identification of influential spreaders in complex networks, Nature Physics, 2010, 6(11): 888\u2013893.","journal-title":"Nature Physics"},{"issue":"1","key":"111_CR12","doi-asserted-by":"publisher","first-page":"35","DOI":"10.2307\/3033543","volume":"40","author":"L C Freeman","year":"1977","unstructured":"Freeman L C, A set of measures of centrality based on betweenness, Sociometry, 1977, 40(1): 35\u201341.","journal-title":"Sociometry"},{"issue":"1","key":"111_CR13","first-page":"1170","volume":"92","author":"P Bonacich","year":"1987","unstructured":"Bonacich P, Power and centrality: A family of measures, Journal of Mathematical Sociology, 1987, 92(1): 1170\u20131182.","journal-title":"Journal of Mathematical Sociology"},{"issue":"14","key":"111_CR14","doi-asserted-by":"publisher","first-page":"1031","DOI":"10.1016\/j.physleta.2013.02.039","volume":"377","author":"A Zeng","year":"2013","unstructured":"Zeng A and Zhang C J, Ranking spreaders by decomposing complex networks, Physics Letters A, 2013, 377(14): 1031\u20131035.","journal-title":"Physics Letters A"},{"issue":"4","key":"111_CR15","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1007\/BF02289527","volume":"31","author":"G Sabidussi","year":"1966","unstructured":"Sabidussi G, The centrality index of a graph, Psychometrika, 1966, 31(4): 581\u2013603.","journal-title":"Psychometrika"},{"key":"111_CR16","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/j.physa.2015.12.162","volume":"451","author":"L L Ma","year":"2016","unstructured":"Ma L L, Ma C, Zhang H F, et al., Identifying influential spreaders in complex networks based on gravity formula, Physica A, 2016, 451: 205\u2013212.","journal-title":"Physica A"},{"issue":"1","key":"111_CR17","doi-asserted-by":"publisher","first-page":"2237","DOI":"10.1016\/j.physa.2017.11.138","volume":"492","author":"H L Liu","year":"2018","unstructured":"Liu H L, Ma C, Xiang B B, et al., Identifying multiple influential spreaders based on generalized closeness centrality, Physica A, 2018, 492(1): 2237\u20132248.","journal-title":"Physica A"},{"key":"111_CR18","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1016\/j.physa.2016.10.086","volume":"468","author":"Z K Bao","year":"2017","unstructured":"Bao Z K, Ma C, Xiang B B, et al., Identification of influential nodes in complex networks: Method from spreading probability viewpoint, Physica A, 2017, 468: 391\u2013397.","journal-title":"Physica A"},{"issue":"5","key":"111_CR19","doi-asserted-by":"publisher","first-page":"2447","DOI":"10.1016\/j.laa.2012.10.022","volume":"438","author":"M Benzi","year":"2013","unstructured":"Benzi M, Estrada E, and Klymko C, Ranking hubs and authorities using matrix functions, Linear Algebra and Its Applications, 2013, 438(5): 2447\u20132474.","journal-title":"Linear Algebra and Its Applications"},{"key":"111_CR20","doi-asserted-by":"publisher","first-page":"9602","DOI":"10.1038\/srep09602","volume":"5","author":"Y Liu","year":"2015","unstructured":"Liu Y, Tang M, Zhou T, et al., Core-like groups result in invalidation of identifying superspreader by k-shell decomposition, Scientific Reports, 2015, 5: 9602.","journal-title":"Scientific Reports"},{"issue":"3","key":"111_CR21","doi-asserted-by":"publisher","first-page":"036104","DOI":"10.1103\/PhysRevE.74.036104","volume":"74","author":"M E Newman","year":"2006","unstructured":"Newman M E, Finding community structure in networks using the eigenvectors of matrices, Physical Review E, 2006, 74(3): 036104.","journal-title":"Physical Review E"},{"issue":"6684","key":"111_CR22","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1038\/30918","volume":"393","author":"D J Watts","year":"1998","unstructured":"Watts D J and Strogatz S H, Collective dynamics of small-worldnetworks, Nature, 1998, 393(6684): 440\u2013442.","journal-title":"Nature"},{"issue":"6","key":"111_CR23","doi-asserted-by":"publisher","first-page":"065103","DOI":"10.1103\/PhysRevE.68.065103","volume":"68","author":"R Guimera","year":"2003","unstructured":"Guimera R, Danon L, Diaz-Guilera A, et al., Self-similar community structure in a network of human interactions, Physical Review E, 2003, 68(6): 065103.","journal-title":"Physical Review E"},{"issue":"8","key":"111_CR24","doi-asserted-by":"publisher","first-page":"2794","DOI":"10.1016\/j.physa.2011.12.055","volume":"391","author":"N Blagus","year":"2012","unstructured":"Blagus N, Subelj L, Bajec M, Self-similar scaling of density in complex real-world networks, Physica A, 2012, 391(8): 2794\u20132802.","journal-title":"Physica A"},{"key":"111_CR25","doi-asserted-by":"publisher","first-page":"027104","DOI":"10.1103\/PhysRevE.72.027104","volume":"72","author":"J Duch","year":"2005","unstructured":"Duch J and Arenas A, Community detection in complex networks using extremal optimization, Physical Review E, 2005, 72: 027104.","journal-title":"Physical Review E"},{"key":"111_CR26","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1038\/nature750","volume":"417","author":"C V Mering","year":"2002","unstructured":"Mering C V, Krause R, Snel B, et al., Comparative assessment of large-scale data sets of proteinprotein interactions, Nature, 2002, 417: 399\u2013403.","journal-title":"Nature"},{"issue":"1","key":"111_CR27","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1109\/TNET.2003.822655","volume":"12","author":"N Spring","year":"2004","unstructured":"Spring N, Mahajan R, Wetherall D, et al., Measuring ISP topologies with rocketfuel, IEEE\/ACM Transactions on Networking, 2004, 12(1): 2\u201316.","journal-title":"IEEE\/ACM Transactions on Networking"},{"issue":"1","key":"111_CR28","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1145\/1217299.1217301","volume":"1","author":"J Leskovec","year":"2007","unstructured":"Leskovec J, Kleinberg J, and Faloutsos C, Graph evolution: Densification and shrinking diameters, ACM Transactions on Knowledge Discovery from Data (TKDD), 2007, 1(1): 2\u201342.","journal-title":"ACM Transactions on Knowledge Discovery from Data (TKDD)"},{"issue":"4","key":"111_CR29","first-page":"521","volume":"26","author":"Y Moreno","year":"2002","unstructured":"Moreno Y, Pastor-Satorras R, and Vespignani A, Epidemic outbreaks in complex heterogeneous networks, The European Physical Journal B, 2002, 26(4): 521\u2013529.","journal-title":"The European Physical Journal B"},{"key":"111_CR30","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1016\/j.physa.2013.10.047","volume":"395","author":"J Bae","year":"2014","unstructured":"Bae J and Kim S, Identifying and ranking influential spreaders in complex networks by neighborhood coreness, Physica A, 2014, 395: 549\u2013559.","journal-title":"Physica A"},{"issue":"314","key":"111_CR31","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1080\/01621459.1966.10480879","volume":"61","author":"W R Knight","year":"1966","unstructured":"Knight W R, A computer method for calculating kendall\u2019s tau with ungrouped data, Journal of the American Statistical Association, 1966, 61(314): 436\u2013439.","journal-title":"Journal of the American Statistical Association"},{"issue":"4","key":"111_CR32","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1140\/epjb\/e2009-00335-8","volume":"71","author":"T Zhou","year":"2009","unstructured":"Zhou T, L\u00fc L, and Zhang Y C, Predicting missing links via local information, The European Physical Journal B, 2009, 71(4): 623\u2013630.","journal-title":"The European Physical Journal B"}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-021-0111-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11424-021-0111-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-021-0111-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,11]],"date-time":"2022-01-11T07:11:56Z","timestamp":1641885116000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11424-021-0111-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,28]]},"references-count":32,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["111"],"URL":"https:\/\/doi.org\/10.1007\/s11424-021-0111-7","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,28]]},"assertion":[{"value":"20 May 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 July 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 June 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}