{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T23:21:22Z","timestamp":1777418482044,"version":"3.51.4"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2016,3,3]],"date-time":"2016-03-03T00:00:00Z","timestamp":1456963200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003549","name":"OTKA","doi-asserted-by":"crossref","award":["K 111797"],"award-info":[{"award-number":["K 111797"]}],"id":[{"id":"10.13039\/501100003549","id-type":"DOI","asserted-by":"crossref"}]},{"name":"MTA-SYLFF (The Ryoichi Sasakawa Young Leaders Fellowship Fund)","award":["Mathematical analysis of centrality measures"],"award-info":[{"award-number":["Mathematical analysis of centrality measures"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cent Eur J Oper Res"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1007\/s10100-016-0439-6","type":"journal-article","created":{"date-parts":[[2016,3,3]],"date-time":"2016-03-03T11:15:07Z","timestamp":1457003707000},"page":"771-790","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Measuring centrality by a generalization of degree"],"prefix":"10.1007","volume":"25","author":[{"given":"L\u00e1szl\u00f3","family":"Csat\u00f3","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,3,3]]},"reference":[{"key":"439_CR1","volume-title":"Computational social networks, of lecture notes in computer science","author":"KE Avrachenkov","year":"2015","unstructured":"Avrachenkov KE, Mazalov VV, Tsynguev BT (2015) Beta current flow centrality for weighted networks. In: Thai MT, Nguyen NP, Shen H (eds) Computational social networks, of lecture notes in computer science, vol 9197. Springer, New York"},{"issue":"3","key":"439_CR2","doi-asserted-by":"crossref","first-page":"16","DOI":"10.17730\/humo.7.3.f4033344851gl053","volume":"7","author":"A Bavelas","year":"1948","unstructured":"Bavelas A (1948) A mathematical model for group structures. Hum Organ 7(3):16\u201330","journal-title":"Hum Organ"},{"issue":"3\u20134","key":"439_CR3","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1080\/15427951.2013.865686","volume":"10","author":"P Boldi","year":"2014","unstructured":"Boldi P, Vigna S (2014) Axioms for centrality. Internet Math 10(3\u20134):222\u2013262","journal-title":"Internet Math"},{"issue":"1","key":"439_CR4","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1086\/228631","volume":"92","author":"P Bonacich","year":"1987","unstructured":"Bonacich P (1987) Power and centrality: a family of measures. Am J Sociol 92(1):1170\u20131182","journal-title":"Am J Sociol"},{"issue":"4","key":"439_CR5","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.socnet.2005.11.005","volume":"28","author":"SP Borgatti","year":"2006","unstructured":"Borgatti SP, Everett MG (2006) A graph-theoretic perspective on centrality. Soc Netw 28(4):466\u2013484","journal-title":"Soc Netw"},{"issue":"1","key":"439_CR6","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S0169-7552(98)00110-X","volume":"30","author":"S Brin","year":"1998","unstructured":"Brin S, Page L (1998) The anatomy of a large-scale hypertextual web search engine. Comput Netw ISDN Syst 30(1):107\u2013117","journal-title":"Comput Netw ISDN Syst"},{"issue":"8","key":"439_CR7","first-page":"1103","volume":"50","author":"P Chebotarev","year":"1989","unstructured":"Chebotarev P (1989) Generalization of the row sum method for incomplete paired comparisons. Autom Remote Control 50(8):1103\u20131113","journal-title":"Autom Remote Control"},{"issue":"3","key":"439_CR8","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/0165-4896(93)00740-L","volume":"27","author":"P Chebotarev","year":"1994","unstructured":"Chebotarev P (1994) Aggregation of preferences by the generalized row sum method. Math Soc Sci 27(3):293\u2013320","journal-title":"Math Soc Sci"},{"issue":"10","key":"439_CR9","doi-asserted-by":"crossref","first-page":"1484","DOI":"10.1016\/j.dam.2012.02.015","volume":"160","author":"P Chebotarev","year":"2012","unstructured":"Chebotarev P (2012) The walk distances in graphs. Discrete Appl Math 160(10):1484\u20131500","journal-title":"Discrete Appl Math"},{"issue":"9","key":"439_CR10","first-page":"1505","volume":"58","author":"P Chebotarev","year":"1997","unstructured":"Chebotarev P, Shamis E (1997) The matrix-forest theorem and measuring relations in small social groups. Autom Remote Control 58(9):1505\u20131514","journal-title":"Autom Remote Control"},{"issue":"3","key":"439_CR11","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1080\/15427951.2004.10129090","volume":"1","author":"S Chien","year":"2004","unstructured":"Chien S, Dwork C, Kumar R, Simon DR, Sivakumar D (2004) Link evolution: analysis and algorithms. Internet Math 1(3):277\u2013304","journal-title":"Internet Math"},{"issue":"1","key":"439_CR12","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s00355-014-0820-0","volume":"44","author":"L Csat\u00f3","year":"2015","unstructured":"Csat\u00f3 L (2015) A graph interpretation of the least squares ranking method. Soc Choice Welf 44(1):51\u201369","journal-title":"Soc Choice Welf"},{"key":"439_CR13","unstructured":"Dequiedt V, Zenou Y (2015) Local and consistent centrality measures in networks. https:\/\/www.gate.cnrs.fr\/IMG\/pdf\/Dequiedt2015.pdf"},{"issue":"1","key":"439_CR14","doi-asserted-by":"crossref","first-page":"35","DOI":"10.2307\/3033543","volume":"40","author":"LC Freeman","year":"1977","unstructured":"Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40(1):35\u201341","journal-title":"Sociometry"},{"issue":"3","key":"439_CR15","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0378-8733(78)90021-7","volume":"1","author":"LC Freeman","year":"1979","unstructured":"Freeman LC (1979) Centrality in social networks: conceptual clarification. Soc Netw 1(3):215\u2013239","journal-title":"Soc Netw"},{"key":"439_CR16","doi-asserted-by":"crossref","unstructured":"Garg M (2009) Axiomatic foundations of centrality in networks. http:\/\/papers.ssrn.com\/sol3\/papers.cfm?abstract_id=1372441","DOI":"10.2139\/ssrn.1372441"},{"key":"439_CR17","first-page":"749","volume":"6","author":"S Ger\u0161gorin","year":"1931","unstructured":"Ger\u0161gorin S (1931) \u00dcber die Abgrenzung der Eigenwerte einer Matrix. Bulletin de l\u2019Acad\u00e9mie des Sciences de l\u2019URSS. Classe des sciences math\u00e9matiques et naturelles 6:749\u2013754","journal-title":"Bulletin de l\u2019Acad\u00e9mie des Sciences de l\u2019URSS. Classe des sciences math\u00e9matiques et naturelles"},{"issue":"1","key":"439_CR18","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s00355-013-0726-2","volume":"42","author":"J Gonz\u00e1lez-D\u00edaz","year":"2014","unstructured":"Gonz\u00e1lez-D\u00edaz J, Hendrickx R, Lohmann E (2014) Paired comparisons analysis: an axiomatic approach to ranking methods. Soc Choice Welf 42(1):139\u2013169","journal-title":"Soc Choice Welf"},{"key":"439_CR19","doi-asserted-by":"crossref","DOI":"10.2307\/j.ctvcm4gh1","volume-title":"Social and economic networks","author":"MO Jackson","year":"2010","unstructured":"Jackson MO (2010) Social and economic networks. Princeton University Press, Princeton"},{"issue":"1","key":"439_CR20","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/BF02289026","volume":"18","author":"L Katz","year":"1953","unstructured":"Katz L (1953) A new status index derived from sociometric analysis. Psychometrika 18(1):39\u201343","journal-title":"Psychometrika"},{"key":"439_CR21","unstructured":"Kitti M (2012) Axioms for centrality scoring with principal eigenvectors. http:\/\/www.ace-economics.fi\/kuvat\/dp79.pdf"},{"issue":"4","key":"439_CR22","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.1007\/s10910-009-9635-0","volume":"47","author":"DJ Klein","year":"2010","unstructured":"Klein DJ (2010) Centrality measure in graphs. J Math Chem 47(4):1209\u20131223","journal-title":"J Math Chem"},{"issue":"6","key":"439_CR23","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s12599-010-0127-3","volume":"2","author":"A Landherr","year":"2010","unstructured":"Landherr A, Friedl B, Heidemann J (2010) A critical review of centrality measures in social networks. Bus Inf Syst Eng 2(6):371\u2013385","journal-title":"Bus Inf Syst Eng"},{"issue":"1","key":"439_CR24","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1037\/h0057189","volume":"46","author":"HJ Leavitt","year":"1951","unstructured":"Leavitt HJ (1951) Some effects of certain communication patterns on group performance. J Abnorm Soc Psychol 46(1):38","journal-title":"J Abnorm Soc Psychol"},{"issue":"1","key":"439_CR25","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.ejor.2013.02.032","volume":"229","author":"RHA Lindelauf","year":"2013","unstructured":"Lindelauf RHA, Hamers HJM, Husslage BGM (2013) Cooperative game theoretic centrality analysis of terrorist networks: the cases of Jemaah Islamiyah and Al Qaeda. Eur J Oper Res 229(1):230\u2013238","journal-title":"Eur J Oper Res"},{"issue":"4","key":"439_CR26","doi-asserted-by":"crossref","first-page":"046114","DOI":"10.1103\/PhysRevE.80.046114","volume":"80","author":"N Masuda","year":"2009","unstructured":"Masuda N, Kawamura Y, Kori H (2009) Analysis of relative influence of nodes in directed networks. Phys Rev E 80(4):046114","journal-title":"Phys Rev E"},{"issue":"5","key":"439_CR27","doi-asserted-by":"crossref","first-page":"056107","DOI":"10.1103\/PhysRevE.82.056107","volume":"82","author":"N Masuda","year":"2010","unstructured":"Masuda N, Kori H (2010) Dynamics-based centrality for directed networks. Phys Rev E 82(5):056107","journal-title":"Phys Rev E"},{"key":"439_CR28","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719512","volume-title":"Matrix analysis and applied linear algebra","author":"CD Meyer","year":"2000","unstructured":"Meyer CD (2000) Matrix analysis and applied linear algebra. Society for Industrial and Applied Mathematics, Philadelphia"},{"key":"439_CR29","first-page":"871","volume-title":"Graph theory, combinatorics, and applications","author":"B Mohar","year":"1991","unstructured":"Mohar B (1991) The Laplacian spectrum of graphs. In: Alavi Y, Chartrand G, Oellermann OR, Schwenk AJ (eds) Graph theory, combinatorics, and applications, vol 2. Wiley, New York, pp 871\u2013898"},{"issue":"1","key":"439_CR30","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1287\/opre.1030.0082","volume":"52","author":"H Monsuur","year":"2004","unstructured":"Monsuur H, Storcken T (2004) Centers in connected undirected graphs: an axiomatic approach. Oper Res 52(1):54\u201364","journal-title":"Oper Res"},{"key":"439_CR31","volume-title":"Untersuchungen \u00fcber das logarithmische und Newton\u2019sche Potential","author":"C Neumann","year":"1877","unstructured":"Neumann C (1877) Untersuchungen \u00fcber das logarithmische und Newton\u2019sche Potential. B. G. Teubner, Leipzig"},{"issue":"1","key":"439_CR32","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1111\/j.1467-9450.1974.tb00598.x","volume":"15","author":"J Nieminen","year":"1974","unstructured":"Nieminen J (1974) On the centrality in a graph. Scand J Psychol 15(1):332\u2013336","journal-title":"Scand J Psychol"},{"issue":"17","key":"439_CR33","doi-asserted-by":"crossref","first-page":"3833","DOI":"10.1016\/j.physa.2013.04.013","volume":"392","author":"G Ranjan","year":"2013","unstructured":"Ranjan G, Zhang Z-L (2013) Geometry of complex networks and topological centrality. Phys A Stat Mech Appl 392(17):3833\u20133845","journal-title":"Phys A Stat Mech Appl"},{"issue":"1","key":"439_CR34","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1137\/0138009","volume":"38","author":"A Rubinstein","year":"1980","unstructured":"Rubinstein A (1980) Ranking the participants in a tournament. SIAM J Appl Math 38(1):108\u2013111","journal-title":"SIAM J Appl Math"},{"issue":"4","key":"439_CR35","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1007\/BF02289527","volume":"31","author":"G Sabidussi","year":"1966","unstructured":"Sabidussi G (1966) The centrality index of a graph. Psychometrika 31(4):581\u2013603","journal-title":"Psychometrika"},{"issue":"4","key":"439_CR36","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1037\/h0084096","volume":"3","author":"JR Seeley","year":"1949","unstructured":"Seeley JR (1949) The net of reciprocal influence: a problem in treating sociometric data. Can J Psychol 3(4):234\u2013240","journal-title":"Can J Psychol"},{"key":"439_CR37","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511815478","volume-title":"Social network analysis: methods and applications","author":"S Wasserman","year":"1994","unstructured":"Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, Cambridge"}],"container-title":["Central European Journal of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10100-016-0439-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10100-016-0439-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10100-016-0439-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10100-016-0439-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T15:00:43Z","timestamp":1589641243000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10100-016-0439-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,3]]},"references-count":37,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["439"],"URL":"https:\/\/doi.org\/10.1007\/s10100-016-0439-6","relation":{},"ISSN":["1435-246X","1613-9178"],"issn-type":[{"value":"1435-246X","type":"print"},{"value":"1613-9178","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,3]]}}}