eigenvector-like measures of centrality for asymmetric relations

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1、SocialNetworks23(2001)191201Eigenvector-likemeasuresofcentralityforasymmetricrelationsPhillipBonacich∗,PauletteLloydDepartmentofSociology,UniversityofCaliforniaatLosAngeles,2201HersheyHall,P.O.Box951551,LosAngeles,CA90095-1551,USAAbstractEigenvectorsofadjacen

2、cymatricesareusefulasmeasuresofcentralityorofstatus.However,theyaremisappliedtoasymmetricnetworksinwhichsomepositionsareunchosen.Forthesenetworks,analternativemeasureofcentralityissuggestedthatequalsaneigenvectorwheneigenvectorscanbeusedandprovidesmeaningfull

3、ycomparableresultswhentheycannot.©2001ElsevierScienceB.V.Allrightsreserved.JELclassification:C00GeneralmathematicalandquantitativemethodsKeywords:Centrality;Power;Status;Eigenvector1.IntroductiontoasymmetriccentralitymeasuresMeasuresofnetworkcentralityexistfor

4、symmetricaswellasasymmetricrelations.Consider,forexample,thenetworksasshowninFig.1.Dependingonthecontentoftherelationship,thesenetworksaremeanttorepresentthatvariousmeasuresofcentralitycanbeapplied(WassermanandFaust,1994,pp.169219).Ifthesearefriendshipchoices

5、andpopularityisbeingassessedin-degree,thenthetotalnumberofchoicesreceivedbyeachindividualcanbeusedasameasure.InnetworkII,positionAisthemostcentralasmeasuredbyin-degree.IfnetworkIwereacommunicationsnetworkwecouldapplybetweennesscentrality;bytheconventionalmeas

6、ureofbetweennesscentrality,position3isthemostcentral,followedbyposition4.WassermanandFaustalsodiscusswhattheycallprestigemeasuresofcentrality,measuresinwhichthecentralitiesorstatusesofpositionsarerecursivelyrelatedtothecentralitiesorstatusesofthepositionstowh

7、ichtheyareconnected.Thisisthetypeofcentralitymeasure∗Correspondingauthor.Tel.:+1-310-825-3017.E-mailaddress:bonacich@soc.ucla.edu(P.Bonacich).0378-8733/01/$seefrontmatter©2001ElsevierScienceB.V.Allrightsreserved.PII:S0378-8733(01)00038-7192P.Bonacich,P.Lloyd/

8、SocialNetworks23(2001)191–201Fig.1.Hypotheticalnetworks.thatwillbethefocusofthispaper.Beingchosenbyapopularindividualshouldaddmoretoonespopularity.Beingnominatedaspowerfulbysomeoneseenbyo