Social Structure from Multiple Networks. I. Blockmodels of ...

Social Structure from Multiple Networks. I. Blockmodels of Roles and Positions Author(s): Harrison C. White, Scott A. Boorman and Ronald L. Breiger Reviewed work(s): Source: American Journal of Sociology, Vol. 81, No. 4 (Jan., 1976), pp. 730-780 Published by: The University of Chicago Press Stable URL: . Accessed: 19/10/2012 11:23 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@. .

The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to American Journal of Sociology.



Social Structure from Multiple Networks.

I. Blockmodels of Roles and Positions'

HarrisonC. White Harvard University

Scott A. Boorman Universityof Pennsylvania

Ronald L. Breiger Harvard University

Networksof severaldistincttypesof social tie are aggregatedby a dualmodelthatpartitionas populationwhilesimultaneousliydentifyingpatternsof relations.Conceptsand algorithmsare demonstratedin fivecase studiesinvolvingup to 100 personsand up to eighttypesof tie,overas manyas 15 timeperiods.In each case the modelidentifieas concretesocial structureR. ole and positionconcepts are then identifiedand interpretedin termsof these new modelsofconcretesocialstructureP.artII, to be publishedin the May issue of this Journal(Boormanand White1976), willshow how theoperationalmeaningof rolestructureisn smallpopulations can be generatedfromthesociometribclockmodelosfPartI.

Duringthe past decade, the networkmetaphorhas becomeincreasingly popularwithsocial scientists;2 it has even penetratedthe conservative

1 Support fromthe National Science Foundation under grant GS-2689 is gratefully acknowledged.In addition to Phipps Arabie, GregoryH. Heil, Paul R. Levitt, and Francois Lorrain (who have coauthored related papers with us), Paul Bernard and Joseph E. Schwartz had substantial,specificimpact on the work. The generosityof Belver C. GriffithN, icholas C. Mullins, and S. Frank Sampson in supplying and interpretingdata is deeply appreciated,as were A. P. M. Coxon's detailed comments on earlierdrafts.The editorialadvice of Carolyn J. Mullins led to notable improvementsin the exposition.Thanks are due the Mathematical Social Science Board for supportingtwo small conferenceson models of role networks,at which early versions of this work were discussed.Access to computerfacilitieswas kindly given by the CambridgeProject and its director,Dr. Douwe Yntema. The senior author wrote a draftof this paper while holdinga GuggenheimFellowship. 2 Network metaphorsdate back at least to Simmel (1950, 1955; firstpublished in 1908) and the so-called formalschool of Germansociologists.Simmelemphasizedthe ubiquity of social networksbased on "the actual similarityof [individuals'] talents, inclinations,activities,and so on" (1955, p. 128) and which cross-cutthe categorical attributesof persons.Von Wiese, stronglyinfluencedby Simmel,stressedthe multiplicity of types of social ties and the analytic desirabilityof reducing network structures.If the "constantlyflowingstream of interhumanactivity"were halted in its course forone moment,von Wiese (1941, pp. 29-30) suggested,we would observe

730 AJS Volume81 Number4

Social StructurefromMultipleNetworksI.

precinctsof economics(Boorman 1975; Marschak and Radner 1972; Schelling1971; see also Leijonhufvud1968). Sociologists'and anthropologistsa' ttemptsto developthemetaphorintooperationaclonceptshave takentwo directionsO. ne has emphasizedthe paths or "threads"in a singlenetwork:the mannerin whichlong chainsof contactwind their waythroughlargesocialsystems(Milgram1967; Pool and Kochen1958; Rapoport 1963; Coleman 1964; Hunter and Shotland 1974; White 1970a, 1970b; Lee 1969; Granovetter1973, 1974). The secondhas emphasizedthe "knittednesso"f interconnectionwsithina networkand the overlaps betweenmultiple (many-stranded)types of networksfor a givenpopulation(typicallysmall; see TheoreticalBackgroundsection, below). Our operationalconceptsfollowthe second traditionbut are consistentwiththe first.

Afterdemonstratintgheutilityof theseconceptsas appliedto fivecase studies,we redefinetheclassicconceptsof roleand positionso thatthey apply to concreteo, bservableinteractionso,rderedby a new framework. We take as giventhe incidenceof each of severaldistincttypesof tie acrossall pairs in a population(see forexamplefigs.1 and 3 below). Ties of each giventypeare treatedas a separateentity(a matrix).Each is a separatenetworkto be contrastedwithothersuch networksr,ather than mergedwiththemto forma complexbond betweeneach pair of actors.This analyticsegregationof networktypesis basic to our framework. From it, aggregationemergesas a conceptwith dual aspects: actorsare partitionedinto structurallyequivalentsets withineach network;simultaneouslyt,houghn, etworkasre mappedintoa set of images thatcan be specificallyinterpretefdorspecificpopulationsT. he resulting "blockmodel"is a viewof socialstructuroebtaineddirectlyfromaggregationof the relationaldata withoutimposingany a prioricategoriesor attributesforactors.Our fundamentaalrgumentis that the enormous varietyof concretesocial structureiss reflectedin thevarietyof possible blockmodels;furthermorbe,lockmodelsprovide tools for orderingthis diversity.

The essentialphenomenonportrayedin networkimageryw, e argue,is the absenceof connectionbsetweennamedindividualsT. he logicalsymmetrybetweenties that are "present"and ties that are "absent" (i.e., all others)has encouragedproponentsof graph theoryto overlookthe

"an apparentlyimpenetrablenetworkof lines betweenmen. There is not only a line connectingA with B, and B with C, etc., but C is directlyconnectedwith A, and, moreover,A, B, and C are enclosed withina circle.Not only is there one line connectingA with B, and not only one circlein which theyare both enclosed,but there are many connectinglines. . . . A static analysis of the sphere of the interhuman will . . . consistin the dismembermenatnd reconstructionof this systemof relations. Outside this network,above and below it, therecan be nothingthat is social, unless we leave the plane of empirical observation."

731

AmericanJournalof Sociology

social asymmetrythat existsbetweensocial action and its complement (Harary,Norman,and Cartwrigh1t965; cf. Simmel1950,pp. 311-16).

Thispaperand itsforthcomincgompanionP,artII, presentno modelsof processesover time; thereare neitherpredictionosf otherbehaviornor explicationosf a stochasticprocessof tie formationand dissolutionthat wouldsustainan observedblockmodelI.n thispaper the argumentsfor a blockmodeals a pictureofsocialstructuraere specificto thecontextof, and the data available for,each case study.4Yet blockmodelsprovidea natural frameworkfor discussingvarious types of structuralchange: numerouschangesin individualties can stillbe consistentwithan unchangedstructuraplattern;changesin the "circulation"of actorsamong thestructuralleyquivalentsetscan stillreflecthesamestructuraplattern fora givennetworka,nd changesin networkpatternscan occurand yet leave setsof actorsunchanged.

The nextsectionof thispaper examinesthe broad theoreticaul nderpinningosfourresearchT. he secondmajorsectionpresentsdefinitionasnd themethodsof analysis.The thirdsectionexhibitsanalysesbased on five case studies.The fourthsectionprovidesan interpretatioonf "role" and "position."

THEORETICAL BACKGROUND

Insightfuelxpositionosf recentworkon networkinterrelationasre those by Mitchell(1969, chap. 1) and Barnes (1972). While we use themas centralreferencesw, e wantto stateone fundamentadlisagreementB.oth see networkanalysisto date as, at best, an eclecticbag of techniques (Barnes 1972, p. 3) forstudyingthe details of individuals'variability around some basic orderingby categoriesand concreteorganizations (Mitchell 1969, p. 10). We wouldlike the readerto entertaininstead the idea that the presentlyexisting,largelycategoricaldescriptionosf socialstructurheave no solidtheoreticaglroundingf; urthermornee,twork conceptsmayprovidetheonlyway to constructa theoryof social structure.

Perhapsthe majorthrustof classicalsocial theorywas its recognition of thehistoricadl issolutionof categoricabl oundariesforsocial relations, whetherthechangewas perceivedas a transitionfromstatusto contract (Maine), fromGemeinschaftto Gesellschaft(T6nnies), frommechanical

3 Recognizingthat the "holes" in a networkmay defineits structurewas a primary substantivemotivationfor the work reportedhere. There are obvious analogies with homologytheoryin algebra (Hilton and Wylie 1960), thoughthe relevantmathematics is quite different.

4 In addition, White (1974b) has calculated probabilitiesfor the occurrencepurely by chance of the simplestblockmodels.

732

Social StructurefromMultipleNetworksI.

to organicsolidarity(Durkheim),fromtraditionatlo means-rationoalrientation (Weber), or fromascribedto achievedstatus (Linton). In our view,the majorproblemwithpostclassicalsocial theoryhas been that its conceptsremainweddedto categoricalimageryA. ll sociologistsd' iscourserestson primitivteerms-"status,""role,""group,""social control," "interaction,a'nd "society"do notbegintoexhaustthelist-whichrequire an aggregationprinciplein thattheirreferentasre aggregatesof persons, collectivitiesi,nterrelated"positions,"or "generalizedactors." However, sociologistshave been largelycontentto aggregatein only two ways: eitherby positingcategoricalaggregates(e.g., "functionalsubsystems," "classes") whoserelationto concretesocialstructurheas beentenuous;or by cross-tabulatinigndividualsaccordingto theirattributes(e.g., lowermiddle-classwhite Protestantswho live in innercity areas and vote Democrat).Both methodshave "oftenled to theneglectof social structureand of the relationsamongindividuals"(Coleman 1958).5 In contrastto thestandardwisdom,thereis a growinglistof empiricafl indings regardingthe effect(and frequency)of "accidents"and "luck" in the actual functioningof societies: the transmissionof usefulinformation among scientists(Menzel 1962), the attainmentof general economic success (Jenckset al. 1972), and the locationof desirablejobs (Granovetter1974; see also Boorman1975). These findingsforceus to ask whetherthe stuffof social actionis, in fact,waitingto be discoveredin thenetworkof intersticetshatexistoutsidethenormativeconstructasnd the attributebreakdownosf our everydaycategories.

Overall Social Structure

Nadel's The Theoryof Social Structure(1957), one of the fewpiecesof sustainedanalyticalexegesisin sociologyi,nspiredthework(White1963; Lorrainand White1971) fromwhichthesepapersgrew.His focuswas theinterrelationosf roles.In dealingwithrole "frames"and theirinterlock,6he confrontetdheinteractionofculturalsystemsand concretesocial structurea, topicon whichwe spendlittletime.However,we do develop, in a limitedcontext,two of Nadel's mostimportantideas. First,social structureis regularitiesin the patternsof relationsamong concrete entities;it is nota harmonyamongabstractnormsand valuesor a classi-

5 There are some exceptionsto these tendencies,e.g., reference-groutpheory (Merton 1959, pp. 281-86), and Znaniecki's (1940) embeddingof "role" concepts in "social circles"; nevertheless,there is a remarkablelack of attentionto aggregationas a central problem for sociological theory. Leijonhufvud's (1968, chap. 3) critique of neoclassicaleconomicsfor avoiding similarquestionsis relevanthere. See also Green (1964) for a more orthodox review of economic aggregationconcepts.

6 This topic,of course,entailsthe attendantcomplexitiesof interrelatingthe multiple perspectivesof actors in actual societies.

733

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download