Social Structure From Multiple Networks

8/6/2019 Social Structure From Multiple Networks

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Social Structure from Multiple Networks. I. Blockmodels of Roles and PositionsAuthor(s): Harrison C. White, Scott A. Boorman, Ronald L. BreigerSource: The American Journal of Sociology, Vol. 81, No. 4 (Jan., 1976), pp. 730-780Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/2777596 .

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Social Structure from Multiple Networks.I. Blockmodels of Roles and Positions'HarrisonC. WhiteHarvardUniversityScottA. BoormanUniversity f PennsylvaniaRonald L. BreigerHarvardUniversity

Networks f severaldistinct ypesof social tie are aggregated ya dualmodel hatpartitions populationwhile imultaneouslydenti-fyingpatterns f relations.Conceptsand algorithms re demon-stratedn fivecase studies nvolving p to 100 persons nd up toeight ypes ftie,over s many s 15 timeperiods.n each case themodel dentifies concrete ocial structure. ole and position on-cepts are then identified nd interpretedn termsof these newmodels fconcrete ocialstructure.art I, to be published n theMay issue of this Journal Boorman nd White1976), willshowhow the operationalmeaning f role structuresn smallpopulationscanbe generated romhesociometriclockmodelsfPart .

During the past decade, the networkmetaphor as become ncreasinglypopular with social scientists; it has even penetrated he conservative

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1 Support fromthe National Science Foundation under grant GS-2689 is gratefullyacknowledged. n addition to Phipps Arabie, Gregory H. Heil, Paul R. Levitt, andFrancois Lorrain (who have coauthored related papers with us), Paul BernardandJoseph E. Schwartz had substantial, pecific mpact on the work. The generosity fBelver C. Griffith, icholas C. Mullins, and S. Frank Sampson in supplyingandinterpreting ata is deeply appreciated, s were A. P. M. Coxon's detailed commentson earlierdrafts.The editorial advice of CarolynJ. Mullins led to notable improve-ments n the exposition.Thanks are due the Mathematical Social Science Board forsupporting wo small conferences n models of role networks, t which earlyversionsof this work were discussed. Access to computerfacilitieswas kindly given by theCambridgeProject and its director, r. Douwe Yntema. The seniorauthorwrote adraftof thispaper while holdinga Guggenheim ellowship.2 Networkmetaphors date back at least to Simmel (1950, 1955; firstpublishedin1908) and the so-called formal chool of German sociologists. immel emphasizedtheubiquityof social networksbased on "the actual similarity f [individuals'] talents,inclinations,ctivities, nd so on" (1955, p. 128) and which cross-cut he categoricalattributes f persons.Von Wiese, strongly nfluenced y Simmel,stressedthe multi-plicity of types of social ties and the analytic desirabilityof reducingnetworkstructures. f the "constantlyflowing tream of interhuman ctivity"were halted inits course for one moment, on Wiese (1941, pp. 29-30) suggested,we would observe


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Social Structure romMultipleNetworks.precincts f economics Boorman1975; Marschak and Radner 1972;Schelling1971; see also Leijonhufvud 968). Sociologists' nd anthro-pologists'ttempts odevelop he metaphorntooperationaloncepts avetakentwodirections. ne has emphasized hepaths or "threads" n asinglenetwork: he mannern which ongchainsof contactwindtheirwaythrougharge ocial systemsMilgram1967; Pool andKochen1958;Rapoport 1963; Coleman 1964; Hunter and Shotland 1974; White1970a, 1970b; Lee 1969; Granovetter 973, 1974). The secondhas em-phasizedthe"knittedness"f interconnectionsithin networknd theoverlaps betweenmultiple many-stranded) ypes of networks or agiven population typically mall; see TheoreticalBackground ection,below). Our operational onceptsfollow the second tradition ut areconsistent ith the first.After emonstratinghe utility f these oncepts s applied to five asestudies,we redefine heclassicconcepts f role and position o thattheyapplyto concrete,bservable nteractions,rdered y a new framework.We take as giventhe incidence f each of several distinct ypesof tieacrossall pairs in a population see for examplefigs.1 and 3 below).Ties ofeach given ype re treated s a separate ntity a matrix).Eachis a separatenetwork o be contrasted ithother uch networks, atherthanmergedwiththemto form complexbond between ach pair ofactors.This analytic egregationfnetwork ypes s basic to our frame-work. From it, aggregation merges s a conceptwithdual aspects:actors are partitionedntostructurallyquivalent ets within ach net-work;simultaneously,hough, etworksre mapped nto a set of imagesthatcan be specificallynterpretedor pecific opulations. he resulting"blockmodel"s a viewof social structurebtained irectly rom ggrega-tion of the relational ata without mposing ny a prioricategories rattributes or actors.Our fundamentalrgument s that the enormousvariety fconcreteocial structuress reflectedn thevariety f possibleblockmodels;furthermore,lockmodels rovidetools forordering hisdiversity.The essential henomenonortrayedn networkmagery, e argue, sthe absenceof connections etweennamed ndividuals. he logical sym-metry etween ies that are "present" nd ties that are "absent" (i.e.,all others)has encouraged roponents f graphtheory o overlook he

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"an apparentlympenetrable etworkof linesbetweenmen. There is not only a lineconnectingA with B, and B with C, etc., but C is directly onnectedwithA, and,moreover,A, B, and C are enclosed withina circle.Not only is thereone line con-nectingA withB, and not onlyone circle n whichtheyare both enclosed,but thereare many connecting ines. . . . A static analysis of the sphere of the interhumanwill . . . consist n the dismembermentnd reconstructionf this systemof relations.Outside thisnetwork, bove and below it, therecan be nothing hat is social, unlesswe leave the plane of empiricalobservation."


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AmericanJournal f Sociologysocial asymmetryhatexistsbetween ocial action and its complement(Harary,Norman, nd Cartwright965; cf. Simmel1950, pp. 311-16).This paper nd its forthcomingompanion,art I, present o models fprocesses ver time; there re neither redictions f otherbehaviornorexplicationsf a stochastic rocess f tie formationnd dissolutionhatwould sustain n observed lockmodel.n thispaper the argumentsora blockmodels a picture fsocial structurere specifico the context f,and the data available for, ach case study.4 et blockmodels rovidenatural frameworkor discussingvarious types of structural hange:numerous hanges n individual ies can still be consistentwith an un-changed tructuralattern; hanges n the"circulation"f actors mongthe tructurallyquivalent ets can stillreflect hesamestructuralatternfor givennetwork,nd changes n network atterns an occur and yetleave sets of actorsunchanged.The next sectionof this paper examines he broad theoreticalnder-pinnings f our research. he secondmajor ection resents efinitionsndthemethods fanalysis.The third ection xhibits nalysesbased on fivecase studies.The fourth ectionprovides n interpretationf "role" and"position."THEORETICAL BACKGROUNDInsightful xpositions f recentworkon networknterrelationsre thoseby Mitchell 1969, chap. 1) and Barnes (1972). While we use them scentral eferences, e want to state one fundamentalisagreement.othsee networknalysisto date as, at best, an eclecticbag of techniques(Barnes 1972, p. 3) forstudying he details of individuals' ariabilityaroundsome basic ordering y categories nd concreteorganizations(Mitchell 1969, p. 10). We would ike the readerto entertainnsteadthe idea that the presently xisting, argelycategoricaldescriptionsfsocialstructure ave no solid theoretical rounding; urthermore,etworkconceptsmay provide he onlywayto construct theory f social struc-ture.Perhapsthemajor thrust f classical social theorywas its recognitionof thehistorical issolutionf categorical oundaries or ocial relations,whether hechangewas perceived s a transition rom tatus to contract(Maine), fromGemeinschafto GesellschaftT6nnies), frommechanical

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3 Recognizing hat the "holes" in a networkmay define ts structurewas a primarysubstantivemotivationforthe work reportedhere.There are obvious analogieswithhomology heory n algebra (Hilton and Wylie1960), thoughtherelevantmathematicsis quite different.4 In addition,White (1974b) has calculated probabilitiesfor the occurrencepurelyby chance of the simplestblockmodels.


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Social Structure romMultipleNetworks.toorganicolidarityDurkheim), rom raditionalo means-rationalrien-tation Weber), or from scribed to achievedstatus (Linton). In ourview,the majorproblemwithpostclassical ocial theoryhas been thatits concepts emainwedded to categorical magery.All sociologists' is-course ests nprimitiveerms-"status," role," group," socialcontrol,""interaction,'nd "society" o notbegin oexhaust he ist-whichrequirean aggregationrinciple n thattheir eferentsre aggregatesfpersons,collectivities,nterrelatedpositions," r "generalized ctors."However,sociologists ave been largelycontent o aggregaten only two ways:eitherby positing ategorical ggregatese.g., "functionalubsystems,""classes") whose elation oconcrete ocialstructureas beentenuous;orby cross-tabulatingndividuals ccording o their ttributese.g., lower-middle-classwhiteProtestantswho live in innercity areas and voteDemocrat).Both methods ave "often ed to the neglect f social struc-tureand of therelations mong ndividuals" Coleman 1958).5 In con-trast o thestandardwisdom, here s a growingistof empirical indingsregarding he effectand frequency) f "accidents"and "luck" in theactual functioningf societies: the transmissionf useful nformationamongscientists Menzel 1962), the attainment f general economicsuccess Jencks t al. 1972), and thelocationof desirableobs (Grano-vetter1974; see also Boorman1975). These findings orceus to askwhether hestuff f social action s, in fact,waiting o be discoverednthe network f intersticeshatexistoutside henormativeonstructsndtheattribute reakdowns f our everyday ategories.Overall Social StructureNadel's The Theory fSocial Structure1957), one of the fewpieces ofsustainednalytical xegesisn sociology,nspired hework White1963;Lorrain nd White 1971) fromwhich hesepapersgrew.His focus wasthe nterrelationsf roles. n dealingwithrole"frames" nd their nter-lock,6 e confrontedhe nteractionfculturalystems nd concrete ocialstructure, topiconwhichwe spend ittle ime.However,we do develop,in a limited ontext, woof Nadel's most mportantdeas. First, socialstructures regularitiesn the patternsof relationsamong concreteentities; t is nota harmonymong bstract ormsnd valuesora classi-

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5There are some exceptions o thesetendencies, .g., reference-groupheory(Merton1959, pp. 281-86), and Znaniecki's (1940) embeddingof "role" concepts in "socialcircles"; nevertheless,here is a remarkable ack of attentionto aggregation s acentralproblemfor sociologicaltheory.Leijonhufvud's (1968, chap. 3) critique ofneoclassicaleconomics foravoidingsimilarquestions s relevanthere. See also Green(1964) for a more orthodoxreview of economic aggregation oncepts.6 This topic,of course,entailsthe attendantcomplexities f interrelatinghe multipleperspectives f actors in actual societies.


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AmericanJournal f Sociologyfication fconcrete ntities y their ttributes. econd,to describe ocialstructure,e must ggregate hese egularitiesna fashion onsistent iththeir nherent ature s networks.The cultural nd social-psychologicaleanings f actualties are largelybypassed n the development.We focus nsteadon interpretinghe pat-terns mong ypes f tie found n blockmodels. ur sole assumption ereis that all ties of a given observed ypeshare a common ignification(whatevertheir content may be). From these patterns,we developbelow (and in Part II) operational oncepts f role and position.7In our view "position," n the concrete ense of officen a formalorganizationrmembershipna committee,s a concept uite ndependentfrom role." The blockmodelsf thispapercan be said to identifyosi-tions, utonly n an elementaryense. n Part II we extend he analysisto encompassmultiple gos and, thence, ole structures; we hope alsothat his xtensionan describe,n the anguage f Mitchell 1969, pp. 45-49), the existence nd interrelationsf "institutions."At best,blockmodelsanmakeonly partial ontributiono the analy-sis offormal rganizationss structuresfoffices.he networkmetaphoris unavoidablen developingmodelsof formal rganization,ven of thesimplest ind (Williamson 970, chap. 2). However, undamentallyewdevelopmentsf the metaphor re needed,such as that proposedbyFriedell 1967) and that mpliedby the argument f Cohenand March(1974).Analyzing ystems f formalorganizations ill require still furtherdevelopments f networkmagery, nd these cannot be divorcedfrommodelsof elites and the ways in whichthey may control arge socialsystemshroughhestructurefnetworkccess. Recentwork n directorinterlockse.g., Levine 1972) and on advisory ystemsMullins 1972),as wellas formallynalogousmodels finterlocksn dual individual-posi-tionsystemsBreiger1974b; Bonacich1972), may pointin the rightdirection.One practical easonforthecautionof Mitchell nd Barnes in usingnetwork onceptswas the lack of satisfactorymethods or aggregatingnetworksmong ndividuals. related easonwas thepaucity f researchon networksmongnodesthatrepresentedollectivitiesnd organizations.There are few ystematicnalyses f networksmong uch nodes but seeFortes 1945, Mayer 1960, and Savage and Deutsch 1960); however,engineeringnd operations esearch ave huge descriptivend normative

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7 Ourstress n relationshipsmong patterns uggested o one of our refereesn analogyto Levi-Strauss'swork on "meaning." He thereby reditedus with too much and toolittle.We use that termwithout he richethnographicnsight f Levi-Strauss;however,we do discuss the falsifiabilityf an ideal-type pattern and (White 1974b) its nullexpectation. In our view, the delineation of concrete social structureshould beanalyticallydivorced from symbolic and cultural analysis.


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Social Structure romMultipleNetworks.literaturesn flowswithin etworkssee Ford and Fulkerson 962) thatmay prove uggestivesee White 1973).8BothMitchell nd Barnes emphasized anchored"networksnetworksseenfromheperspectivef a particularmember), ecausetheywanted oshowhow networkoncepts lluminatehemanipulativectivities f con-crete persons n real situations. heir conceptual pproachdiffersromour observer iewpoint n this paper and themultiple-ego iewpoint fPart II. In particular, hey mergeddifferentypesof tie and inferreda complex, verallqualityfrom he multiplex ondbetween he anchorpersonand each of his contacts.'3n contrast,we argue for the value(fromtheobserver's iewpoint) f treating he network ased on eachanalytically eparable type of tie as a separate entity. Furthermore,Mitchell nd Barnespaid more ttentiono thedifferentacets f meaningmeasured oreach typeof tie; they lso stressed he mportancef richobservationy a participant bservers, for xample, n Kapferer'swork(1972).10 n contrast, e argue, ollowingurkheim, hat theoryhouldbe developed nly n terms f the overall tructurehat s the context orparticular ransactions. e cite as evidenceBoorman's 1975) model ofjob informationxchange, oting hat his results egardingtabilityndoptimality ere btained rom ostulates f a very imple, verallnetworkstructure."1Mitchelland Barnes treated sociometry, speciallybalance theory,with omedisdain.12 lthoughmanypowerfulnalyses fdata have useda variety f sociometriconcepts see, e.g., the excellent urvey rticlesby Glanzer nd Glaser[1959, 1961]), manyof the data are from xperi-mental groups" and otherpopulations ggregatedwithin sociologicalvacuum.Moreover,with the crucialexception f the analysesby Davis,Holland, and Leinhardt see Part II), balance theorists ave had little

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8 Both thispaper and Part II deal wholly with data on individuals,but our motivefordeveloping hemethodsreportedherewas partly that we thinkthey will be fruit-ful for analyzingdata on networks mong collectivities see Breiger,Boorman, andArabie [19751 reanalyzing ata of Levine [19721).9 But note the lament of Mitchell's colleague Boissevain (1973, p. xi) that "theproblemof handlingmultiplex or many-stranded elationships emains, n spite ofthe increasingly ophisticated analytical apparatus provided by networkanalysis."10Kapferer went even further, ttempting to develop an exchange theory fortransactions etweenpairs in a network.11We believe that blockmodels,which represent tatic structure,will be a usefulframeworkfor developingsocial exchange theory.Ekeh's (1974) recent review of"the two traditions" n social exchangetheoryurged the importanceof interactionbetween restricted xchange (Homans) and generalized exchange (Levi-Strauss).Blockmodels eem a naturalcontextforsuch a merger.12Mitchell (1969, p. 7) ventured o far as to term balance theory, he most interest-ing analyticdevelopment n this tradition see e.g., Harary et al. [1965, chap. 131),''a toy of the lecture-roomheoretician."


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American ournal f Sociologystomachforactual data. Yet we thinkMitchell nd Barnes too hasty.Our ownapproach wes much to sociometry,articularlyts encourage-ment f systematic ata reportsn contrast o rich ntuitive bservation,and blockmodelsncludevariousforms fbalance theory s special cases(see Part II).ContrastswithSociometrySociometry's ost ommon oal for single ypeoftie was the dentifica-tionofcliques or similar onfigurations)f tightlylustered ndividuals;a secondary oal was chains fconnectivity.he clique concept mbodiesthe root dea of aggregationy relations ather hanby attributes hat sindispensable o blockmodels. ociometry's thermajor goal (most not-able inbalancetheory) as been to interprethe nterpenetration,r over-lap, amongdifferentypes f tie.We nowdraw five ontrasts etween ociometrynd blockmodels.hefirst woare prompted y the restrictiveature of the clique concept.First,persons ot n cliquesare usuallydisregardedi.e., treated s out-sidetheeffectiveociometricystem). n contrast, lockmodelingequiressearchingor complete artition,uchthatsetsofpersons an be struc-turally mportantegardlessfwhetherhesets resemble liques. Second,evenwhen as in MacRae 1960) cliquesare defined s we define truc-turally quivalent ets i.e., bysimilarityntiesto third arties atherhanby choicesof one another), he clique imagery s retained nd is oftenallowed to limit the interpretation.n blockmodels, n the otherhand,partitioningf individuals s onlyone side of a dual problem;the otheris to interprethe pattern ormed n the one or more networks y thepartition.13The third ontrasts in use of spatial magery.Most sociometry ealswithonlyone typeof tie, sometimesn overalltypeconstructedromseparatekindsof data. Several nvestigatorse.g., Laumannand Pappi1973) eschew he crudity fclique description,referringnstead o viewthe population s embedded n some abstract pace (usually Euclidean).Even ordinalmeasures f similarity etween airscan be convertedntoquantitativemeasures f location nd distance hroughomevariantofmultidimensionalcaling Shepard 1962; Kruskal1964a, 1964b; McFar-land andBrown 973; Arabie nd Boorman 973; Shepard1974). Cliques,as well as manyother ociometriconcepts e.g., connectivity),an thenbe expressedn terms flocations nd distanceswithin he space. In con-trast,blockmodels ssumeno such spatialembedding. resumably ach

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13 Basic to our workhas been our desire to conceptualizemany ideal-typepatterns,each suggestive f a differentormof social organization, nd to perform ests thatreveal which (of all conceivablepatterns) actually exist in a population.


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Social Structure romMultipleNetworks.representunawarenessfmanorhiswork," istinguishingairsof indi-viduals who reciprocate unawareness" the right-handmatrix) frompairs in whichonly one individual ndicated n "unawareness" ie (themiddlematrix).Only an arbitrarilyhosen ubsetof 28 membersf thefullsample (N = 107) is included.Blockmodelingeginswithweakeningnd extendinghealgebraic on-cept of "structurallyquivalent"actors in a network Lorrain andWhite 1971). A self-consistentearchprocedures used to partitionpopulation nto sets of structurallyquivalent ctors blocks.In eachdata matrix, e rearrangeherowand column feachindividual,o thatthemembersfa block aregrouped ogether.We also use theterm lockfor rectangularubmatrixnwhich ies ofthegiven ypefrommembersof one block to members f anotherblock are reported.The contextwillspecifywhich f the twomeaningss intended.)Attentions focusedparticularly n blockswhichhave no, or veryfew, nstances f ties:these are termed eroblocks.Look ahead to figure , in which he28 personsn figure have beenpartitionedntofourblocks. For example, hefirst lockhas fivemem-bers: individuals umbered , 26, 23, 4, 1.) The rowsand columnsforindividuals ave been rearrangedo thateach of the threematrices anbe seenas 16blocksdisplaying iesfrom ne ofthefour ets (blocks) ofindividuals o another. or example,n eachmatrix ffigure theupperleftblockreportsnytiesamong he first ivendividuals; djoiningt ontheright s theblockreportingnyties from hesefive o thesecond et[block]ofsix ndividuals; ndso on.There reeight eroblocksn the eftmatrix,ive nthemiddle ne, and fourn theright-handne. The patternof zeroblocksn thisfigures interpretedn thenextsection,where asestudies re discussed.A blockmodels a hypothesisbout a set of data matrices: t specifiesfor achmatrixwhich lockswill be zeroblocks hen omecommon arti-tion of thepopulations imposedon all thematrices as in fig.3). Ablockmodelonsists f a squarebinarymatrix,alled an image,foreachtypeof tie.Each imagehas a rowand a correspondingolumnforeachblock in fig. , thetoppanel ofthree X 4 matriceshows n imageforeach typeof tie). The orderingfblockswithin heblockedmatricessarbitrary,s is theordering fmemberswithin block.Five ideas are basic to blockmodels. irst,structuralquivalencere-quires thatmembers f thepopulation e partitionedntodistinct ets,each treatedhomogeneouslyotonly n its internal elations ut also inits relations o each other uch set. Second, theprimaryndicator f arelation etweenets s nottheoccurrenceut theabsence ftiesbetweenindividualsn thesets.Third,manydifferentypesof tie are needed toportrayhesocialstructuref a population. ourth, henature f a type

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Social Structure romMultipleNetworks.to-face ontact, ll ofwhosemembers re automaticallycquaintedwithone another.t maybe a contact etworkn which particular ersonmaynever venhave heardofhalfthe others, s in figure . Blockmodelsrewhollypplicable o suchcases.The blockmodelypothesizedor set ofmatricess an interrelatedetofinferencesrom hosedata to an aggregated attern f tiesamong er-tain etsofpersons. he membershipsfthese ets (theblocks)are influ-encedby eachother hrough he ncidence f tiesofevery ype cross hewholepopulation. onds s the term'6 ssigned o thoseblockswhich renotzeroblocks,venthoughmany rmost ftheentriesre blanks.

Sociometrictars and otherconcepts hat tryto capture ndividuals'popularityhave no direct analogue in blockmodels.17egregation fchoices, s between oysand girls n grammar chool classroomsBjer-stedt1956), has oftenbeen noticed n sociometricnalyses.This phe-nomenon an be described y zeroblocks n a blockmodel, ut has ap-parently een investigated nlyfor a priori ategories f persons, uchas male and female.Withreferenceo less extreme orms f segregation,think f zeroblockssuch as those n themutualcontactmatrix f fig.3) as marking heboundaries fchoices y subgroups. ecauseindividualpopularity ependson the size and compositionf the group or unitunder onsideration,t may be arguedthat thisclass of sociometricon-ceptsdependsogically nblockmodelsor some losely elated pparatus)fordelimitingheboundaries f such units.Within he top leftblock ofthefigure mutual ontactmatrix, orexample,t is apparent hatthefirstndividual #9) is mostpopular he is chosenby each of his block-mates) whilethe second ndividual #26) receivesfewer hoices. Thisfact s masked, owever,n theunpermutedata offigure ,which howsindividual#26receivingmore hoices verall han ndividual#9.Images fromReciprocitynd ReflexivityMuch ofsociometrymphasizeshedistinctionetween reciprocatedieand an asymmetricie (Davis 1970). This distinctions used in block-modeling, ut usuallybetweenblocksand not between ndividuals.Ontheotherhand, reflexivitys merely technical uestion n sociometry,whereas n blockmodels he existence f diagonal entriesfora givenimageinvolves crucialsubstantive uestion. n sociometryhereare

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16 Breiger t al. (1975) used the term"1-block" instead of bond.17 Connectivityn a sociometric raphmay depend cruciallyon a singletie betweentwo individuals nd is therefore ard to relateto blockmodel deas (compare also theconcept of a sociometric"bridge" suggested in Granovetter1973). Holland andLeinhardt 1973) exploredthe sensitivity f sociometricmodelsto measurementrrorin sociometry, ut they came to unjustifiably essimistic onclusions.


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Social Structure romMultipleNetworks.mustrequire hat f any one of the refined locksbeingcombined nto acoarseblock s a bond, the coarse block must lso be a bond.Often woblocks are not sufficiento capture ven the grosspatternsn a block-modelfor case study.19Observethateach bond in the C,F pair of imagesfortwo blocks salso a bond n theE,F pair: evenwhen he number f blocks s thesame,one blockmodelmay be a refined i.e., more demanding)versionofanother.n principle, ne can constructn inclusionattice1 of block-models, n a givennumber f typesof tie, beginning ith thoseon twoblocks nd then xtending he latticeto three nd moreblocks. n prac-tice,the possibleblockmodels re far too numerous orthis to be useful.For example, here re 104 single mages with threeblocks,which redistinct nder ermutationf blocks.Formally, hepair of magesC,F is simply more emanding ersion fV,F,but (as will become pparent) the social structures escribed avequite differentualities. Blockmodels rovide frameworkormakingsubstantiveudgmentsnd interpretations;hey supplya set of formalanswers.However, he solutionmustbe proposed, s well as validated, nsubstantiverounds.Two AlgorithmsFor the cases studied o date, up to half the blockshavebeen zeroblocks.Intuitively,t is surprisingo find ny partition f rows nd columns ora set of arbitrarymatriceswhich it blockmodel ontainingmanyzero-blocks,but in principle herecould be many. The number f possiblepartitionss astronomical. . H. Heil has devised an efficientomputeralgorithm orconstructingll assignmentsif any) of men to blocksforwhichthe rearranged ata matrices bey the givenblockmodel. hisalgorithm,alled BLOCKER, is described n detail elsewhere Heil andWhite1974).In carrying ut BLOCKER, one can identify ersonswhoseassignmentto one or more particularblocks in the blockmodel ffectivelyeter-minesthe placement f many other persons.Such individualsmay be

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does not change the information. fter a partition s imposed, the blocked matrixfor a given relationcontains the same pair data as before. The use of blockmodelscan be urged on the purelymethodological roundsthat theypermitflexible ggrega-tion whichretains hispermutationnvariance see White 1974a).19 True for the biomedical and the monasterycases examined below. In contrast,the essentialpatterns, nd thus qualities, n the Newcomb fraternityan be describedby a pairof images (V,F).20 Szasz (1963) provides relevantlattice-theoreticackground.When building sucha lattice, he order of blocks is obviouslysignificantn comparingmatrices.


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o 0z o 0

1 0 0 0C DO O 0 10 i 0 0x yO 0 1 0

1 0p 0 1

0 1N 1 01 1 0 0G SO 0 1 11 0 0 1H T1 0 0 1

1 1 0 1E F1 0 1 1

1 0 1 1V w1 1 0 11 1U 1 1

FIG. 2.-The 16 possible 2 X 2 binary matrices. Grouped into 10 rows, one foreach set that is equivalentunderpermutation f the two blocks. The letter abels usedhere and in the text are applied only to these matrices (never to designate otherimages or to data matrices).


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Social Structure romMultipleNetworks.termedrystallizers:they esembleociometrictars nimportance,otbe-cause of the numberf choices heyreceive utbecauseoftheir trategic,"structural" ositionntheoverallmatrix ollowingrom hehypothesizedmodel.Other ersons re allowedmultiple,lternativessignmentsy theBLOCKER algorithm; hese are termed loaters.They are somewhat nal-ogoustothesociometricsolate,whoreceives eworno choices.21The number fdifferentlockmodel ypotheses,ven with ust two orthreeblocksand just twotypesof tie, is so largethat some otherap-proach s desirablefor nitialexploration. reigerhas developed hier-archical lusteringlgorithmhat partitionsmen ntopossibleblocksandthenfinds blockmodel y inspectinghe data matrices earrangedc-cording o the partition.22t is called CONCOR; its formal ehavior sanalyzed n Breiger t al. (1975); some mathematicalropertiesre de-scribed n Schwartz 1974).The differenceetween he two algorithmss as follows. ONCOR pro-duces from aw data an assignmentf individuals o blocks, nd thencesuggests blockmodel ypothesis.LOCKER demandsa blockmodel y-pothesisndderives rom tany assignmentf mentoblocks hat atisfiesthehypothesisorthegiven et of data matrices.Matrixentriesn anynumerical orm an be directnputto CONCOR, whereas ach tiemustbecodedas either or 1 before LOCKER canbe used.Substantiveudgmentis requiredn both: in CONCOR, on whento stopthe furtherplitting fblocks; nBLOCKER, onwhatblockmodelsonstituteppropriate ypotheses.

BLOCKER searches orpurezeroblocks; n assignments rejectedforblockmodel ypothesisf even one tie thereby ppears n any zeroblock.CONCOR partitionshepopulationn a way thatmay be intuitivelyhar-acterized s yielding harpcontrastsn densities f tiesbetween ifferentblocks.The imagesuggested y CONCOR can be refined y varying hecutoffevelof tie density elow which block is coded as a zeroblock.

745

21 See AppendixA formorespecificnformationbout theassignment fmento blocks.22 Specifically,given k matrices,each of size n X n and reporting ies among apopulation of n actors, a two-dimensionalmatrix (MO) with k X n rows and ncolumns s formedby "stacking" each of the k matricesone above the other,takingcare to preservecolumnordering. Alternatively,he 2nkX n array of each matrixand its transposemay be formed.) The n X n correlationmatrix (M,) of product-momentcorrelation oefficientsmong columns of MO is then formed.This processis iterated MJ+1 is the matrix of correlations mong all pairs of columns of Mj)until a limitmatrix s obtained,whichmay be permuted o yield a bipartitedivisionof the actors (columns) into exactlytwo subsets (blocks) of sizes s and n - s. Arefinement o any desirednumber of blocks may be obtained by creatinga newarray Mo with k X n rows and s columns,k X n rows and n - s columns,etc.In theirdetaileddescription f the algorithm, reigeret al. (1975) includeextensionsand comparisons with multidimensionalcaling and hierarchicalclusteringmethodsin the literature.We wish to thankA. Tagg of the University f Surreyfor callingour attention o the anticipation f this algorithm n McQuittyand Clark (1968).


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AmericanJournal f SociologyThe imagerequired y BLOCKER canbe refined y followinghe nclusionlatticefor mages.In the theory nd interpretationf blockmodels,either LOCKER norCONCOR is indispensable. t is possible,though aborious, o findandtestblockmodel ypotheses y simply nspectingmany permutationsfthedata matrices.FIVE CASE STUDIESThis sectionreports ive case studieson whichwe testedblockmodels.Four concerndults nwork ituations; nlyone (the Firth-Sterlingor-porationmanagement)ncluded ll of thepopulation's elevantuthorityfigures.wo are panel studiesusingat least fourtime periods.Four ofthepopulations re primarilyace-to-faceroups f fewer han20 mem-bers, nd one is a subsample rom larger ample N = 107). Four areexposed onormal urnovernmembers. llfive nclude ystematic ata onindividualttributes. ll thepopulations re twentieth-centuryndAmeri-can. This section oncludesby illustratinghe use of blockmodelswithovertime ata fortwoof the studies.For four four case studies all but the biomedical esearch etwork),detailed ndependentnalyses re presentedn theoriginal tudies f theinteractions. hese discussions ave informedur search forblockmodelhypotheses sed as inputto BLOCKER and are also used to validatesomeof our findings.We cite herefivegeneralfindingsrom he case studieswhich llustrate his validation f the blockmodelsnd also additionalinsights btained. 1) CONCOR, a mechanicalearch lgorithmotdepen-dent nourperceptionsf the"meaning" fthe data,produces partitionof individualsntoblockswhich s equivalent t thethree- r four-blocklevel ofrefinemento the dentificationfmajorgroupingsn theoriginalstudyof the interactions,n all fourcases for which uch comparisonsmaybe made (see results eportedelow nd in Breiger t al. 1975). Thisstrong indinguggests hevalidity f ourapproach o networkggrega-tion. (2) Even thoughmany of our hypotheseswhichare testedbyBLOCKER are informedy ourreading f theoriginal tudies, lockmodelsconstructedcross severaldifferentypes f social relationn each studyarevaluable nportrayingheoverall ocialstructure.3) BLOCKER parti-tionsforcoarse (two- and three-block)models gree withthe partitionsindependentlyerivedby CONCOR. (4) In each case study,we suggestadditional nterpretationbased on a finer artition f individuals ntoblocks nd/or considerationf thepatterns f relations rought ut intheblockmodel)which oesbeyond he analyses f theoriginal ccounts.(5) The case of thebiomedical esearchnetwork,orwhich a detailedanalysis fthe nteractionsmong hepopulation'smembersoesnotexist,746


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Social Structure romMultipleNetworks.illustratesheutility fblockmodelss an exploratoryrocedurensearch-ing for tructure hen he only vailable cluesconsist freportsf inter-action mong airs f ndividuals.A BiomedicalResearchNetwork

Data.-Griffith t al. (1973) identified73scientiststudyingheneuralcontrolfhungerndthirst. fthese, 07respondedoGriffith'suestion-naire. In morethan half the possible nstances as fig. 1 shows) onerespondent asunaware f another,s canbe expected n an open popula-tion.Blockmodel.-In order to apply BLOCKER to these data, each entryin thematricesmustbe coded n binary orm. nly a reciprocatedhoiceOnlmutual ontact"was regardeds strong nough y itself opreventzeroblock; thussymmetrichoices on mutualcontactwerecoded "X"and the restcoded"blank.""Unawareof" is notlikeother, ubstantive,types f tie, o unreciprocatedhoices n it were reated s a distinctypeof tie, withreciprocatedhoicesconstituting third ype.A blockmodelhypothesis,tated n the top panelof figure, for hese hree ypes f tiewas developedby systematicallyxploringntuitively lausible block-models.At the left n figure is thepartition-theunique assignment(definednAppendix )-of mento blocks hat LOCKER yieldswhen hedata are tested gainstthehypothesis. he bottom anel showsthedatamatrices ith ows ndcolumns locked nconformityith hispartition:inspectionhows heblockmodels confirmed.Interpretation.-Interprettheblockmodeln status terms. Blocks areordered romhigh to low status.) On symmetricmutual contact,"thebottom woblocks reconnected eithernternallyortooneanother,ndthe bottom lockhas no connections ith nyblock, ncludingtself. hebottom lock belongs o thepopulation nly n thecultural ensethat thas no asymmetricnawarenessf theblock that s obviously he eadingsetof researchers. o blockhas asymmetricnawareness ies to the topblock; yet thatblockhas asymmetricnawarenessntries o each of theothers;we might all this snobeffect.Further ests.-CONCOR was applied (not shown here) to the datamatrices or"mutualcontact" and "unaware." ts first plitof the 28menyielded partitionimilar o BLOCKER'S: thefirst wo groups n thelatter ecameone group, nd the ast two a second, xceptfor wo nter-changes.After womore plits, he partitionwas

(1 4 9 23 2 10 26) (24 19 12 14) (6 7 28 11 15 13 16)(18 22 3 5 8 17 20 2125 27). [1]The extreme locksare close to those of figure ; themiddle two are

747


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IN~~ N4 N N N I ~NN NN N

o I I0

0000 1 - - -___ -- ------ 0m0 I I I N |

!~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0-=> ~~ ~ I IC I) I; I - Ft

I) ID I) I ID tI Ift0 j I I I O

I I- - - --I - - - -M~~~I- ~~~~~----- ----- -- - --I N IN I I I~~~~~~~~~~~~~~~~~N I N I I I I~~~~~~~~~~~~~~~~~2 I N I - - -I I -4 U0000 0 IN~~~~C-0C) tI N4j WC. t0 I.tC V GC4 ' t )oC)V4 t b,-I~~~~~00U I~~C- 1 q C 4 4C -I I4 -1V qV _ , 4C,


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Social Structure romMultipleNetworks.moremixed.For all three ypes ftie,we constructed blockmodel romtheCONCOR artitiony defining zeroblock s anyblockwith ess thanspecified ractionfthe veragedensityfentries or hegiven ype ftie.For any cutoffraction etween1/10 and 1/2, theresultinglockmodelwasvery lose tothat ffigure .Each oftwoadditional rbitrarilyhosen etsof 28 persons not over-lappingwith achother r with hefirst)wasthen lockmodelednexactlythe sameway,again usingCONCOR. The tworesulting lockmodels ereclose to each other nd to theblockmodeln figure . Although hefullsampleof 107 had notyet been simultaneouslyartitionedsee Breiger1976), we inferredhat n the arger tudyboththeblockmodel atternand theblockmemberships ouldcorrespond ith the resultsreportedfor hese ubsamples. veryonen thenetwork nows hetop dogs (blocka), butalthough hese opdogscollaboratewith omeresearchersn lowerstrata, hey ppear to remain gnorant f most essermortals.Membersof block b appear to be very activeresearchers,ware of one another.Unlike hose n the bottom lock,membersf thethird lock c) are notjust on the sidelines; theyfrequentlyee at least some researchersnhigher locks.Clearly, hecompletenterconnectednessf a face-to-facegroup rother ommunitys notnecessary or hecoherencefthis ocialstructure. either heseblocksnor more mportantly)he globalpatternof relations ver the networkwould emergefrom ounts of individual''popularity"rfromonventionalliqueanalysis.

A Monasteryn CrisisData.-Sampson's (1969) detailed accountof social relations n anisolatedAmericanmonasteryhouldbecome classic.During 12-month

period,muchof it in residences an "experimentern vision,"Sampsondeveloped n extraordinaryariety f observational,nterview,nd ex-perimentalnformationn the monastery'social structure. oward theend ofhisstudy, majorblowup n themonasteryulminatedn a massexodus fmembers yexpulsionndresignation.Sampsondefined our ortsof relation-Affect,steem, nfluence,ndSanction-on which espondentsere o givetheir irst hree hoices, irston thepositive ide and then n thenegative. igure shows hese hoicesforhis fourthimeperiod,before he blowupbut after newcohort fnoviceshad settledn. For example, ovice#3likednovice#1best, andtherefore 3 (representingighest hoice) is enteredn theintersectionof the #3rowand the#1column f thetopleftmatrix an entry f 2means econdchoice nd a 1 means third hoice).We assigneach monka number rom to 18 (roughlyn their rder f oining hemonastery-thesameorderSampsonused). We give each of the eightpositive nd

749


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Americanournal of Sociologyill 500 110 100Oil 110 050 050

LIKE ESTEEM INFLUENCE PRAISE51 1132 1 I 1 1132 1 I 321S I II I I91I1 312 I II1 3 21 11 I I 1 132 I II I6 112 31 I II1 32 1 I 112 3 11 I 1132 1 I4l3 12l I 1 12 13 1 I 112 13 1 I 112 13 1 I I11 12 31 1 I I 1 23 I I I 32 1 I I I I 3 21 SI I8 1__123-_ ...... I.. . 1 _221 l.....I I--- 1 - l 1 - -----? I- - I I-- ..211 1 -- -- I..----12 1 1 32 1 1 I 1 321 I I1 1 32 1 1 II I I Ii I 11 2 13 1 11 312 I II1 12 3 11 II1 12 3 lii2 1 123 11 Ill 21 3 I II1 123 ii 1 123 ii I14 113 2 I I I 1132 2 I I I 1132 2 I I I I 33 2 11 I15 I 12 3 1 I I I I 132 I I I I 32 1 I I I I 132 I I7!1 11 3 21 I I 113 121 I I 11 3 21 I 1 I 3 121 I.1? .. .. . _ _2_.l......l I I ?.. . 11 3 22_.l----..I I-- -- - .- -2.l.. ----.. I--- -- 2 --.13 12 I 1 1 31 13 11 2 1 1 13 1 1 2 1 1 13 2 1 I I3 I I 3 12 121 I I 3 12 111 I I 3 12 1 I I I 3 12 1 I17 1 Il 1 231 1 Il 112 3111 Ii 1 231 1 I I I

111 ill 101 ill110 110 110 i11ANTAGONISM DISESTEEM NEGINFL BLAME

io! TI I TIT I I IT T T T I5 I I I I I 1321 I I I 1321 I I I II 1 3211 1 I 11 321 1 Ii 1 321 1 I I I61 1 12132 11 11 3 122 11 I 3 1211 1 I 3 112114l 1231 I I I 1 231 I I I 1 231 I I I I 32 11 I11 I I 13 I 2 1 I I 13 11 2 1 I I 3 I 121 I I 1 I 231-a I--- -- _ 1 - .-2... -- --- ---I ?- 1 _..22 ---? -- ? 3- - 12---.. I-- -- -I--- -- 1- 221I12 I I I I I I I I I I I I I I 2 I 131ill1 1 2311 II 1 23 11 112 I 11 31 1 2 1 1 3112 1 3 21 Il II1 3 1 112 11 3 1 12 II I 13 114 l 3 21 1i I 22 1 13 111 I 2 I 13 111 I 32 1 Ii Ii5 1 1 I 132 I I 31 1 1 2111 I 3 I 121 I 1 I 132 117 1 23 11 I I I 32 21 1 21 1 I 32 21 1 21 1 I 12 I 1 3 II ? I ?-- --- 112.1. -- _? --? ?- 1.2211 --- 22 ?1--- -- 1 - l I---? ?_ ? ?--- 112221I13 1 2 11 3 I I I 3 I 2 Il I I 2 11 3 I I I I 1 I 2313 1 23 12 11 II1 23 11 I II1 23 11 I II1 3 121 I I17 1 31 21 I I I 32 11 I I I 32 11 I I I I I I18 12 ?--2 -- -- -I...... I I .. 22_31 ..... .. ... I I--..122. 1- -- -? I----. I I-- -- -I-- -- -I..---- I

FIG. 4.-Blockmodel for the monastery, ime 4: images and data matrices. n thelatter,3 stands for first hoice, 2 for second,and 1 for thirdon each type of tie.Source: Sampson (1969).negative elations distinct ame. n all of our case studieswe use "Like"and "Antagonism"orpositive nd negative ffect,espectively.Blockmodeling.-CONCORwasappliedto all eightmatricesffigure23This algorithms notexplicitlyoncernedwith ocating eroblocks;dataof all three hoicerankingsreprocessed y it. After wo plits heparti-tion nto hree lockswas

(10 5 9 6 4 11 8) (12 1 2 14 15 7 16) (13 3 17 18). [2]This partitionwas then mposed n theeightdata matrices the resultsare shown nfig. ). We assumed hat n a population f 18 persons, nlythetoptwo hoiceswere trong nough o invalidate zeroblockestablisha bond), so each blockwhich containedno entrygreater han 1 was

750

23 Slightlydifferent esultsare reported n Breiger et al. (1975) because they, likeSampson, summed plus and minus entries o combine the eight typesof tie into fourmatrices orCONCOR input.Our choice s perhapspreferable ecause it makes less strongmeasurement ssumptions; see also n. 24 below.


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Social Structure romMultipleNetworks.representeds a zeroblock. he resulting lockmodels shown n thetoppaneloffigure.To apply LOCKER, which equires inarynputdata, valuesof2 and3were odedas 1, therest s 0. Whenthe blockmodelhownnfigure wastested n thedata using LOCKER, theunique ssignmentoundwasexactlythatderived rom ONCOR!Direct nspectionffigure confirmshisfind-ing note that hird hoices, oded s 1,should e ignored).In the imageforesteem, he threeblocks are ordered n a completelinearhierarchy, hich s certainly lausible n a monastery.he bottomblockhas a bond to itself nd to each of the higher lockson everykindof positive elation;yet it also has reciprocatedonds withboth of theotherblockson all four negativerelations. ikingbonds are universalwithone exception: hesecondblockdoesnot match ts esteem ondforthe firstwitha likingbond. The two top blocks exchangeno positivesanction "praise" in fig. 4); however, he first lock, top on esteem,concedes nfluenceo the econd.Refinementsnd interpretations.-Ife return o theCONCOR approachand raise the cutoff ensity orzeroblocks o half the average density,theresultinglockmodels

1 0 0 1 0 0 1 1 0 1 0 00 1 0 0 1 0 0 1 0 0 1 00 1 1 0 1 1 0 1 1 0 0 1Like Esteem Influence Praise

0 1 1 0 1 1 0 1 1 0 1 11 0 1 1 0 1 1 0 1 1 0 11 1 0 1 0 0 1 0 0 0 0 1Antagonism Disesteem Neg. nfl. Blame

The Like image s identicalwith Esteem, nd DisesteemwithNegativeInfluence.As in thepreviousblockmodel,he top two blocks exchangenegative onds of all four ypes,but there s only one kindof negativebond from he bottomblock to the second block.The concrete ocialstructureuggested s much the same foreitherversion:a top-esteemedblockunambivalentlyositive oward tself, n conflict ithbutconcedinginfluenceo a second,more mbivalent, lock, o whichs attached blockof osers.Forthis mallpopulation, urtherefinementf thepartition y mechan-ical application f algorithmss not justified, ut hints n Sampson'shistoricalccount nd inspectionf the matrices uggested refinement751


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AmericanJournal f Sociologyof thepartitionnto fiveblocks,with ach of thetwo eftblocks n [2]being plit s:(10 5 9) (6 4 11 8) (12 1 2) (14 15 7 16) (13 3 17 18). [3]This s theorderingfrows nd columns sed n figure. BLOCKER, appliedas before, erified hatthispartition rovided heunique assignmentora certain lockmodel; he question s: Does theblockmodelmake sense?Consider irst he esteemmagefrom LOCKER in thisrefined lockmodel(the ines howdivisionsnto heblocks f [2] ):a b c d e

a 0 1 0 0 0b 1 1 0 0 0c O 1 1 0 0d 0 0 1 1 0e 10 1o 1 1(Recall thatthis magefits hedata with 's and 3's coded1 and all otherentries .) Name theblocks from op to bottom nd fromeftto righta, b, c,d, e. In brief,within he old topblock, is now a hanger-ono b;within heold secondblock, defers o the coreblockc. It was c, butnotd, that steemed he nitial op block, nd then t only esteemed he core(b). Moreover, t was the hanger-on,, who conceded nfluence o theinitial econd block, but only to its core, c. (The old bottomblock oflosersremains he same; it [e] esteemed nly thehangers-ona] of theold topblock.)The other mages n the refined lockmodel an be readfrom he datamatricesn figure . All fourpositivemages onfirmhehangers-onnddeference tructureswithinthe former locks. There are three morelikingbonds thanesteembonds,but exceptforthis factand thespecialasymmetryn esteem nd influencemongthe top blocks already men-tioned), the fourpositivemages re almost dentical. he refinementfnegative onds s simpler: n each of thefournegative magesthere rereciprocal onds betweenb and the bottom hreeblocks (c, d, e) butalmostnoneto b's hangers-ona). And the oser, , though eceivingmanyorall types fnegative ondsfromheother our locks nd reciprocatingto botha and b, sends no negative ondto d; however, sendsall fourtypes fnegative ondtod's masters c).

Comparison ithSampson's nalysis.-Boththe blockmodelsorthreeblocks and that forfiveblockscan be comparedwithSampson'sownanalysis. ampson 1969, p. 370) positeda definitelique structure orthe monasteryt timeT4, on the basis of sociometricraphs drawnfrom hedata shownnfig. ), hisownobservation,nd his interpretationof events nd personal ttributes. is YoungTurksare led bymonks2,752


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Social Structure romMultipleNetworks.1, and 12 (in descendingrder f leadership),with14, 15, 7, and 16 asfollowers. is Loyal Oppositions led by 4, with5 a popularmember,and 11 as members,nd 9 less fully ttached.He saw threeOutcasts:3,17,and 18. The other hreemonks 10, 8, and 13) waveredbetween hetwo cliques,whichhe described s being n intense onflict.BothCONCOR andBLOCKER agreed n the split ntothree locks shownin fig.4). Sampson'sLoyal Oppositions wholly ontained n the firstblock; theYoungTurks are exactly he menin the secondblock; theOutcasts re wholly ontainedn the thirdblock.Sampson'sWaverersand 10 are in the Loyal Opposition lock,whereasWaverer13 is in theOutcast lock.Our refinedive-blocklockmodelplits heYoungTurksexactly s didSampson,with1, 2, and 12 as leaders;however,hefirst woblocks plittheLoyalOpposition ifferently,s well s enlargingt.Monk5 is changedfrom ampson's socio-emotionaleader" (p. 360) to membershipn theLoyal Opposition's angers-onlock.Sampsonearlierobserved p. 322,n. 32): "His [monk 's] circumspectloofness romnterpersonalonflictsserved o preserve is relatively ighranking n mostmeasures hrough-out the study,but as a consequence, is influencen otherswas morethatof a detachedrole modelthan a framerf opinion r action." AndWaverer is in the eadingblock (b) of theLoyal Oppositionccordingtotheblockmodel.Thepatternfrelations ivennfigure's blockmodel theeight mageson threeblocks accordswithSampson'sbasic contentionf a fight e-tween heLoyal Oppositionnd theYoungTurks.The blockmodeleportsstrong mbivalencewithin heYoungTurks simultaneousositive ndnegative onds f many ypes but nonewithinheenlarged oyal Opposi-tion;all ofthesereports ccordwith he detailed tatementsn Sampson'sanalysis.The blockmodelmakesthreefurthermportantssertions: heYoung Turksare conceded opposition n a linearhierarchy f the threeblockson influence, hiletheenlarged oyal Opposition s conceded opspot na hierarchynesteem. hird, hebottom lockhas but one nternaltypeofbondwhich s negative; t also receives ike bonds from bove,as wellas thenegative ondsthat tsmemberseturnn kind:this mpliesthatthebottom lock s a meaningfulocial unit n a sensedifferentromthat fSampson'spseudo-group."Bits of evidence n Sampson'sdetailedtextual ccountsupport hese

furtherssertions; or xample,monk13 nominates,nd is the onlymanto vote for,3 as chairman f an importantmeeting p. 354) 24 Our

753

24 Monk 13 is placed in the Loyal Oppositionby Breigeret al. (1975) because ofthe way they apply the Breigeralgorithm;see n. 23 above. Yet when they did amultidimensionalcaling analysis for comparison,using Kruskal's MDSCAL algorithm,


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AmericanJournal f Sociologyassertions ontradict ome of Sampson's summary tatements,ut thisfact per se is not as importants the fact that blockmodelingas per-mitted s to move beyond he picture ampsondrew-beyondthekindsofinferenceshatare technically easible rom ociometric iagrams. heblockmodel n fiveblocksnecessarily iffers rom ampson's onclusions;it analyzes nits iner hanhis factions ut ignores hedistinctiveehaviorof individuals hat he emphasized.Until the matricesforearlier timeperiods re takenup below, hemainsupport orthe refined lockmodelis the consistencycross mages f the patternwithin achfaction.One week fter heperiod o which hesedatarefer,n explosiontarted.The Superior nd theNovice Master, ogether ith he handful f seniormonks none of them ncluded n the sociometric opulation f the 18monksntraining), ecided n their egular eview rocess o expelmonks2, 3, 17, and 18. The reasons ivenby the senior taffwere,for he atterthree, hatthey were "too immature" nd had "personality roblems,"whilemonk was considered too independent,uestioningnd arrogant"(Sampson 1969, p. 373). Only monks1, 2, and 3 of the 18 had beentocollege ndwere andidates o be full lericalmonks;theywereolder ndrestless venunder hedrastically educed iscipline heir eniors ad insti-tuted yearearlier, efore heir rrival nd thatofmonks 0 through8.Almost t once,monk voluntarilyeparted. hen,within week,monks16, 15, 14, and 7 left,n thatorder.A fewdays ater,13 and 8 left, lsovoluntarily. month aterstill,monk10 left.Of the sixremainingromthe18, notethatfourhad been there n the old days before hechange fdiscipline,nd fivewere n the Loyal Opposition. puzzle n bothSamp-son'spicturend the blockmodels whymonk12 remained. therwise heblocksfoundnbuilding herefined lockmodelrom ure ociometricatafitthe initialdepartures erfectly:monk 1 followed is blockmatem-mediately,nd the nextwaveof fourwas precisely he blockasserted obe their ubsidiary; nlyafter hemdid monk13 leave, and he precededthe wofromheLoyal Opposition.Cliques and Strata n the Bank WiringRoom

Data.-Homans's (1950) classic account of the Bank Wiring Roomsuggested six-block lockmodel;25 nly after ssessing his hunchwillwe applythe twoalgorithmsn theusualway. The originalmonographictreatmentin Roethlisbergernd Dickson1939; hereafterbbreviated s

754

monk 13 was placed substantially loser to other Outcasts, a placement consistentwith our presentblocking.25 This is a slight simplificationf an earlierblockmodelon seven blocks, reportedin White (1974a). Inspector 13, a separate block there,has been combined withthe third block (Wiremen W2 and W5).


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AmericanJournal f SociologyAntagonism,ut three thers eport ontext-specificypes:"Games" s thedesignation or kind of affectionateorseplay including pinging" heupper arm); "Help" (with production asks) is our name fora secondtype; "Windows" reports hronicquarrels over openingwindows. heobservers aw these as stable interaction atterns stablishedwhen thesection ad settled own. n all typesbutHelp,eachtie s reciprocated.manneed not "send" any ties of a given type.When applying LOCKER,eachtiereporteds present as coded 1."In addition o two nspectorscalled hereafter1 and 13, afterHomans),therewere nine wiremen numbered romWl to W9 by positionn theroomfrom ront o back) and three oldermenSi, S2, S4). Layout wasfixed:W1-W3 wereassistedby the solderman t the front f the room,Si; W4-W6 by S2; and W7-W9 by S4; I1 and 13 shared nspectionfbanks rom hemiddle eam.Interpretingll the kindsof evidence,R-D, followed y Homans, on-cluded that thesocialstructure as basedon twocliques, ocatedmainlyin the front nd the back of the room, espectively.hey listed he mem-bersin the front s Wi, W3, W4, Si, and I1, and those n the backas W7, W8, W9, and S4; but theyalso saw nuanceswithin ach groupand discussed ther ndividuals s fringemembers. t other laces n theiraccounts, heyemphasized hatindividuals ave differentialtanding rprestigen the informalocial structure. o us, theiraccountstronglysuggested hangers-onatternwithinachcliqueas wellas strata uttingacross he liques.Developing blockmodel. Games ties weredescribed s friendly,ndforboththem nd Like ties the hangers-onatterntheE elementwithinthe clique) seems ppropriate. ut Gamesties weremuchmorenumerousthan Like ties,so it seemed ikelythere houldbe moremenin a coregroup n Gamesthan n a coregroupon Like. Like and Gamesbetweenthem husshoulddifferentiateach clique intothreeblocks.Antagonismwas concentratedn, and within, he set of menwhomboth R-D andHomans udgedto be, at best, marginal o the cliques,and whowouldappear n thebottom locksof thetwocliques.These three ypesof tiesuggested blockmodel or ix blockson Like, Games, nd Antagonism;it was not clear what pattern o expecton Help or on Windows, xceptthat the atter houldbe concentratedn thebackof theroom.This ap-proach uggests otonlythe magesbut also themembershipsf at leastthehigher locks.The initial lockmodel as adjustedby inspectionftheactualchoices;it is shownnthe top paneloffigure as thefirst hreemages.The data,also shown n figure , fit this blockmodel: LOCKER indeedyieldstheunique ssignmenthown see AppendixA). Two important oints hould756


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Social Structure romMultipleNetworks.be made. This partition s consistentwith indeed a refinementf-Homans's liques.The partitions(W4 S1 W3) (Wi 1i) (W2 W5 13)(W8 W9) (W7 S4) (W6 S2). [4]Furthermore,ach of the three mages s close to our first uess for t.Nested hangers-onatterns ver Like and Games, foreach clique, areshown, ogether ith ne symmetricond oining hecliques.AllAntago-nism ies are within r with hebottom lock n eachclique; in addition,the front lique'smarginalmen receivemostof thenegative ondsfromboth the front nd the back cliques.The bondsin the last two imagesin figure (Help and Windows)were imply ead fromhe data matricesupon which he givenpartitionwas imposed.Testing the blockmodel.-When ONCOR is applied to all fivedatamatrices, he first plit s exactlybetween he first hreeblocks and thelast three.When ach of thetwo ets of blocks s routinelyplit, he resultis (W4 Si W3 WI I1) (W2 W5 13)(W8 W9 W7 S4) (W6 S2 , [5]againperfect onformationoboundariesn the full ix-block lockmodel!CONCOR first istinguishedetween hecliques and then,within ach setpositively ound ogether,istinguishedtrata.A blockmodel n thesefourblocks anbe aggregated rom he oneon six blocks n figure by takingthe ogicalunion fthe first worows nd the first wocolumns, nd thendoing ikewise or hefourth nd fifthows nd columns.One can also emphasize hedifferentiationnto strata s the overridingfeature, ather hanthe split between liques. Supposewe combine hefirst nd fourthlocks f figure , thesecond nd fifth,nd the third ndsixth.Whenunions f the correspondingows nd columns re computed,thefive mages ecome

L G A H WI I 0 1 1 1 0 0 1 1 1 1 1 1 11 0 0 1 1 1 0 0 1 1 10 1 1 10 0 0 1 1 0 1 1 1 1 1 1 1 1 1

Whenthisblockmodel as applied by BLOCKER to thefivedata matrices,we obtained single olution: hetopblock s theunionof thefirst ndfourthlocks ffigure, andso forth.The analyses f the BankWiringRoom n R-D and inHomansare thebasis fortheblockmodel nd so can hardlybe cited as independentvi-dence.

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AmericanJournal f SociologyTest based on reasons for work stoppage.-In the original report,Roethlisbergernd Dickson (1939, pp. 428-32) stated that the bankwiring epartmentllowed the nine wiremen o claim allowances orun-usualwork toppages beyond heir ontrol."Wiremen requentlylaimedmore ime llowances han werenecessary contrary o the ntent f thewage-incentivecheme) because theywere willing o trade some loss ofincome for some gain in security expressed s uniformityn outputcurves).Each time wireman laimed time llowance, e was supposedto give the reason for the delay. R-D coded 12 classes of reasons ndthen cross-tabulatedhe claims by reason and wireman.Generalized t-titudes eed have little elation o specific ositionn a particular opula-tion, ut context-specificttitudes uch as thesereasons houldbe affectedby one's position nd should,hence, esemble hose fothersn equivalentpositions.In thiscross-tabulation,ach wireman as a column nd each reasonrow.We usedCONCOR to splitthewiremen n the basisof their espectivecolumns fcounts.27he result s

(WI W2 W3 W4 W5) (W6 W7 W8 W9). [6]It is at once apparent hat the split s precisely hatbetween he blocksofthe front lique and thoseof the back (see [4] or [5]). In particular,the marginalmembersW2, W5, and W6, whomHomansdid notplace, areeachgroupedwith hewiremen rom heappropriatepperblocks.In only twoof our case studiesdid the populationhave specific obassignments,nd only the Bank WiringRoom also had fixed ocations.Let us return o the ix-block artition iven n figure . We alreadyknowthat ointmembershipn a block follows either rom aving he ame oneof thethree obs nor fromhavingdifferentobs. Sayles (1958, a mono-graph n industrial orkgroups) criticized he earlier iteratureorgivingtoo much ndependentmportanceo dynamicsn smallgroups s such;thekeysto social structurend process, e argued,werekindsof ob andthe flowof work mposed mong obs. At first ight, t seemsthat ouranalysis provides counterexample; owever, lose examinationhowsthat the split between liques is as important determinantf the sixblocks s is thedivision mong trata, nd the cliquesclearly merge romthe ayoutof theroom. imilarly,or ll types f tie exceptAntagonism,the pattern fbondsbetween locksdepends n theclique splitas muchas onstrata.Newcomb's econdFraternity

Data.-Newcomb (1961) analyzed two experimentsn which17 pre-viouslyunacquaintedmaleundergraduatesivedtogethern a fraternity-

75827 See AppendixB for further etails.


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Social Structure romMultipleNetworks.stylehouse, xpenses aid.They were ubjectto observationnd requiredto supply manyself-reports,ncluding complete ankordering f theother 16 by "favorableness f feeling" uring ach of the 16 weeksoftheexperiment.ewcombreported nlymeasures f association ortherankorderingswhichcontributednly ndirectlyo his accountof thesocial-psychologicalynamics).Herewe take polar types f tie (Like andAntagonism),bstracted rom he rankorder for the last weekof thesecondexperiment,nd suggest blockmodel orthreeblocks.The indi-vidual-level ata weredescribed yNewcomb's ssociate,Nordlie 1958),whodeveloped n independentnterpretationhatis moreexplicit hanNewcomb's.ndividuals re numbered s in Nordlie'sAppendixA, as areranks from formostfavorable o 16 for east; no tiespermitted). Theparallelfirstxperiment illbe discussed n Part II.)Developing blockmodel.-In a population f this size, the top tworankswerebelieved orepresenttrong riendshiphoices;thebottomwo,strong ntagonism. here is a scapegoat n thisgroup (man 10), whoreceived ne of the bottom hree hoices f eachof theother16 persons.For application fBLOCKER, the toptwo choiceswerecoded as Like ties;thebottom hree, s Antagonismies. There seemedto be a top groupthatdisdained heothers, o the V,F blockmodelfor twoblocks) washypothesized.he resultwas a split f men ntoblocksforwhich ike andAntagonismatisfy heblockmodel;men 13, 9, 17, 1, 8, 6, and 4 were nthetopblock.This is theonly plitthatyields solution, nd it stipulatestwofloaters men2 and 5) who can be placed separately r togetherneither lock see alsoAppendix ).An obviousrefinements a splitof thebottomblockinto (1) losersand (2) a stratum otinternallyntagonisticnd ambivalentlyrientedtothe opblock f even: theblockmodels

1 0 0 0 0 11 1 0 1 0 11 1 1 1 1 1Like Antagonism

Developing a blockmodel.-BLOCKER, using this model,yielded thefollowing: secondblock (men 7, 11, 12, 2) and a bottom lock (14, 3,10, 16, 5, 15); the top block is unchanged, ut the two floaters renow morerestricted.CONCOR was then pplied to the complete ankingseach rank treatedas an integer) o yieldthreeblocks.These were denticalwiththe threeblocksBLOCKER yieldedfrom he top twoand bottom hree hoices.Todefine he blockmodel,we state a cutoff ensity the highest veragedensity f "choices" n a blockthatpermitt to be coded as a zeroblock

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American ournal f Sociologyfor that type of tie)28 With the top two ranksdefined s Like choicesand thebottom hree s Antagonism,or ny cutoff ensity elowone-fifththe averagedensity n that type of tie, the resulting lockmodels thesame as the one presentedbove. When the cutoff ensity s raisedfur-ther, he first onds to disappear re the bottom lock'spositivebondtoitself nd its negative ondto the secondblock.Comparison ftheblockmodel ithNordlie's nterpretation.-Nordlie's(1958, pp. 67-77) study f "sugbrouping" ields n assignmentf men to"clusters" orweek 15 that is entirely onsistent ithour blockmodel.For each pair of men,Nordlie computed he rank correlation oefficientof thechoices entby each to the 15 others, xcluding hemselves. hismatrixof "intra-pair greement"was then clustered s describedbyNordlie 1958, pp. 70-71) to produce ubgroupsfnonoverlappingem-bership nd a residueof men assignedto no cluster.Nordlie discoversfive ubgroups orweek15 ofthe second xperiment:1, 5, 6, 8, 13), (2,4, 17), (7, 11, 12), (3, 14), (15, 16). Men 9 and 10 are not assigned.Each of the five subgroupss containedwithin single block of ourthree-blocklockmodel,f the two floaters men 2 and 5) are allowedeither f their ssignments.Nordlie does not distinguish ike and Antagonism,nd he does notgo on to examineand interpret oncretepatterns f ties among hisclusters. he blockmodel bove suggests combinationfbalance theory(in some form)withhierarchys the forces t work.Management onflictna Company

Data.-This section develops a blockmodel n eight types of tiespecificallyelevant o the business ctivities f the16 top managers in1958) ofFirth-Sterling,companywith bout 2,000 employees roducingspecialty lloyandabrasives roducts or ndustrial se (for fulldescrip-tionof the data, see White1961). The blocksand patterns itwell withindependent vidence White 1960, 1961) of chronic onflicts ver re-search nddevelopmentfnew products the primemanagementssue na companywhoseproduct ine turned ver everyfewyears n the era ofthe R&D fever).Managers renumbered s in theoriginal eport White1961, table 1): 1-S are R&D managers;6-8, sales managers; and 10,production anagers; 1and 12, xecutives; nd 13-16, op taffmanagers;in addition, , 9, and 12 are vice-presidents,nd 11 is the president a

760

28 It would not be satisfactory o use average rank order in a block in place ofdensity of choices. The former measure averages Like and Antagonism choicesnumerically.Ambivalence would be excluded; in contrast, blockmodel permits agiven mageto containbotha bond on Like and a bond on Antagonism.


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Social Structure romMultipleNetworks.man of elite social and business tanding roughtntotheailingcompanya fewyears arlier).Developing blockmodel.-With uch ties, there wereno precedentsforhypothesizing blockmodel.ONCORwas appliedto thedata matricesfor all eight detailed typesof relation the seven reported y White[1961,p. 192], with hoices n thefifthype-RespectforKnowledge ndRespect forDecisions-separated nto two matrices).The partitionntothreeblocks found29 as

(11 9 13) (2 4 6 7 8 1 15) (5 10 12 14 3 16). [7]Since each choicehad been carefully onsidered y the respondents,the cutoff ensity hosen forzeroblockswas zero (i.e., a single choicein a block prevented ts being coded as a zeroblock).The top panel offigure reports ur blockmodel n three mages:SimilarBusinessPolicy,Personal Friendship, nd Uncomfortableness.he blockmodelwas ob-tainedby imposing heabove partition ntothematrices orthese rela-tions. he bottom anel hows heresultinglockedmatrices.Obviously-

110 000 011110 111 101101 011 000SIMILAR POLICY FRIENDSHIP UNCOMFORTABLENESS

11 X I I I X XI xx Igl I I I I I I I I Ix II31X I XXI _ I I _ _ II IxIXx2 IX I XX I I I XIX I I I I XX I4 I I I I I I X I I I I I6 1 1 1 1 1 I XX XI I I x I I X I7 IX I X X I I I I XX I I I X I I8 IX I x I I I I xx XI I I x lx I51 I 1 X I I I I x XX I I IX I IXXX I5 1x_ I XX- I I I-X I IXI - I -1 IlXx I I I I X I I I I I Ilo IXXX I I I I I I I I I14 1 1 1 1 1 111 1 1113 I X I I I I I I I II16 I- ? I ?xI I I_ _ _ __ _ ?FIG. 6.-Blockmodel for Firth-Sterlingmanagement: images and data matrices.Source: White (1961).

761

29Following the usual procedure, ll eight 16 X 16 data matriceswere first stacked"into a 128 X 16 array. t was then foundthat two of the 16 columns n this array-those for men 8 and 16-consisted solely of zeroes. As theproduct-momentorrelationis undefinedfor vectors with no variance, these two columns were removed andCONCOR was applied to the remaining14 columns. Men 8 and 16 were then placedarbitrarily nto blocks.When BLOCKER was applied to test fig. 6's model against thedata shown there, men 8 and 16 appeared as the only "floaters." We note that noothercolumnscontain zero variance in any of the data matricesfor the five casestudies.


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AmericanJournal f Sociologyan implication f the zero cutoff ensity-thispartitioning atches hatproduced y BLOCKER for hisblockmodel.)

Included n both the Policy and Uncomfortablenessatrices f choicesare guesses bout thequestion who . . . might ingleyou out . . . ?"(for each relation). Guesses were requested n order to increase thescope of choices, especially on uncomfortableness.ndeed, 19 of the27 guesses oincidedwithdirect hoices,whilefewwerereciprocatedanindication hat these were surrogatehoicesrather hanrealistic ercep-tionsofothers' hoices). Everyguessthat did not coincidewith choicefell nto one of the 10 bonds shown n the images; none fell nto any oftheeight eroblocks.Interpretation.-Wenow turn to a substantive xamination f theblockmodel,onsideringirst he division f men ntoblocks.The partitionis neither ntodepartmentsor ntoformal anks.WhenCONCOR was ap-plied twicemore to split the two big blocks), thenmen 4 and 15 wereseparated ut withinhe eft-hand lock; and men3, 16,and 5 were plitfrom he rest f theright-handlock see [7] ). These five locks, rderedas in thepermutationhown bove,correspondxactly o thegroupingfmanagers y their ttitudes o R&D (inferred rom heirquestionnaireresponses,nterviews,nd actions n specific onflicts verR&D [White1960, 19611). Indeed,the permutationlassifiesmanagers y degreeofhardheadednessoward R&D. The Executive Vice-President12), theTreasurer 14), and the Directorof AbrasivesProduction 10) wereutterly keptical.The PersonnelManager (16) and the two R&D man-agers concerned ith lloys (3 and 5)--the moreroutine ideofproduc-tion, nwhich nly outine evelopmentas carried n-were close econds.All three ales Managers, lus the overallcoordinatorf R&D (1) andthe man (2) whoran the mostspeculative esearch roject,weremostoptimisticnd favorable o R&D. The President's rouble Shooter 15,in charge f expeditingome new products) nd manager (a respectedengineerwith everal nventions hat he was tryingo produceby a jobshop operation)werefavorable ut not optimisticbout results. n themiddlewere thePresident 11), the Vice President orProduction9),and the Accountant 13), in the observer's pinion the most realisticpersonsof the entiregroup; all threewere acutely aware both of thepoor record f Firth-Sterling's&D and of the crucial mportance forthecompany'smage nd borrowingapacity)of having n R&D program.The blockmodel n thethreemainblockswith he three pecificmagesmakesequal sense. n figure theblockof 11, 9, and 13 is put on top,consonantwith ts obviouspreeminencen the eyesof all. It exchangespolicybondswith he Sales block themiddleblock n thepartition 7])and receives policybondfrom hehardheaded lock; in addition, achblockhas a policybondto itself.On PersonalFriendship,hetopblock

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Social Structure romMultipleNetworks.sendsnobonds, nd t s notchosen ythehardheaded lock a fact how-ing therealism f the atter); whereas he Sales block, n the mostvulner-able position n R&D, claimsbondsto all threeblocks.There s no Un-comfortablenessondwithin nyblock.The top block nd theSales blockare uncomfortableith ach other, nd each is ill at ease withthe hard-headedblock.The latter ad repeated pecificlasheswith he Sales block(it seems ikely, rom he nterviews,hat thehardheadswere simply n-willing o reveal pecific egative hoicesfor nyreason).We havenotreproduced erethe matrix f choiceson "the managerswithwhomyou have the most dealings."The imagefortheseobjectivechoiceswould ontain nlybonds,nozeroblocks.ndeed, fthedensitiesfchoices recomputed yblock, heresults re

(11 9 13) .50 .14 .11(2 1 6 7 8 4 15) .57 .17 .12(3 16 5 10 12 14) .33 .10 .10.The striking eatures thehomogeneityfentrieswithin olumns. very-one claimsmostdealingswiththePresident's lock,nextmost withtheSales block, nd leastwith hehardheaded lock; but in this mallpopu-lationof top managers,ach blockshows ome heavy contactswithman-agersneach other lock.Blockmodels ver TimeBlockmodels lso makesense out of data describingocial structurevertime.The possibilitiesre numerous. locks can be stable over time,withtheblockmodelhanging. n theotherhand, blockmodelmaybe stable,with heblocks'membershipshangings roles ndpositions otate mongindividuals of course,we would need independentonfirmationf suchchanges).Or there anbe complete tability, t least for hecoarseparti-tions ntoblocks together ith associatedblockmodel mages.Successiveobservations f choices xistedfor twoof the cases analyzedabove, themonasterynd thefraternity.he results re quitesimilar.The fraternityata.-The stability f both the blockmodel nd theblocks, fter he first ewweeks fmaneuvering,s themainresult or hefraternity.e imposed he three-blockartition ound orthefinalweekon thedata foreach earlierweek. We also computed he density f thetop two choices n each block foreachweek (number f choicesdividedby number f cells n which hoices ould occur); we then omputed hedensity orthe bottom hree hoices.Figure7 showsthe results f thisprocedure or electedweeks: 0, 3, 5, 8, 13, 15. The developmenteemsclear. n the nitialweek, he blocks how ittlevariation n density; hus,there s littleustificationor ssertinghat hethree locks xist s distinct

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AmericanJournal f SociologyWEEK LIKE ANTAGONISM

.21 .18 0 .14 .18 .310 .14 .25 .05 .29 .08 .12

.10 .20 .10 .24 .12 .17

.25 .07 .04 .02 .21 .333 .20 .15 0 .25 0 .20

.20 .08 .06 .21 .12 .20

.28 .04 .02 .02 .07 .435 .11 .42 0 .11 0 .37

.21 .08 .03 .14 .04 .37

.29 .04 .02 0 .10 .438 .14 .33 0 .07 0 .42

.20 .12 .03 .07 0 .50

.31 .04 .02 .02 .07 .4313 .10 .42 0 .03 0 .46

.21 .08 .03 .02 .12 .43

.33 0 0 0 0 .5015 .10 .42 0 .07 0 .42

.20 .12 .03 .05 .04 .50FIG. 7.-Newcomb's second fraternity: ensityof choices n each block, for selectedweeks. Partition of men into blocks: (13 9 17 1 8 6 4) (7 11 12 2) (14 3 10 165 15). Blocksare taken from he blockmodel ested nd sustainedon data for week 15.

structuralntities. y the thirdweek, hough, patterns clearly iscern-ible; the top twoblocks clearly howno internal ntagonism, nd thethirds clearly t the bottom f a three-partierarchy. hen,by at leastthefifth eek,notonlythe final locksbutalso the final lockmodel aveemergedwithremarkablelarity. hereafterhestabilitys marked.Nowif either LOCKER or CONCOR is applied to thedata for an intermediateweek,much hesame blocks nd blockmodel re found,whereas eitherclear blockmodel orclearblocksemerged rom heir pplication o datafor hefirst woweeks.This conclusion as little nterestfmen are simply epeatinghesame764


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Social Structure romMultipleNetworks.choicesweek fterweek; theargumentnoursection nmethodswasthatmen houldbe expected o change heir hoices vertime, utwithin heconfines f blocks thatcontainbonds.For example, ake choicesmadeby the topblock. n week0, these even men made 14 Like choices toptworanks); eightwere of differentersons rom hosewhom ach chosein the finalweek.Ofthese ight hoices, ive reatedbondsnotpredictedin thecoarseV,Fmodel that s,thebondswerefromhetopblockto theother lockof 10men); three ddedto theexistingond.By chance, newouldexpect an outcome ike this: 10/17 in the forbidden lock and7/17 n the block llowed ccordingo the Like image.In orderto complete hisexample,we repeated he comparisonwithweek 15 for achweek n turn.Define changeforweek tobe a choicein week that s notmatched y a choice n week15. We then ummedchanges orweeks0-4 and compared hemwith hanges ummed orthe10 weeks5-1 .30 Data forthe first iveweeks how as manychanges findividual ike choices 38) as weremade n the ast 10. In thefirst iveweeks, 0% of thechangesfall n thezeroblock-exactlyhechance ex-pectation-but n the ast 10 only34%oofthe (relatively ewer) hangesare nthe eroblock f theweek15model.Whenparallel ountsweremadefor Antagonismhoices (the bottom three ranks), a similarpictureemerged: 5%o ftheearlyweeks'choicesdifferedrom hose fweek15,comparedwith22%ofor he lateweeks.For theearlyweeks, xactly hechance xpectation40%) fell n thezeroblockn theF image,while nly14%o fthe (relativelynfrequent)hangesn late weeks ay in thisfor-biddenblock.There is some indication, hen,that individuals' hoicescontinuehanging ven fter blockmodelasstabilized; naddition, fterweek 4, the changes-both forpositive nd fornegative ies-conformmuch etter othefinal lockmodel.31The monastery ata.-Sampson claimedthat, duringthe period towhich isdatarefer,roupingsmerged ithinhemonasteryndpolariza-tiondeveloped mongthem;blockmodelingoes notshow suchclear-cutchanges ver time.AtperiodTi, before henewcohort fnovices rrived,monks , 5,and 6 were hecoremen,with and 8 more eripheral; wasisolated, ut mmediatelyecamefriendly ithmonk16 in thenewgroup.By T2, according o Sampson's bservation, onks1 and 2 stood out asthe mostrespectedn thewholegroup f 18. Thenincidentsmultipliedstraditional iscipline urfaced even thoughn muchmilderform): for

30No data werecollectedforweek 9.31 In furtherwork (not reportedhere) on both fraternityxperiments,we distin-guishedfiveblocks in the late weeks. The patternwithinthe top block reported nthe text,when split, is stable, but the personnelassigned to each half "circulate"over time. Withinthe split top block,the elementsE and S are the images on Likeand Antagonism: hangers-onpatternreinforced y commonrejectionof the lowerhalf.765


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AmericanJournal f Sociologyexample, ome newnoviceswere hockedwhen hown he waxedwhipfortheOrder's raditionalmortifications.bout periodT3, monk2, withoutexplicit isapproval rom he officials,nstigatedmeetings f the novicesto discusstheir outine. n the formal oteforchairman f themeeting,he received 1 voteswhilemonk1 received hree onlymonk4 was notpresent).Our analysis f change s confoundedy thefact thatthesociometricdata used here are retrospectiverom 4. Thus thedata forperiodsT2through4 showonlymoderate hanges. ven when he refinedartitioninto fiveblocks s imposedupon the earlierdata matrices,he counts nblocks are quite uniformcross time periods.The sums of weightedchoices, y block,forLike are shownn thetop paneloffigure .Like:

T2 T3 T42 12 0 3 1 2 10 4 0 2 4 11 2 0 2

11 5 6 2 0 10 12 1 1 0 9 14 0 1 03 0 8 5 2 1 3 11 4 0 0 0 11 4 3o 2 15 9 0 1 0 16 9 0 0 0 16 8 02 0 10 2 10 2 0 5 1 16 2 0 5 1 18

Antagonism:T2 T3 T4

00 0 0 6 0 0 0 0 6 0 0 0 0 60 1 2 8 13 0 1 16 0 6 0 0 13 4 94 7 0 1 6 3 10 0 0 5 1 5 2 3 11 7 0 0 17 3 12 0 0 10 0 15 0 0 94 15 4 1 0 0 19 5 0 0 2 17 6 1 0FIG. 8.-Monastery data: sums for Like (top panel) and Antagonism (bottompanel) choices over threetime periods. (Individual choices contribute ither+3, +2,or +1 to the sums,depending on tie strength.)Since the same blockmembershipsre used foreach periodand theblocksare of nearlyuniform ize (with either hreeor fourmembers),it was unnecessary o convert o a densitymeasure. t is clear that theblocks from 4 also standout as distinctivenitsat the earlierperiods(i.e., the groupings xistedfromthe beginning).Certainly here s a

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Social Structure romMultipleNetworks.consistentecline n Likebetween he top twoblocks roughly,ampson'sLoyal Opposition) and the middle two (the Young Turks); however,thebuildupof likingwithin he bottom lock (whichSampsondismissedas the Outcasts) is equally striking.o also is the increasing ocus ofliking ies within he Loyal Oppositionlargelyfrom ieswithdrawnromthe ther locks) upon heireaders.The parallelsums for Antagonismre shown n thebottompanel offigure . Again, he fiveblocks re discerniblet the earlier eriods.Theonly notablepattern hanges re the concentrationf antagonism romtheleaderswe identifyn the Loyal Opposition pon theYoungTurks'leaders these Loyal Opposition eaders, n turn, re increasinglyislikedbyfollowersithin heYoungTurks).Much the samechanges ver time re seenin theother hreepositivetypesof tie and in thenegative ypes. Even the refined artitionntofiveblocksyields harpdiscriminationn the twoearlier eriods. ampsongave careful nstructions orthe retrospectivehoices,remindingachrespondentf a salient ventmarkinghatperiod.But it is impossibleovalidate hem s faithful epresentationsfperceptionst T2 and T3.We noted n the section n methods hatconstraintsn data collection,random luctuationn social relations,nd thedifferentialaintenancendconcealment f ties over time aive rise n a naturalway to "speckled"blocks bonds) thatare onlypartly illedwith hoices.Ourmodel llowsforchanges n thenovices'ties over time,but our hypothesis as thatsuchchangeswouldgenerallyonfine hemselveso bonds and wouldnotaffecteroblocksas defined y theblockmodelorperiodT4). If choicesforT2 and T3 are really ust surrogates orT4, they houldfallwithinthebonds specified y theblockmodelf T4; the sameoutcome houldalsohold fthey re truly or differenteriod ut the ameblockmodelshypothesized. ccording o the "top-two, ottom-two"utoffs sed inapplying LOCKER, amongthe 25 blocks n each image,about half arezeroblocks. f the 131 choices n thefourpositive ypesof tie at T3, athird 43 choices) do notcoincidewith omechoiceat T4. Of these43,11 createdbondswithin eroblocks. or negative ypes of tie, the cor-responding iguresre: 128 choices, 8 T3 discrepancies rom 4, and 7entries alling t T3 into blockswhich re zeroblockst T4. To put thisanotherway,ofthe 2,183entries hatare zero n the eightdata matricesforT4, themajority59%o) are in zeroblocks; owever,f thecells thatare zeroat T4 but not at T3, four-fifths80%o) are confined t T3 toblocks hat re bonds n theT4 blockmodel.f T2 is compared o T4, thefigures orpositive ties are: 130 choices, 62 discrepancies; 0 of thelatter ppear in zeroblocks f the T4 blockmodel. or negative ies thefiguresre 121,69, and17,respectively.The implicationseemsimple nd agree n generalwiththeNewcomb

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AmericanJournal f Sociologyanalysis bove: the Sampson lockmodels largely tableacrosstimewithrespect o bothblocks f men nd images, nditemerged uickly fter hepopulationwas constituted.o bring ut the significancef theseconclu-sions, t isworth rawing contrast ith volutionn a more lassic ense.There s little upport ere for naive borrowingf ideas from iologicalevolution,wherenaturalselection s classicallyviewed as producingtsresults raduallyn a time cale of manygenerationsMayr 1963; Levins1968). Instead,thepicture onveyed, t least by these data, is one of"saltationist"volution, here daptationsriserapidly nd withfinality(Ford 1955). To take another arallel, his findings in part consistentwith heeconomists' iewof a system f actorswhomaximize rofitsrutility ffortlesslynd instantaneously,houghwiththe crucialdifferencethatno explicitmaximizingehavior as yet been dentified.IMPLICATIONS: CONCRETE SOCIAL STRUCTURESociologists ave long been tortured y their nability o specify learlythemeaning f twofundamentalerms, role" and "position" see theexcellent riefreview y Catton [1964, pp. 936-43]). All agree thatnocogent theory f social structure an dispensewiththe concepts heseterms ry o capture one reasonMitchell 1969] is so soft-spokenboutnetworkss thatthey eem conceptually emote rom ole and position).Part of the trouble,we submit, s the ack ofgenerallypplicableopera-tionalizations: o matterhow cogent the prose discussion f role andposition or cognate erms), he senseof insight ades as the writer orhis reader) tries oapply them o various oncrete ocial structures.32We now suggest hatthe purposely eutral erms mployed ntilnow-block and blockmodel-provide perational efinitionsorthe substan-tiveconcepts f role and position.We thensuggest way to interpretconcreteocial structuresn these erms.We require hree rimitiveerms:

(1) claim-the genericerm or ach nstancef a tie from ne mem-ber of a populationo another. laimsmay be made either y themembershemselvesas inthebiomedicalcientists'ata) or by an out-side observeras in theBankWiring oomdata).(2) type of tie (abbreviatedoft)-a network f all claimsof aspecifiedype.The meaningf "type" s initiallyand explicitly)eft

768

32 The study by Gross,Mason, and McEachern (1958) of the school superintendencyis one of the veryfew systematic pplicationsof such conceptsto concrete ituations.Because theydeal with explicitofficesn explicit formalorganizations, hey bypassthe derivationof positions fromnetworksof relations at the cost of otherconcep-tual difficulties).n our terms, hey moved directly o the interpretationf types oftie, using data on perceptions of rights and duties among counterpartoffices;inaddition,they were aided by pooled data fromdifferent oncretepopulations thatare, by definition, arallel in organization.


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Social Structure romMultipleNetworks.open, hepostulate eing hat sharedmeanings accorded achtypethroughouthepopulation.(3) population-the set of persons r other ctorswhose laims rereported.ts memberships thechoice f the nvestigator;t neednotbe restrictedoa naturalnclave r a set nwhichach ctor nowsmostof theothers.

The data are a set ofnetworks: or achtoft, he claims ssuedby eachpersonregardingll others n the population re reported s a binarymatrix.Mostcommonlyhe data willbe sociometric,nd thentheclaimscannotbe considered o be acknowledged y thetargets.Withrespect oclaims,the choiceof jurisprudentialanguage s not accidental: Block-modelsmayhave natural pplications o theanalysis f complexawsuits,and they eemparticularlydapted to handling ounterclaimsnd cross-claims n multiple arty itigatione.g.,Lasa perL'Industriadel MarmoSocietaper Azioniv. Southern uilders, nc., 45 F.R.D. 435 [W.D. Tenn.1967],reversed,14 F.2d 143 [6thCir. 1969]).Blockmodelss Roles amongPositionsA blockmodel s a hypothesis, representationroposedforthe socialstructurehatexists n thepopulation's laims.Threeterms an be usedtodescribe blockmodel:

(4) position-each of the ets ntowhich hepopulations partitionedis a position. he technicalermblock" s a synonymor his ubstan-tiveconcept.33(5) bond-a nonzerontry rom nepositiono anothernthe magefora toft.(6) image-the eport,n theform f a binarymatrix,f thebondsona given oft mongll positions.By its definition,blockmodels a simultaneousraphhomomorphismin mathematicalerms Heil and White 1974). Mapping thepopulationintopositions equiresmapping ach data graphmatrix imultaneouslyonto thecorrespondingmage.By thedefinitionf a homomorphic ap-ping,there s no bond from ne position o another f and only f thereis no claim from ny member f thefirst osition o anymember f theother osition. hus, n the terms sed earlier,ach mage s fully pecifiedfrom tszeroblocks hen hepersons n a datamatrix repartitionedntopositions.

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33 We agree with Catton (1964, p. 942) that therehas been an evolution towardclarityabout these concepts.Our definitions an be seen as operationalizing hoseproposedby Larsen and Catton (1962) after heir houghtfulnalysis of the literature:"position . . locationof a person or a category f persons n a set of social relation-ships . . ."; "role . . . a patternof collectively eld expectationswhichdefine ppro-priatebehaviorforpersons n a given social position."


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AmericanJournal f SociologyThe theoretical ontent f a bloc

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Social Structure From Multiple Networks

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