i-3.J.v.....,. 5.2.1.1.. .. Jaw ... .... .r. ‘1! , - I 1 ‘ .7 ‘ Z .. . . . . . . ‘ . _ .; . . . . - . . a . , ‘ . , . _ v . |¢ . u A . . V c . . . V . . 0 v , . o . . .V ,. . _ . n , r. _ . nunA : 0 . . . n . . . . . . V .. n . q . . _ c . .. .. , ... . . , u . 1 a. ._ . w _ ‘ . . . v . .‘ . _ . x . . . ,. . . r . u , I . . n . . . .. . v v W . V . w y . _ , . u w . V1. .31.! I ‘ a; o ‘ u at.vi.’i.¢2'i.. .vri. .01‘t‘..& ol:§ . . ,l. _ 7....xt . tray}; 1 7 ‘ . \k: , ylfia. 9v... . if: 1:; ...s........ :15}... e .s..§?.=.._¢z... $..§t......~.3u!:£ a.......1::.:: 355?: :1 .’ I. ., ‘ ‘. I, A " I l t ' I]. IIIIIIIIIIIIIIIIIIIIIIIIIIIIIII [HUN/WWII!!!”MINIMUM}!!!IUIWHIHIH/Hl 300068 9954 ABSTRACT ,_ ' , <1" 6:; .-"I '_ . ‘ 1 . . L “' ' 4 ‘ -“ . “A _ --. :4“,).’,~ . , ,' ,1; .‘a. mum mummmm IN THE s'nm . .. or W1. commma'xm .,. “ by Ly'ttm L. aximaraes Amajwargmtofthemsmtthesisisthtcammication mmmizedirudividualbemviw,mdmglectedggg— mimetic) interacticn processes . (he alternative to foaming m 'individmlsassepamtemxits,istochangetonetmks9_1:mlatims mag individuals as units of analysis. Under the latter pu'spective, theindividalistmatedaspartofalargersystammfixerthanas an isolated or inlepexzdsnt unit. Two mjcr data-593mm tecmiques are wists far rela- tional studies: (1) the "srmballing" technique, and (2) the "satu- mdm" sample. Sccianetric-typs questions, as a PM 31: W, allows the idmtificatim of nebnrks of camunicaticn mums-wag each mspmdeut. mflgwgnmmm smdiesmaybeacammica- tim systan. A cammicaticn system anbrsces subsystem as dyads, chains, cliques, and W. In additim, it curtains such elements asllcannmicatim leaders, liaison, and is tea. The analfiis of relatiaaal data, with fOOJB m a camunicaticn systemwrmmyof its subsystem) naybepafmuedwimflueuseof (1) charts, such as swim, m, and socianatrices, or (2) by means of matrix nultiglicatim . 'I'hennjorobjectiveofthepresmtthesismstoeaminetm relative merits of the matrix nultiplicaticn appmmh (as canpared to LyttmL.(-hixnames finsocicgrun,fl1edigraph,andthesocianatrix)inflieamlyaisof Wrists. Wobjectivecfflumsmtstmymstcillusmtatm use of the mtrix nultiplicatim technique with relational data fran unfit-ailincmndties. mmmmthatcmbedrmfruntmmsmy isfiat,fa'nlatimalamlysis,themtxdxmltiplicetimappumch hasadvmtages ammly representational techniques (e.g., socio- m,digxapln,aociattrices). Nadinpwtmtly,theusecfthe Multiplicatimapptoachdoesnatemlndetheuseofanwm offlutlmctlurtectn'dxpea. Hun using the matrix mltiplicatim approach, different re- eearclmcanmzipllatethemrelatimaldata,andthemlts yieldedwilltmdtcbesindlar. Simplediagruuneticpmaurtatian, mfinaflmm,maypmcvidediffmtviwalimages.dependmm flunythayanccnstmcted. Minter-pretatimofthemultayielded byfiiemtrixmltiplicatimappmoachismlativelysinple,m meemambusamanddiffimlttcintwpnt,especially MaMivelylargeaanplesizeisinvclved. eratmweof the matrix mltiplicatim appmech is objectivity in intermtatim, milewtatiaaldefices,oftenm11tmatrialbasis,might nctbeasfneefrunm. The applicatim of the matrix mltiplicatim technique to relatimal data obtained in a "undem" and a "traditimal" camunity inHinasGuuis, Brazil, lends wppwttcthefaegoingcmclnsims. 'me mthcd allavs the identificatim of fatally defined structmes of l[.[’tllall.|lll'ar‘ll‘{l [[[flll( ti. Lyttcn L. Guimarees thecaunmicatimsystsm, asmllastheanalysisofindirectrelatims. As a data-romc'tim technique, the matrix nultiplicatim approach allow thfcruatimcfindicesandproceesvariables,whichinmmallow, when denim with relatimal data, a shift in the focus of analysis: from the individul to dyads, cliques, subgroups, or larger systems. It is clear, l'owever, that for certain situations (i.e., visual effects), a cmbinatim of the matrix multiplicatim approach and diagram is desirable. When dealing with relatimal data , the matrix rmltiplication approach produces a series of indicators of the patterns of inter- cmnectims of a camunioation systen (e.g., umber of isolates, dyads, W, cliques, etc.). Sane of these indicators seem so interrelated that it becomes difficult to determine, at this point, whether they are really independent estimtes. to important task fcr futm'e research is tofimtlnreauninetheseindicatcrowiththeparpcseofredmingtrm to valid arireliable indices. Anothw research realm that requires attention relates to con- ceptualandfirscreticalproblene. Avariablethatneeds furthertheo- retical (and mflodological) consideration is cammicaticm W. The ideathat firediverseparts ofacamunicaticn systemmrmallyco— ‘rmeinaoaeoatam'mte fashicnneyproveusefulindiffererrt contexts. It my help to explain, for example, how menbers of a social systan accept, reject, crnodifyimovatimsmicharedifmsedfrunorthsr system. Administrators and change agents may be guided by the concept of camunication integration in their effort toward introducing innova- tions into "less developed system." Cannmicaticn integration has not LyttmL.Giimarees beenstudiedasamajw variable, but meant developments innodern societyandinbehaviwressarohpointtothesaliemeofthecmcept. Acceptedbyfimefamltyoftheneparmentofcammicatim, College of Caunmicatim Arts, Middgan State University, in partial mlfillnnrrtoftherequirmrtsfcranasterofArtsdegree. $32,062:”? )flUHUD(P1fl31PLICAIION'IN THE STUDY OF'INTEREERSJWUL(IlfllflflxfiflTDN Ignnxrllu GMdmarees ALTHESIS Einndtted to .Michigan State university in partial fhlfillmant of the requirements for the degree of MASTER.OF.ARTS Department of communication 1968 MWWIEIIRENTS mmwisl'estoexpresshisgmtitudetotlmewlo cmtrihated dizoctlyandirdirectlytothe present work. Dr. EverettH.Rogers,thetheaisdirectcr,providedguidanceand valuablemggestims. Asdirectcrofthe Project "Diffusimof humtiauinmrelSocieties,"lnmsinstrunentalinenabling the m to 13mm graduate studies at Michigan State University We'fifflnimneseamhfellwsmp." Martinisgretemltohiscamitteembere,m~.R. Vilma: Parana and Ir. Paul Hiniker, for significant oaunants and suggestion. HealsowishestotlanklluJ.DavidStmfield,fcr stimflatingdismssiauandprovidingermaganemfcrtmpresem thesis. Totherespmdmts—farsersoftmcamnitieeinmnas Gmis,Brezilwfixemfimeo¢endshisappreciatimforprwiding finedataeminedinthepresentstudy. Mama'swife,0ristim,u1ddaughtersViveka,Hargit, andNicole,providedthemthcrfixeewtimalwppcrtfwacccn- plislmtofthewcrk. TABIEOFCO‘ITEMI‘S W8 0 O O O O O O O O O O O O O m w m C O O O O O O O I O O O um or mm 0 O O O O O O O O O O O O 0 Chapter I II III mm 0 O O O O I I O O O O O mannerisms of Garmmicatim Research Needed Wis (11 Relational Analysis 'Ihe Unit of Analysis in Relational Studies The Techniques of Analysis in Relatiazal Studies Objectives of the Present Study WOFREIATIMALANAIXSIS...... The Sociogram The Digreph The Socianatrix Digraphs and Matrices Summary MIRRWUI‘IPLICATIGIINTB‘IANAIXSISOF M'ERPERSONALCCNMJNICATIW . . . . . . Clique Identificatim Identification of n-Chains The Distance Matrix communes IN'I‘EBRATIW IN 1W BRAZILIAN WES C O O O C C C C O O O O The Selection of the 'lho Camunities Definiticn of Ccmmnicatim Integratim Operationalizatim of Caunnficatim Integration iv Page vi vii doll-4 H (010 12 12 15 21 2H 27 27a 31 36 37 M2 ‘42 1M ‘66 IV (contd) Indicators of Caumnication Integration '48 Cmclusions 50 V W, CDMZIUSIGJS, MD SLBGESTIONS EUR m mi 0 O O O O O O O O O O O 53 Suumary and Cmclusions 5 3 Suggesticns for further Research 56 Further Applications of the Matrix Miltiplication Approach 56 Indicators Deriwd from the Matrix mitiplioation Approach 57 Camptual Problems 58 BMW 0 O O O O O O O O O O O O O O O 6 l LISTOF TABLES Page Table l PossibleIrdicatcx-sofcammicatimlntegretim inabbdemandina'l‘reditiaralCaxmmityin MimeGereis, Brazil . . . . . . . n9 2 PheahdiaibcpcsmeinaModemandina 'IraditionalCammityofMinasGerais, Brazil . . . 51 13 110 LISTOP FIGURES fininflneroestructureofafive-menberhypo- fluticalgrow,asrepresentedbyasociogrmn. Dmleoffamdiffermtsociogrmerepresenting finsmstrucmrelrelatimsinahypcthetioal five-manta group. Ehsmple of a digraph with its custanary notatim. haul. of a socianau'ix with a hypothetical five- manber group. leofadigreph (D) withits adjacency matrix A(D). Daphofadigrephwifizitsadjacencyand sqmedmatrices. Dmleofadigephwifixadjacencyandsym- mtrioalmatrices. hamleofasqmrodandmbedsynmetricmu'ix. A digraph illustrating the problan of redmdant sequences. Duple of a digraph Wifll its distance matrix. Dayle of a digraph with its distance matrix. Illustratim of canprtaticm procedures for a distance matrix fer A, A2, A3. Possible relatimahips mag external cammica- tim integration , internal cannmioatim inugretim , and irmovativeness . Paradigm of variables and cmceptual relationships with camamicatim integration . vii Page 12 15 18 22 25 28 32 32 37 38 39 H0 52 60 WI WON Matias of Gamericatim Research Omtbpastbncrthroedecades,therehasnergedafocaas otresearohandtheoryinsocialsciencawimcounmicatimasits carter. nuiswu'kl'nscmreredawiderangeofirrterests. Manycan— nmioetim,orommication-related questions, have attractedthe attardmofmeocialscimtists,withtheresultthata volmninau ounmioatim research literature is today identifiable . ”Woffilisliterem,asperlnpsofsocial aciamoeroaearchliteretuoingml,isthefacttlatitis largelyliaitedtodenomuetimtheinportameofmefactor,or variable,inaffectingmemnrxectherfactors,wmriables. lazarsfeldmdotrers(19u8),fmmle,dmxstreteinfinirnw- funnvotims‘mdytheimpcrtameofperemalinfluenceinthepro- case of political decisim—ueldm; similarly, Levin's (19%) classic snadycmpuingtheefficacyofalectmearriagoupdiscussimin WWm'cpinimsaboutmfccds,srmstherelevance cfgroupdisalssimininsfitutirgclmge. mmmmtauampimafimmmmt indicativeoflxesenttrurdsincalnmioatimstudies. Buttheac- cmmlatedresearchreportsintheareaoffliedifmsimofimo- mummforeacnplmalsoreflectthistmdencytumdthe 1 2 categwizatim of concepts as dependent and independent (Rogers , 1962)‘ In fact, the list could be extended indefinitely, and many mlescouldbechmfronallareasofconmmicatimresearch. Itmightbesaidthatnostofwhatistodaygenerellyregarded uodmnfioatimresearohisinthevariable—searohing stage, inthat it is comerned with demnsueting the existence of bi-variate rela- tionships. This cmditicn is apparently part of what Coleman calls the "w'e-matl'unatical state" in research: "A casting about, identify- ingfllecutlimsoffliephermemtobestudied, searchingforthe best accepts by valich to represent the prernnena" (Colman, 1960, p. 11). i ' Apart frun this euphasis on dexonstrating the existence of re- lations, rather than fileir precise form, this calmmication research literature also reflects a general emcern with single (zero-order) relatimships betveen variables, that is, the effect of X upon Y, rather than with their functimal interdependence . Altrmgh single relation- ships nay eventaally form a caljumtim of interocnnected generaliza- tions,andperhapsbecaneathecry,takeninisolatimtheycanbe viewed ally as single quantitative statements . ** fixatendencyofshavingtheexistemeofrelatimshipsandthe general cmcern with zero—order analysis, coupled with the problem of *Since the publication of Rogers' book, in WhiCh more than uoo diffusion studies, of different treditims, are examined and synthe- sized, over- 600 new research reports have been incorporated in the Diffusion Dcmnents Center at Michigan State University. Most of these 1,000 empirical studies cmcern the analysis of pairs of inde- prudent. and dependent variables. See Rogers (1967). And, as such, of relatively lover value. 3 adequtemrt,1avemldulbteilyirfllibitedoertaindevelopnmts inca-micatimreeearoh. artperhapsanevennoreeerimsobstacle totlnflleaotioalandmefllodologioaldewlepultofeammioatim researohistlutndemytostudyindividualbehavior,oftmincor~ rectlydisguisedascalumicatimbehavior. Marystadiesvalidlareamrtlylabeledas"cammioatim" minaeanlitystudioeorimivimalhahaviot». Immgthesewecan imludenoetoffllosegroup-caltmdinvestigatialsinvmidlthegroup isleduadmndtasasystuofcounmioatimbehviwabwtmidx gruelintialswthsa-iesaretobedeveloped,butsimplyaeacm- turtwithinuhid'ltheindividlalacts. 'Ihegroupisof‘tenusedasa mniwlablesocialstimlus,mdthefowsofcmcemisupmthebe- Wordlemdividlal within it. PestingerarnCarlnith's (1959) study,invalidlthemntofeartumljmtificatim(m)received bythambjectstolieabmttheperforwoeefadflltaskierelated tooomiflvedissmmce,ismuunpleofthisuseofthegroup. The mammmnondfestinguarIdCarl-nith's,asmllas finso-called"fearappeal"eaq>udmtsaroalsoomp1esofhmdrods ofmchirmstigatianinvddchthegroupis"cmtrolled"bytheex- perimter.‘ Bapcrtsoffiueseinvestigatimsslmfilatthereseardnr isinfactstldyingindividmlberuviwinagrolpsitntim,rether than‘groupbehaviw(orinterperomalrelatianhips)assuch. 'lhese elqaerinmtsmydevelopgenereliu‘dnlsaboutthebdlaviorofm *San of the studies an "insufficialt justifioatim" are: Brena laid Galen (1962); Aruuon UK! Carlsmith (1963); Nuttin (196M); Julia and Gilnrre (1965); etc. Dumpla of "fear appeal" stadies are: Janis arr! Peshbach (1953) and Janis and Milholland (19510). L I‘ \‘\ \ \\ Mividnlwdu'certainsocialcmdifims,hltleavemmminedflle betavimofmeeocialsystanvhichcmstitutestheseomditions. kmdgadaewhufluecmofcamsecmmetode Wofmdelsofirdividnlbehaviorwithinaeocialconteut, hrtflnyreflectauadidaulpsyclologicaltendencytamdanomdic vimdm,thatis,thetmdmcytoviavtheirdividualinisolatim, altdhiaeocioolltuelcarteact,ortouseWatzla&dckandad\ere' nodal, out of his "canalrlieatim name" (Watzlawiok, 1967, pp. 21-22). Worm-muse,fllerefm,canservemlyasmecmpmentof cumin-timescale. mistlecreticalorientationmiglrtexplainthe rmfllymoetmmicatimnodelsimplylimarityormidirectim- ality (e.g., the Westley-Mun nodel)‘ in that they seen to limit the stdyofoanmioatimasau—myphmmflransasoetoreceiver), r-glectingtolcdcatcalamicatimasaninterectimpromes. \/ Acapletecmnnioa‘dmmodelmtdealwithasyet-aofbe- llviminmichtlnindiviaalismlyapart.1bqucteairrulistell: "mirldividlaldoesmtcannicategremgagesina‘becaneepartof calamicetimw mention-lasasysten,ttm,ismttobe m'lderstccdalasinplesodelofactimandreactim.... Asasystan, itistobecmuehendedmfintransactinnllevel"(8ir¢dlisten, 1959, p. 10“). Watzlmickandcmars(1967)realizefileseproblans. 'Iheyargue fintmmicatimisaprocessofsymtricalmdcglmrtaryintgy m,depudingmv&ntlnritisbasedmequalitywdiffm. .’ \ ‘See Westley and Macllean (1957 and 1965). 5 Iftvopar-trmmuohcdm'sbdnvior,theirinterectimis buedmeglality,mdietherefaeemtric. Ifmepartrw'ebe- m"oupl-lrtsfiutoffiuofller,famirgadiffmrtswtofbe- mWa"mmthe i.e.,basedcn mdniaatimofdifferenou (Watzlniidcandodlers, pp. 69-69). The mmmmmmmmwmnmm- nitimflutfluirrlivinnl'spceitimgmlmdablesfl 1967,p.7l). a; InarocmtpapernogenandJain(l968)hringthsem prrblutoflnrealmofdiffmimrosearch. Intheiropinion,oneof fin'hiaees"iwlicitlyadoptedbydiffusim researcherfiasimpcaed upmflmbyhistoricaldevelopnntsofflnfield,istheirfocusm "individual,intre-peremal variables,1arge1ytctheooclnsimof sooialszar-iables." 'I‘heyclaithtbeoauetluindivimals mgumllyfinirmitsofm,diffinimmm- «lye-meataueixaivianlalaomotoheenmitormg.“ Neeoeorhplaaiemaelatiaulanlyeie Asearlyasadecadeago,001¢nan(l958)m'gedsociologiltsto abandmtheircmcernwithindividlalsasseparateandirdepudart mete. Heproposedachangetomtmaggrelatimsanmgindivirhlals asmitsofmalysis. RogersandJain(l968)subea-ibetotheuideas arugobeymdtosuggesttlntfltisentirelyappropriatetoutilize relatia'nhipoeplif‘iflsfiecluins-asqmmitsofamlysisindif- Miminquiry,refl1ertlmindivimals." 6 Mplminfavorofrolatimalstudieshavesofarreceived cmspicamlylittleattmdm. Queuplmatimfwthisneglect, Colm(l958)clain,liuindndata-gadwirgtedmiquesofmst nmyreseardl: Mmlu,duichonlybyaocidentincluded"two mmmm,"intervimcaulctedwifllmeindividml "asmatcndsticartity,"mdrospauescoded"artoseparatelfl4cards, ms for each perm" (Colman, 1958). Yearsago,theuseofnnweyresearchmethodsmighthavebealas Wafactmascolmindioates. altnostreoently,"evenwith ‘themeci'flrveymtrnds,...vermtedmiqmsofmasmeult, datum,maataunlyeiaombeutiliaedtopmvioeromam nlatianhipethImmindivi " (RogersandJain, 1968). Mme specifically, the incorporationof socimtric—type questianintomyresearoh,asatedmiqueofmasumrt,allom finiderrtificatimofmtwaicofcmmicatimsurmmingeachre- sparhnt. hepalsestomchquestimsas: ‘Wundoycuvisitme fiequrrtly?"cr,"flmywnsedadviceonmch—ard—smhauob1en,m doycuusullyseek?"-canbeaggregatsdcvereadlsystea(e.g.,a groupwacanamity)tocharecteriuitscmmioetimpatterns. (he aayalsosingleartalbsystanssuchaedyads,chains,cliqree,mdeo on. ’ ’ almdisalsseeinsanedetailsevereleanplirgpooemres Wetsfwdnthecalls'rolatialalanalysis.“ (heisthcso— ‘nelationalaul mayheoerineouaoethooelogioal approachTtosm'vey )inmicheachindividlalrespmdem: seeshimelfasafiofonearnoresocialsystaae. 'nus,there- spmdartismtu'eatedasanisolateorindspmdentmit,wtasan 7 called "flattening" tednique, uhiohcmeists essarrtiallyof inter- ‘viewircfiretamllealplsofpsrm,thmaskingfinseperoauto irdicatefinirbestm,fcroemple,andtrmasldngthceeeo nmdfloflnirmare,intervieuingfiun,andeom. Another W,uhichcolanancalls ”sensation sanpliru,"istoirrterview everyolleuiminarelevantsystn. mmtpcinthmisfinttmindivimalistreatedas partofalargersystun,mdmtasanisolatedorirdependurtmtity. Andthisisdanviaflnfamlatialcfthequestim,eumlim,mdin finllbeeqtmrtulalyaisofmedata. 'nlenlyeisofrelatimaldatahasitselftvoilqaortmtand interdependentupects:mereferetothemitor1mlofanalysis, mdtheodrartothsma'techniqmsofanalysis. 'nleulitofkulysisinlblatianlStudies Dumitofanalysismaybemyoffluaggregatedsystm referredtoprmdanly,thatis,adyad,achain,asubgrmp,acliqre, wflxecammicatimsystmasauhole. l. aggiemmlleetmlytioaleuheyetenwitmntlnoon- mioatialsystemgitcmsistsoftmpersmsmtuallyemagedininterh actim. misirrterectimmaybesymuical*wcalplmwy,aslalg as it satisfies the criteria; of reciprocal mientatim. M in a larger whole (a relatialship). *Syme‘tricalinterectimisthatbasedmecpalityofbehavim. W “mm °" 3" ...... M" ‘° W °" W" ererlces (seeratzlawick and others, pp. 69-69). 8 2. Ammfmtogmofparticipmtsofamlica- timsystunvdloareirrteroamectedatagivenpointintima,byagivm cunnlioatial input (e.g., a message). 8. Amamistscftmormeindividualslimosd Egg—hit not mimivelynby unreciprocated relations . u. Afleisaubsystmmfthscommicatimsystawin idlichatleastthreenunberswtuallyinterect. 5. Ammicadmsystenmaybepartofalargersystem,alch asagroup,acmnmity,wanaticn. It isthelargestidentifiable madcatimmitwithinalargersystan. Itthereforemlbrecessuch cummioatimsubsystsseasthedyad,thechain,theclique. Rather- we, itcnntainssuchelcrentsascammication leaders, liaisals, “isolates. (1)Acammlicatimleaderisapersmwhoislooked upmbyhispeeroasbothareceiverandasmlroeofcola- migration. Porthisreasm,heissov.ghtbyothermbers of the coluunicatim systan with relatively greater fre- quencythannostelenmts. (2) A__li_a_i___sa1isapersmwhointeroamectstvow nae subgroups orcliques in the calmlnication system.* (3) Mingteisapersmvmoneitlmseeksrmis salghtbyanyothermberofthecamunicationsystem. *Jacobsm and Seashore (1951) initiated studies (11 the role of liaison individuals within a social structure. Weiss and Jacobson (1955 and 1961+), and Schwartz (1968) have also studied liaison roles within formal manizatims. 9 MWofmmaiainRslatiaulsmdiu f 'mo-ulyshol’nladauldatmwithfocusmanyofflumb— WMMinfiuMimW(i.e.,adyad,adnin, acliquo,aoanmioatimsystu)maybopsrfmmdwiththsussof (DMQmmhasfiociogn-m,""dignfiu,"a~"aocio— ntioso,"w(2)hymotwmltiplioatim. Eadmofthsao tuonjwappxuchu,alflwghmtnsoumilymtmny mhsimfims itaadvantaguuudits limitation. It maybemlativsly any, for mh,toplotasooim,adigmph,orasocianatrixofttnoan- WWofaI-allmofmormm,mtbovuy diffiwlttooaqrdnnd thodataomtainod in than. Multiplica- tim.mthoordnrhmd.iamoofanmbsrofpossiblelppmaohuto "partial nMiutim"of mum data. A: authod of data- mmim,itallanthfomstimofindiossardofpmousmiablss, mummpouiblondmdulimuithnlatianhipo,awt mfiumitofcnlysi-z mmmww,m,moom. chctimofthl’ruentsmdy Mnjwobjootiwotthopmtstudyistomimthsmla- tin units of tho numb: mltiplioatim toolufique in the dialysis of min-pacifisdomumioatimmlatiaummmofaoocial system. Perthiapm'pooe,aoaxpariamismdswithtmalmtivo WMmtiand (fluoociogxu,tkndignph,andtm oooianatrix). Wobjootimofthoprumtstudyistoillustmtstluuss ofthonttrixmltipliottimappmaohwithmlatianldatanmtwo 10 Brezilimoommnities. Therelatims dealt withereessentially ofthe $3—mtyps,mbuo—velusd relatims,asillustmtsdbythefollow— ingsaomplss: 1. Gannmioatiauorfriendshiprelatims:1ndivichnligge_;§ «mgmindivichnliasafiiexdwapemmwiflumm interacts. 2. Wmdanimuoerelatiom: Individualifior mgdmssiasaninflumtialpemminthesocialsystan. Althotuh the matrix mltip)".zatim approach has been used in thspast,sspeciallyinsocialpsyc1nlogicalresearch, someofits amialaspsctszemainlargelymxclear! mosevdnlavenedeuseof this approach apparently do not deem it necessary to discuss in detail the Operations and procedures involved, or else they maintain their discussion at such a level of mathematical sophistication that many readersorpotemtialusemofthemethodseemtofeelalienatedfrun its "unatl'uemstioal coupleadties , " with the result that its applicatim mine largely restricted to mathematically-inclined researchers . Weaiminthepresentfl‘uesis toexanineindetailsamofthese unclear problem and attempt to show that the matrix multiplication approach is tether simple, and can be appropriately handled with a minim lowledge of natrix algebra. The assumption is that studies such as the present have “Lin (1953) used this technique in a study dealing with inno— mtims in school systems. As in previous repats, however, he does not discuss in detail the procedures involved. ll theoretical and methodological consequence. One potential methodo- logicalomu'ibxdmisarefinenentofpmcednesforthetreatrent ofzelatiaualdata. mflwdologioalimpmvenmrtsney,mflueotherhand, contribute to the developxmt of a theoretical fremamk capable of madequatelyhandlingoertaintypesofcannmicatimdata. The development of both fleoxetioal and methodological aspects may in turn omtribute some fully to the dissanination of lmowlsdge derived fran ommfioatimreseareh,assundxugt}utthemoresophistioatedthetmo- retioalandmthodologioaltools,themereliablethsywillbe. Toparepm'esonutlewin:Nofliingisnmepractioalthanagoodfl1eory. Agoodthsa‘yrests, rovever,mequallygoodmethodology. emu MOPMWALANAIXSIS 'Ihepurposeofthisohapteristobrieflydsscribethsmst cumuly used Wes to relatimal analysis, and thus establish a basis for cauparison with the netrix nultiplicatim technique , which ismusdinfiuenextclupter. Sociograrrsazedescribedfixet,then digraphs, follmdbyabrief acoountofuses of 'Wuo—to—vman"cr node-nutrient. 'nuslastsectimofthepmsentchapterdsalswith somoftheralatimships between dimphsandmatrioes. ’IheSociogmm 'I‘zeditianlly , relatimal data derived fran sooiamtric-typs quss‘tiausMwbsenpsesmtsdbyneansofgrephsordiagrum.suohas flusmeinl-‘igmel. Figurel. 'I'heinflmstrmtmofafive—manbwhypathetioal greup,asrepresentedbyasociogzun. Sudu,gmptuca11edsociogxem,havebmusedtoillnstmts mankindsofstmctmelorzelatimal intsreornsctions withina 12 13 group. 'nuscizelcsrepresentgreupmubsre(here,a,b,c,d,ande); fluduoiossornaldxntimsmfluanarerepresarmbyfiuedirectsd 11m,ardtluarmhsadsindioatsfluedirectimofflusrelatimship. mlinsbstwsmcaurib,forequ>1e,usuallyneanstmtcduooses basafrisndwinfluantial. Inmdiagrenefixedirectimisre- versed,m,forinflnencsrelatimships. Unlessotherwise spscifisd,a11arrwsappsaringinasinglesociogrmrepresmtths mtypeotrelatim. 'misxneansthatmuallyaeinsletwaofintm earnedm(s.g.,infhmuce)withinthagrwpisrepresentedinany palm-rm." Wmtfliediagruninf‘igmelrepresentstheinfluence Wotafive-mubsrhypofietioalgreup,memayintuitivelysay fintshnsb'sixflluanemincmdestmesofthsoflerfam meoffinm,mmghtbsa_;lsad£_,wminfluentialpuemin fingreup.“ Oathsctherhand,d,whomitherduosenorwaschosen bywoflmmumbw,nightbsm_i_sg_l£inthsgrmpinfhmme structure. Byfmflweamingmesociogminrigmel,wsmticsthat *The "socianetr-ic approach" to group analysis was originated by Haeno (19316). For a reviav of the remarkably large qmfity of research cmmcted within this orientation in a relatively short time, see Lindsey and Bugatta (1951;). Much of Moreno's work and that of hisassociatsshasbeensmuerizedinmrenouSGO). Arecentdiscus- aim au socianstry (procedures for data collectim, applicatims, etc.) may be found in Borgatta (1968). Socicnetry and The Internatiaxal Journal 95 Socianetry, founded by Moreno, are joumals dedicated mostly to Ema—'3, (r closely related, areas of research. “A persm's influence danain is the amber of irrlividuals in his social system whan W—Eectm or indirectly. [([ll [.I ,l‘l ‘[ ill [I ‘ [111‘IIIYIIIViIIIIIIIIlil/L [I ll . ill l’lf" [ll.[[ l 1n ae-stspsyuetricalmxectimssodstbetmmpersmsa,b,ande. Taken together, these three sets of relaticns formagggge, defined asasystuninwhiduatlsastthresmmberslnvereciprooalintw— actim.‘ Taken individually,eachofthethree sets of synmtrical relatims (1.0., ne—ob, ae-oe, and be-ee) forms a gag, defined as‘mopersausmutuallymagedininterectim. A am is therefore a representatioml device used to i1- lustrete certain types of relatims (usually two-valued) between pairs ofindividualsinagreup. Assuch,sociogrenshavebeenwide1yused insocialpsycholoyandsocioloy. Often,hoaever,thesediagruna boomeomfiusingtofimereader. Muenthemnnberofelanentsina misrelativelylarge,ormeufl1emnberofchoicesallmedeach respaudsntisinoreased,thestructureofrelatimstendsalsotoin- meals in carplexity, with the result that the pictorial representa— tim of these relatiauships may become cmbersare and difficnt to cmprehond. Inadditim,csrtaingrephic representationsmaybs retlm'ndslcacflng,asoanbesembyfiueexalplepmvidedinfigme2. mlythrcughoarefulsxamimtimwillmsperesivetmtthe fcmsociogm(a,b,c,mxld)infigure2representthesmnestmc- tumlrelatiaus. misissoespsciallybeomsetharearenospecified standardmlesfcrtheoonstructimofsociogruns. 'Ihslocatimof thscirelesmpaesentingeachgroupwuberisarbiuerilyarrenged. Infact,differentreseamhersusingthesanedatamaybuildasmany .Pestinger and others define this particular type of subgroup as "an extreme instance of clique formation within a group," in that itiscalposedofthreeindividuals "allofwhanchooseeachother mutually" (Pestinger and others, 1950, p. 1%). 15 different sociogrene as there are researchers. (T) 0 W I/OE (\V A 0/. A. 1 W2. Emphoffcmdifferent sociogremsrepresenting the same structurel relations in a hypothetical five-menbsr gram. Emlyattmptstodealwi‘d'uthispreblan, soastomakesocio— grmmremderetandableandna'euseful fortheanalysis ofsocial structures , have resulted in several alternative techniques , but sat- isfactory opereting rules for the construction of such diagaus have yet to be developed. ' Northway (191m and 1960) proposes a system called a _1_:_a_rge__t_ socicgrem which snphasizes "choice status," indicated by emcentric circles, wifiufiuepersmreceivingfluehighestnnfluerofchoioss placedat theoenter'ofthecixele.. Patterns of relatimships ate shomintheusualway. Powell (1951) suggests theuseofsynbols of different sizes to differentiate people m the basis of the number of socionetric nominatiaus they receive. Proctor and Loomis (1951) make usecfplysicaldistancebethempointsmthesociogrmtorepresmt m distance between persms (e.g., mutual choice, very close; mutual rejectiau, very distant, etc.). Still other devices are offered by different authors, but the fact mine that 35 malflc u_;_t_i_1_i_.1.z g the sociogrmnWEQEgli-mited, wfimgm 16 restricted to. descriptive statements . * Studmts of graph theory have undertaken systanatic investi- gatiauofflrsuopsrtiesofdiagrem,usingternesuchassimpleuues (topology), circuit diagrams (physics and engineering), crganizatimal stmctures (econoudcs), digraphs, etc. The latter term was proposed by péuyssm isusedbyI-iarer'y and others (1965). Thenext sectim affluepresentchaprterisabriefdiscussionofdigrephs,arritheir potential use in relational analysis . m Disrupt! The theay of graphs, or graph theory, deals with abstract con- figuretims called "graphs."** A m}; consists of certain points, a, b, c,andd,oa11editsvertices,andcertain1inesegsmtscumectirg .Spilerman (1966) suggests a method for analyzing socianetric informtim using a mutual choice sociomatrix. According to Spilerman, fluecamecticumatrixdevelcpedbyfluisroutinecanbeeasilytrens- famed intoasociogrem. Acanputerprogmmwhichcausflmts the matrix directly from socicmatr'ix data is mentioned by Spilerman, but details are not given. ”The first paper (:1 graph theory was written by the faunaus Swiss nefluunatician Lea'mard Euler (1707-1783) and it appeared in 1736. One of flue first systematic treatnents of graph flreor'y was provided by KCnig (1936). Initial applications of the theory were, lucwever, "little wmfluingmreflmgivingnanestopoints, linesandparticularcm- figuretims of points and lines" (Coleman, 1961;, p. 1093), with per- haps little interest for flue social scientist . Subsequent works have gmebeyaud this initial state, as exenplified by the works of Berge (1962) and Planent (1963) in France, and Ore (1962; 1963), Busacker and Saaty (1965), and Harery and others (1965) in the United States. In neflmematics graph theory is classified as a branch of topology; but it is also strmgly related to algebra and maflix flueory. Graph flueory derives, in fact, from theories about nets and relatiaus. A net cm— sists of a finite set of points together with a finite set of-fl'nes, wereeachlineisanorderedpairofpoints. Arelatimisanetin michmtmlinesarepamllel (Ore, 1963; andHareryamorfluers, 1965 . l7 vertioes such as ac, db, etc., which are calledtheegggsof the graph (Ore, 1963, p. 5). There are different types of graphs which turn up inmnyusesofgrephtheory. Quetypeofgrephhasadirectimor orimtatia'u associated with each one of . its edges. This special type of graph is generally called a directed m}; (Ore, 1963; Busacker and Saaty, 1965), (1' simply a 11m (Baron; and others, 1965). A M causists fluerefore of minis and directed lines! The primitive or undefined term of the axiom systen for di- graphs are the following“ Primitives: P1: A set V of elanmts called REEF-3° P2: A set X of elatents called ling: P3: AfuncticufwhosedanainisXardduoserwugeis omtainedinv. Pu: AfmctiausvmosedanainisXandwhoseruargeis cautainedinv. headmofadiagrefiuare: a 'lhetermnetworkisfrequentlyusedinsteadof ordi- , especially {3% quantitative charecteristics are ed to points and lines , in additim to the purely structural relation- ships that are the defining characteristics of a digraph. (he speaks, fcr eucmple, of electrical netwcrks, and flow netwcrks, in which quantitative measures of energy, and flow, respectively, are associated with fl: edges (Busacker and Saaty, 1965, p. viii). Unless otherwise indicated, the retaining discrssion of greph theory, aswellasthedefinidmsgivenhereafter, arebasedon Harery and others (1965) and E'lauent (1963). 18 A1: The set V is finite and not anp‘ty. A2: The set X is finite. A3: No two distinct lines are parallel. A“: There are no 100ps.* Indiscussing digraphs, pointsaresanetimes referred tobythe notatims v1, v2, vp, and scnetimes by letters such as u, v, w. Influepresautfluesiswewillsinplyusea,b,c,etc. Thelinesofa Warefrequuentlyirxiicatedbyxbxz,...xq. Aline,interns ofitsthoints,isindicatedbyvygforalinefrunvltovzcruv fcralinefrunutov. An example of a simple digraph with its custanary notation is providedinFigureS. Thesechasthreepoints(p=3)andthesetX col'rtairusfcmlines(q=|u). Theflureepointsaredemteda,b,cand fluefourlinesare: x1=ab;x28ba;x3=ac;xuaoa. Assmnirugfluatthedigreph(D)inFigure3representsafriend- shipstructure, onecf its interpretations mightbethe following: the Figure 3 . Example of a digraph with its custanary notatim . a . Two linesoxl and x2 are parallel if f(xi) = f(xj) and s(xi) = 8(Xj). A line x 18 called a 1292 If fix) = 80:), i.e., if it has the first and the secmd pomts. 19 pointsa,b,crepresentflueepaeonsandeachlineindicatesfriend- shiprelaticnsbetwsenflusm. Simetherearenolines'joiningpoints aandc,memayinferfluatfluetmpersonsrepresentedbyfluesetwo pointsarsnotfriends. Onflueoflm'rand,fluelinesconnectingaand bandaandcillustretedyadicinterections,neaningfluatpsreona hashendcasnutualfrimds. The thea'y of directed graphs is concerned with the abstract rotimoufstructure. Assuuch,itdealswith patterns ofrelationships anmgpairsofabstrectelements. Thus,theflueorypgr_§gnekesm referencetofluearpiricalworld. Asshominnenystudies,however, itcanserveasamathematicalnodelofthestmcmrelpropertiesof mlafioruhipsmugpirsofelenents, since it provides campts, W,andmefluodsappropriats to structurelandrelational analysis. Haruaryandofluers(1965, p. 3) giveflureeprincipal benefits whichinflueirOpinimfluereseamhermygainfrunmployingdigreph theayinhisfleatmwofstrucmrelwrelatia'ualdata: 1. Hisvooabularyfordescribingeupiricalsmmesisen- richedbyusefulncvtermhavingprecisemeaufings: fluelanguuageof digrephscmtairnalargenwmerofomceptsmichrefertorelatively omplexstmcmrelproperties. 2. Digrephflueoryarudassociatedbrerucluesofmflmdcspro- videteclniquesofcouputatimandformlasforcalculatingcertain quantitative features of anpirical structures . 3. 'I‘l'ueaxiansfwdigraphflueoryleadtoanextensivebodyof lop'oally derived statements: each of these statenents (1‘ Moms become a valid assertion about any anpirioal structure that satisfies 20 fluodomofdigraphfireory. Perinpsmeofthemintesestingapplicationsofdigaph theayflrunthesocialscimtist'spointofviswisincormtim with the so—oalled balanced primiple of social psychologists. As prwosed by Eatery (19514; 1955; 1959a), whenever the relatian between adyadombeviawedaspositivea'negative, theirbalameor'im- balance can be determined. This procedure is accanplished by nulti- plyirg the signs around each flof a digreph.* The relatimal structm‘ewillbsbalancedifthelroductispositive, andunbalanoed if negative. Flaunt (1963) developed this notim further. With the useoflattioes, redeterminedtheminimunlengthpathtl'maghmich anmbalmoedgrephoanbecarebalmcedbymcoessivedxamesoflirflcs.” When oaupared to merely representational devices a." descriptive tedmiqms such as sociogrems (as treated in the present study), di- graphs otmtain any note mstkmtioal preper'ties, and therefore offer considerably greater possibilities for mathematical analysis of struc- tural and relatimal data. Nmetheless, sane authors believe (e.g., Berge, 1962; Coleman, 1961+) that the Operations yet available in this bremhofnnfluematiosaremthermak. Thewhole approachneeds tobe further- developed in order that it may be usefully applied in several different danains of social and behavior research. (he of its obvious *A le of a digraph omsists of a nontrivial path (i.e., a pathcmsis ofnrrethanonepoint) together withaline firm the terminal to the initial point of the path (Harary and others, 1965, pp. 39"“2’0 “A finite ordered set is a ~lattice if every one of its parts possess a supericr limit and an inferiSFTimit. The super-icr limit of a subset of parts is their unim; the inferior limit is their intersection (Flaunt, 1963, p. 1“). 21 limitations (as tintofthesociogram) hastodowiththemnberof elmmtsinfiregrmzpmaderoonsideretiua. The largertheN, or sanple size, the me oauplax the representatim of its structural relations. It in perhaps the recognition of some of these difficulties tlutledsmdentsofgrephtheorytoeaqaandtheirinterestinomer brambles of mathematics. Putz-ix algebra has an especially close rela— tim to the theory of directed graphs. In fact, one of Hunt's main interest is what he calls l'analfie Wtficielle des structures or the matrixgrephic analysis of structures (Fluent, 1958b, p. 130). Barge (1962) and Harary and others (1965) also deal exten- sively with the relationships of graph theory to matrix algebra . Many offlnseiupcrtmtrelatimshipsoarmtbeexanfinedinthepresent study, but at least sane will be reviewed briefly in the last section of the present crapter. 7‘ The Socicmatrix Porsyth and Katz (19% and 1960) developed an alternative pro- oemre for I'm-Idling socicmetric data , the socianetric matrix or simply socianstrix. 'IhisisanatrixobeyNdimensionscorrespordingtoa group of N persons. Conceptually similar to the sociogrun, the socio- natr'ixdiffersm-inlyintheeasewithwhichoertaintypesofdataoan be handled. myth and Katz's (191:6 and 1960) idea is simply to list thepersms inthe 83181581113101}; thermandthecolmmsinthesane cxvder. mmconespmds tOthePa‘Bmsnakingtherunimtionsor sociamtric choices. and the colmns to the psrscns receiving the 22 nominations . The choices made by any of the group members are then entered in the appropriate cells. A plus (+) sign is used for posi- tive choices (i.e. , to indicate that a person chooses another), a minus (—) for negative choices or rejections, and blanks for indif- ference or no mention. The cells along the principal diagonal cor- respond to self~choices and may be filled in with x's. Figure 14 illustrates the form in which the data can be recorded. It is read horizontally, thus: a chooses _b_ and g, is indifferent to _c_:_ and Hardness abode Nominators c + + x + - d - -. x .. e - + t K Figure I». anmple of a sociomatrix with a hypothetical five-member group. rejects d. Column one is read thus: a is chosen by b and by g, and rejected by e, whereas d is indifferent to a. Forsyth and Fatz (19"6 and 1960) swwest a few manipulations in the original matrix to produce a new matrix which will exhibit the grmp structure in a standard form. These manipulations consist of rearranging the position of group members in sucn a way that the new matrix will show (in a cluster along the rain diagonal) the persons who have positive mutual choices, and those who do not choose each other as relatively separated. The tendency is for the blocks of minus sighs 23 to appear at the upper rightly-aid and 10481" lefthand oormrs of the matrix, while the amine isolates will tend to appear at or near the editor of the matrix. Variations of the socicnntrix have been used by different re- searchers. Bales' (1950) interacticr. matrix, for example, is a special use of the sooiamtrix, which is also called "who—to-wlm" nan-ix.“ The sociomatrix or "win-tom" matrix allow the mesentstim of hall titration m a given item of sociautric choice. It spreads allfiasdatshsfomtheresesroherfwhisscmtiny. Unlikethesocio» gram, or the digraph. it is appropriate fer grows of any size. It does enable are to single out subgoups and isolates, but it does not in itself Mass the labor of analysis; if the matrix involves a large umber of elements, detsmining the group structwe, oocmxicatim paths, etc.. is still a lengthy and tedinas tank. A m sophisticated variation of Porsyth and Katz's (19106 and 1960) prosecute was proposed by Dunn and Brmmdage (1950). It mists offirstassigzingmightstothrmoffinmstrix (franmstou bogimingwithmewttanrow), trmthsaveregsproamtofthselcnents ineschcolmnandtheconesmmdingweightismaximized fweach colum, while the sum of the squares of the elansnts about the principal .aslssmdhiscolleaguesatthshsrmrdlabmtoryofSocial Relations have developed a method of "interucticn process analysis" for observing, mlyzing. and comparing behavior in wall groups-especially grmps devoted to minim-making cr problem—solving. Bales uses a "mxo-to-wrm‘ matrix to study, for awards, acts as indiomts of the relationships mug the group where. The Bales Instrix allows also up); “human” as which when of the group talk to which other number. 2Q diagaal is minimized. The matrix is then rearranged so that the column with the highest average (rank one) is moved to the extreme left anifimeoorrespmdingrowismvedtotheextrmetop. Thenext- rerfldng oolwm is placed next and the corresponding row is placed in positicn two from the top, and so on. One advantage of this improved technique suggested by Beum and Brundage (1950) is that the nmerical values of the cell entries are not limited. They may be choices, ratings, rankings, percentages, or any other W8 of interpersonal relations. In addition, the final solution can be used for further types of analysis, such as the factor analytic procedure suggested by McRae (1960). More important, it can be adapted fcr canputer Operation, as shown by Borgatta and Stoltz (1963) . Digraphs and Matrices The present section centers on some of the relationships between digephs and netrioes, and a few concepts that are basic for an under- standing of these relaticnships. They will perhaps be better explained by i11ustretim.* Camider a digraph (D) of five points, V = {a, b, c, d, e } whose relations consist of ordered pairs (ac), (as), (da), (do), (do), (ea). Figure 5 shoes this digraph with its adjacency matrix.“ .The terminology as well as the mathematical notatims in this area seem to vary from author to author. The terms used here, and their definitim follow Host closely Harery and others (1965) and [use and Perry (1966). MGiventadJIggriap,hD itsedjapen acen,cymatrix A(D)=[:ifi]’ isa squarematrixwithmerowandmecoltmmforeadipointo ' which theentryai =liflineaa isinD,whileai Oifaia isnotin D. Adigrephmayhavenorethanmeadjacency trux,depen3ing°fonh:he mingofthepointsofD. 'I'hus,ifwealtexedtheorderirgof 25 a b afoulofiz J,' bOOOOOO D. A(D):c000000 \ d 1 0 1 o 1 3 °—-—->-° e 1 o o o 0 1 d C L... .. ColmmSum 2 0 2 0 2 Figure 5. Example of a digraph (D) with its adjacency matrix A(D). Certain features of a digraph may be readily seen in its ad— jacency matrix. An example is the sygmegy or WE of a relation (or of the digraph itself).* If a relation is asymnetric, the existence of the line aiaj precludes the existence of a line ajai. Thus if aij = 1 then “ji 8 O. Symetric relations, on the other hand,are those of animal choices a" two-way camunicatim, for example, the relations (as) , (ea) in digraph D and in its adjacency matrix in Figure 5. Another important feature in the adjacency matrix is its row and colwm suns, which indicate the number of lines originating and temlinating at each point of the digraph. If we take digraph D in Figure 5 and its adjacency matrix to represent a cmmmicatim network, points of the digraph sham in Figure 5, we might obtain a different adjacency matrix (although the digraph might renain the same). We will refer to the adjacency matrix of a digraph assuming that the order of the points is understood. For detail discussion, see Harary and others (1965). e . . Luce and Perry (1966) use the term antnmetry in the same sense of asynmetry as used here (i.e. , lack of mutual choice in a relation). 26 each of its points (which could represent persms) can be classified as follows:* Transmitter - A point whose outdegree is positive and whose indegree is 0 . In a commnication network a transmitter corresponds to a person who can send but not receive messages. In digraph D, the individual represented by point 9 is an example. Receiver - A point whose outdegree is 0 , and whose in- degree is positive. A receiver corresponds toapersonwhocanreceivebutnotsend messages. In digraph D, __c_ is an illustration. Carrier - A point whose outdegree and indegree are both 1. Corresponds to a person who can both send and receive messages. In diagraph D, g is an example. Isolate - A point whose outdegree and indegree are both 0. An isolate person in a commnioation net- work can neither send nor receive messages. In digraph D, b is an example. Any other point not included in this classification is called an ordinary point. As a rule, a person in such a position can both send and receive messages, as for instance, the individual represented by point a, in digraph D, Figure 5. One may see at once that liarary and others' classification is very similar to that mentioned in the last part 0; Chapter I. There we referred, for example, to connunication leaders, liaisons, and isolates. on. n...— 1"This classification scheme is borrowed from Harary and others (1965), and is used here for illustrative purposes. Obviously, other typologies may be used in the same context. The term outdegree of a point a, written od(a), is the number of lines from a. The od(a) of a point a, written 1d(a), is the number of lines to a. The 1d(a) of the cor'reSponding pomt is given by the column sum of the adjacency matrix. 27 A commnication leader could be a person represented by an ordinary point, in Harary and others' classification. A liaison could be a carrier, and an isolate is similarly defined in both schenes. Swmm'y The purpose of the present chapter was to briefly examine ap- proaches to relational analysis. As we saw in the course of our dis- cussion, each of the three approaches reviewed here (i.e. , the sociogram, the digraph, and the socicmatrix) has its advantages and limitations. (he advantage of both the sociogram and the digraph is that they offer a pictorial view of the patterns of interconnections of the system under consideration. 0n the other hand, they are both difficult to canprehend when dealing with a relatively large N, or sample size, or when the types of relatims studied are canplex in nature (i.e., when several alternative socionetric choices are allowed). The digraph has certain obvious advantages over the sociogram, in t1 at the former is usually constructed m the basis of mathematically-derived rules , while the latter is usually wilt unsystematically.* The socianatrix does not have the pictorial effect of sociograns or digraphs, but it also spreads the data before the researcher for his scrutiny. mrdlemnre, it is appmpriate for groups of any Size. What is mom important, however, is the fact that different algebraic manipulations are feasible with sociomatrices. The next chapter focuses on one such type of algebraic manipulation, that is, matrix nultiplication. *Spilennanf1966) developed a canputerized method that allows the. construction of digraphs (of symmetrical relations only) directly from sociomatrix data. CHAPTER III MATRIX MJLTIPIJCATION IN THE ANALYSIS OF INTERFERSONAL C(M‘ILINICATION A significant step forward was taken when Festinger (19%) and Luce ard Perry (191:9) outlined the application of matrix multiplica— tim fw the sociaratrix. This procedure allows identification of m faunlly defined structures, as well as the analysis of indirect relatims. Essentially what they propose is the manipulation of matrices by means of raising them to n-powers in order to determine n—chains mag group members, as well as the tendency toward subgroup or clique formation. If A is a square matrix, its power can be failed: A2 an AA, A3 = A2A, etc., and, A° = 1 The entry of A2 is:* “i? " ailalj * a‘12‘32j ” ” ainanj As an illustration, consider a simple digraph D of four points. V = {3, b, g, g } whose relations are (1b), (91;), °'°, (93). Such a digraph, and its adjacency matrix together with its squared .This means: the number which goes into the cell corresponding to row i and column of the squared matrix is obtained by multiplying each row i of the original matrix by the corresponding cell in column 1, and then adding up the product. The pI'OOJC‘t will be different from zeroonlyifaunitappears bothinthe immrdinthelcellbeinz; considered. For discussions on matrix Operations, see, for example, Kemeny and others (1966), Host (1963), or Mcmnn (1962) 27a 28 matrix, A2, are shown in Pigme 6. a b . > . o/fi o d c a b c d a b c a a o 1 0 fl a 1 1 1 H b 0 0 l l b l 2 0 l A A2 : c 0 l O l c l l l l d l 0 0 ' 0 l l 2 L3 _. d __ __, Figure 6. Example of a digraph with its adjacency and squared matrices. Let us suppose that digraph D and its adjacency mauix A in Figure 6 represent the choice patterns in a hypothetical fair-number group. Readingacrossmnlinmatriwaefindtl'atperemgchooses personsbardd.’Cohmmlshowst1atpersma_ischosenbypersondc. By inspection, we can therefore perceive in matrix A direct, ale-step corrections among the group members. The squared matrix A2 sham, however, indirect, two-step connec— tions amurg the group members. Fm example, in the squared matrix A2 we see that cellglasavalueofl (intheoriginalmatrix, A, this cell has a value of 0). This means that achose another person who chose g. In fact, the following relationship can be seen in digraph D: sap—+9.. In cell 93 of matrix A2 we also find a value of l. in- dicating the relationship: c—-—+ 515—93. 29 UnlikematrixA,thesquaredmatrixA2hasvaluesotherthanO's ardl's. hemlueshigherthanmeinmatrixAzindicatethenmber oftwo-clninsbywhich‘mopersmsmeconnected. Fwexample,ifcell actusavalueofhwemaycmcludeflatgdnsetmpemmsmodose g. attaincecellagrasavalueofl,welcmt}at_adiosemeperson whochoseg. ThiscanbeseenindigraphD. MatrixAhas 0'sinitsmajcrdiagonal (therewerenoself- choices). mtrixAz,hwever,hasl'sand2's. Theserepresentthe nnberofmmaldrcicesreceivedbyflregrorrpnmemlere. Cellsglgand ddbofleretwomutrnlcmices,whilecells§gandc_gmmeead1. Wecmsee,then,thattherowsandcolumnsofthesquared matrix A2 chm how well connected to the group an individual is. As Pestinger and others (1950, pp. 1uo-1u2) point out, the meaning of these indirect comecdms between group members is quite imtcrtant, be it indicative of influence, channels of communication, or any other type of interperemal cmnection . For example , if the original sociaretric choices are designed to measure patterns of influence within a social systemsuchasacomunity, matriwawld indicate thatpersongg exerts direct influence upon person y. The squared matrix, A2, would however indicate the extent of indirect influence which person 35 has within the system, since it shows which other persons he influences indirectly, that is, through y, 5, etc. If the original sociametric choices are designed to trace channels of communication, the squared matrix, A2, would show that a given item of information originating with person _x_ (i.e., a transmitter), muldmachpersmsv,w, and_z_intwosteps. Ifanyofthesethree 30 persons is a carrier (a person who can both send and receive messages), the item of information may also be received (in three-steps) by persmsq, \_1_, etc. mtheotherhand, ifindividualvisareceiver (he can receive but not send messages), the item of information that readeshimwouldmtbepassedmtoothercamnmitymembers. By adding the original and the squared (or nth) matrices, the researcher may know, for example, how many elements in the camunica— tion system receive any particular item of information if this message is started with perscn _x_. He may also obtain answers to such questions as: "Who influerees whom" in a specified number of steps? Which elements are influenced by arly a few other elements, and which are influenced by a large number of them? Who are the persons in the sys— ten most indirectly connected to each other? What proportion of all possible connectims actually exist? Who are the communication leaders , liaiscns, isolates, and so forth? howledgeoftheindirectcormectionswitlfinagroupmayalso provide the criteria for classifying people according to their position alorg n-chains (i.e., (me-step, two-steps, etc.) in regard to a given information input. The :1th matrix can be partitioned into subgroups (or submatrices) representing persons who exhibit similar claracter- istics along the n-chains dimensim. Lin (1968) combined awareness data with sociaretric data for three Michigan high schools,* by *Mareness refers to time of initial Imowledge of an innovation. Sociametric data were based on nominations of three individuals whose Opinicns respondents frequently sought . Lin's intent was to determine whether differences found in the variability of awareness dates in three schools were due to differences in communication patterns. Ill- I '1' 1 \II‘ I I I. l I l [f 31 ader'ingtherespaiderrts inthematrix (A) sothattheearliestlmower occupied the first row and column in the matrix, while the latest lorower occupied the last row and column. The matrix was partitimed into groups of respaidents who became aware of the innovation during the same month. Three types of submatrices originated from this, each representing me type of camunication pattern: 1. Ugaard cammication, representing a respondent's nomination of another member of the system who had became aware of the innovation earlier than himeelf. 2. Domward canmnication, representing a respondent's nomina— ticn of anotha‘ persm who had become aware of the innovatim later than himself. 3. Horizontal camunicatim, representing diagonal cells. Clearly, similar procedures may be applied to other social systems , such as a cannrnity. Clique Identification Festinger (191:9) and Luce and Perry (191:9 and 1966) give special attention to the problem of clique identification. what they recommend is to extract a symmetric submatrix S from the original matrix A. The entries of the matrix S will be determined by Sij = 1 if aij = l, and otherwise Sij = Sji = 0. To illustrate this procedure, digraph D with its adjacency matrix A (the reciprocated choices are in parenthesis), and the submatrix S, are presented in Figure 7. If a matrix is symmetrical about the main diagonal, the corre— Sponding ms and columns are identical. As can be seen in matrix S, . [III II. [I t I fill {Ii 32 Figure7,mameisthesamascolrmnone,rmtmisthesameas a b '0'; 3 O A Iii/q a . d c abcd abcd F“ ... 1p- ‘1' a0(l)0(l) «10101 b(l)00(l) blOOl A: S: 00100 c0000 d(l)(l)10 (13100 Figure 7. Eatemple of a digraph with adjacency and symmetrical matrices . column two, etc. When a symmetrical matrix is raised to the nth power, treproductisalsosymmetric. 'Ihisisshominrigure 8,whichrepre- sentsthe2ndand3rdpaversofmatrixs. a b c d a b c d a 2 1 o 1 a 2 3 o 37 b 1 2 o 1 b 3 2 o 3 32: 33. c *0 o o o c o o o o d 1 1 o 2 a 3 3 o 2 L— ...1 ... ..J. Figure 8. Example of a squared and cubed symmetric matrix. The matrix S3 has a similar meaning to that of the squared matrix S , with the difference that it shows the three-step links between in— dividuals in the group. For this reason, it provides criteria for 33 clique identificaticn. As previously defined, a clique consists of a subsystemofthreeormore elements each inmutual interactionwith each other element. The major diagonal of matrix 33 indicates which iniividualsinthegouparecliquemmrbersammicharenot. Ifan individual's cell in the main diagonal shows a value other than zero, he isa member of a clique. Otherwise he is not. In our example, mlygisnotacliquemember,afactthatoanbereadilyseenby examining digraph D in Figure 7. Besides identifying clique numbers, the values in the main diAanal also indicate the number of individuals in the clique. Pram ma‘u‘ixS3aiecansee, forexample, thatpersonghasaZinhismain diago'ralcell. 'Ihisvalueof2meansthataoanreachhimselfbym different three—step comectims, that is, gag—a bad—1a, or _a_—-_d_ dig—+5. We can see, therefore, that a is a participant in a three- memberolique, theothertwomembersbeingbandg. When dealing with large groups, where more than one clique may exist and these cliques may be composed of different individuals, the nwmberappearinginthemaindiagonalofthe33 foreachpereonwillbe equal to (n-1) (n-2) (Festinger and others, 1950, p. 11m). A person in a clique of three members would have a diagonal cell value of (3-1) (3-2) = 2, which is in fact the value appearing on the diagonal cells ofa_,_b, middmmatrixs3, Figure 8. Apersoninacliqueoffour members would have a diagonal cell value of (“-1) (“-2) = 6, and so on. (hoe we have established which individuals in a group are clique members and which are not , as indicated by their cell values in the main diagonal, it may also be desirable to identify the other clique 39 members. This may be done as follows: their cell values in the 83 matrix rm will have a minimum value of (n-)(n—2) + l (Chabot, 1950, p. 139). For a clique oftlree members, as in our example (matrix 83, Figure 8), this value will be 3. Ifwe take b, for instance, we can see that g and g are the other members of the clique, since they have a value of 3 along his row. Several investigatiors subsequent to the original formulatiors ' of the matrix multiplicatim technique by Festinger (1999) and Luce and Perry (19159) were directed toward analyzing ever more complex types of relatiorships, as well as toward solving some of the problems involved in the use of this system (e.g., Katz, 1953; Harary and Ross, 1957, Hubbell, 1965, Cartwright and Gleason, 1955; Sabidussi, 1966; Spilerman, 1966). One problem with the matrix multiplication approach relates to situation in hhich an individual is a member of more than me clique. Underthsse circumstances, theuse ofamatrix like 83 does not seemto be of much help. One alternative is, of coarse, to refer back to the original matrix, A, where the corrections may be individually traced. Another alternative proposed by Lme,* corsists of computing the matrix pacer-s, A, A2, ..., A", and then adding up the product (A + A2 4' ... + A“) to form a matrix B(n). Next, a pseido-structure B'(n) is formed, with 0's where B(n) has zeros, and 1's where B(n)’has positive entries. The symmetric part of B'(n) is then extracted and the cliques are ..--... *Cited by Chabot (1950, p. 139), from an unpublished paper by human R. Luce. 3S carwtedasifitwereanordirmysocianetricnatrix. Accordingto lace, the cliques of B'(n) are identical with the n—cliques of A. The nethcd seam, however, a bit carplicated and laborious. Harnry and Ross (1957) extend Festinger's (19149) and Luce and Perry's (1999) approach to the determination of the cliques in a group having three or few cliques. They begin by identifying a "unicliqual" person (i.e., a person who belcngs to exactly one of the cliques in a group) , tlEn by an inductim—reductim method, they proceed to identify the cliques in the group. Waking with the transpose of a matrix identical to that used by Festinger “ Luce and Perry} and drawing on Katz' work (1953), Hubbell (1965) discusses a method for clique identification based (:1 a generalizatim of hmtif's input-output nodel. Hubbell's discussion centers (1’: the notion that ifpersong chooses personbas a friend, then there is a likelihood that _b_wi11 be able to influence a. Hubbell's approach departs frcm previms work in the sense that it allowsmighmdlirflcsbetweenOemdlinfl‘neryNnatrix. 'l'heweights can be positive, negative, or neutral. As with other procedures, cliques are identified on the basis of clusters of individuals with synnetrical relaticns. One additional feature of this technique is that all powers of the matrixcan be used, thus eliminating the arbitrary choice of 83 set up in earlier attempts (e.g. , Festinger (19149) and Luce and Perry (1999). ~---... - ___ _ i . . . The transpose of a matrix, A, written A13, is the matrix obtained by writing the rms of A, in order, as columns. In Hubbell's terms, aii denotes, therefore, j's choice of i, rather than i's choice of j. 36 Hubbell illustrates his presentation with data from McRae (1960), and then compares his resulting cliques with those identified by McRae, concluding that the input—output model has greater dismiminating power than McRae's factor analytical technique. Identification of n—Chains Another problem that arises in ccmrunication research has to do with the precise identification of what Luce and Perry (1966) define as n—chains, i.e., links of n~steps in length firm i to j_. Cartwright and Gleason (1966) discuss this same problem within the frenework of graph theory, and prefer to use the terms padre and cycles. The problem, however the cmtexts of its discussion, is to fine the number of ways one can go from are point to another using a given number of lines, without passing through any point more than once. One may want to know, for instance, how many ways a message can go from person a to person 5 through a neth in exactly n-steps while satisfying the requirement thatmpersmhearthemessagemrethanmce. The method of matrix nultiplicaticn, as suggested by Festinger (lQHQ) and Luce and Perry (1999 and 1966), allows what Colman (1969, p. M47) calls "doubling back," that is, the same links are counted Irorethanonce. Forexample, athree-personchain fromgtobin digraph D (Figure 9), using matrix nultiplication, will result in the connections: 93—» 9:" cit—~13. 37 In an attempt to solve this problen of redundant sequences , Coleman (196“, pp. Im-uue) devised a method which consists of Figure 9. A digraph illustrating the problen of redundant sequences. separatirg each rw vector rather than using the entire matrix, so that each perem's camectims are calculated separately. art as Coleman himself aclmcwledges, this alternative is only an approxima- tia'n of what muld be desirable . While the older method of matrix multiplication is marred because it allows redundant sequences , Coleman's alternative procedure counts too few. For example, in digraph D, Figure 9, the chain a—ed—eb—ac would not be counted whei Colanan's pro- cedure is used, because that chain includes the connectim b—ec, already part of the chain a——>b—+c. Ross and Harary (1952), and Parthasarathy (1969), offer alter- native solutims to the problem of redundant sequences , but their foruulas are quite formidable and there seems to be little likelihood that a general solution is practical by their nethod. The Distance Matrix Both the problem of nulticlique membership and that of the determination of n-chains seem to be satisfactorily overcane by the 38 use of a distance mtrix.* Harary and others (1965, pp. l3lt-138) define the distance 95333. of a digraph as "the square matrix of order 'p' whose entries are the distances dij“ [dij "whip, the distance «1(ajai) from 6.5 to ai]. if there is no path from ai to aj, then dij = a. The distances in a digraph such as the one in Figure 10 are not difficult to figure, and are shown in the distance matrix DUI): a b a b c d 'M-' r .— A ' a o 1 2 3 D: i 7 I ¢ b 3 0 1 2 ; -fr 0 D(I): 3 d c c i 2 3 0 l d 31 2 3 o k Figure 10. Example of a digraph with its distance matrix. Matrix D(I) presents two main features: (1) its major diagaial' has only 0 entries, because the distance from every point to itself in digraph D is 0, and conversely, and (2) every one of its entries is finite. On the other hand, three of the entries of a point a in matrix DCI), associated with digraph D, Figure 11, are no, because a is a transmitter and, therefore, cannot be reached from any other point. A distance matrix D(I) is constructed from an adjacency matrix A as follows: (1) enter 0's on the main diagonal of D(I), so that dii = 0., (2) enter 1 in the MI) wherever aij = 1, so that dij = l. -“M-Mo--““~-“l aCartwright and Gleason (1966) present a method for findin'z both the number of Eths and cycles of any given length through a series of Operations with the distance matrix to analyze sociometric data for three school systens in the State of Michigan. 39 Far n-powers of A, enter {1 wherever ai?) prim ij entry in the MI), so that dij = n. In case any cells rennin 81,andaslongasthereisno b a b c d a 0 2 3 D D: b o 0 l 2 o-—(——————. 13(1): (1 c c a- 2 0 1 dL-l20 ad Figure 11. Example of a digraph with its distance matrix. open an 0(1) after the Ari-1 power has been emprted, enter - in all (Barfly and others, 1965, p. 135). These procedures are illustrated in Figure 12. If matrix A in Figure 12, were raised to the fourth power (An), all four cells on its main diagonal VDUld be 1, consequently, all entries on the min diagonal of matrix D(I) would be u. Harem, we )mow beforelmd that dii: 0. Thus, unless one is particularly interested in analyzing the lines that have the same first and second points (loops), there is no need to go beyond the A““1 power. In actual canputatim, it may be more practical to substitute . for zeros , but this does not seem to be of major relevance. In additim to showing the caunmicatim patterns of me, two . . or n—l steps or drains, the distance matrix permits the 0011111- taticn of the camunication danain of each group member, 01 the basis of which subgroups, cliques, dyads, liaisons, and isolates can be identified . '40 a ;__b D: d c a b c d a b c d a o 1 0 0T a F0 1 .. J b 0 0 1 0 b - 0 l 0 A 8 MI) = c 0 0 0 1 c «- o 0 1 d 1 0 0 0 d 1 c- 0 (H L— A b a b c d a b c d 7 “ - 1 a 0 0 1 0 a 0 1 2 a 2 b 0 0 0 1 b c- 0 l 2 A a LCD = c 1 0 0 0 c 2 c- 0 1 d L'0 l 0 0 d l 2 0 0 a b c d _a b c d a o o o 17 a o 1 2 31 3 b 1 0 0 0 b 3 0 1 2 A = MN = c 0 l 0 0 c 2 3 0 1 d 0 0 l 0 d 1 2 3 0 Figure 12. Illustration of canputation prgcedues fcr a distance :atrix for A, A2, . ur A person's camunicatim danain is the number of systen neubers directlyor indirectly connected to him. _C__1_i_$_e_s_and Ware identified by siuply selecting the persms with the Mghest camunica- timdanainandthentmcingthosewhoaredirectlyorimlirectly cmnected to than. Once cliques and subgroups are identified, dyads, liaisms, calmnxicatim leaders, and isolates, can also be found. The distame matrix provides also a basis for the amputation of a centrality index and a prestige index foreach element in the eyeball. 'mecentmlityindexisthesunofallchairmintheinfluence damindividedbytleinfluence danain. Theprggflgofeachelment isflaeinflnencedamindividedbythepredmtofhiscentrelityindex and the amber of other elements (N-l). Carputatimoftheseindicestusbeenprogrmdforcarwter use,andaredescribedinnmedetailinthenextchapter.* *These indices may be computed through a program written by Dr. Nan Lin, of 'Ihe Johns Hopkins University. CHAPTER IV WICATION INTEGRATION IN TWO BRAZILIAN COMMUNITIES The two preceding chapters deal with the use of different techniques for the analysis of relational data. As shown in Chapter III , the untrix nultiplicatim approach is suitable for the formation ofindicesaniprocessvariables,whichintm'nallm,whendealing with relatianl data, a shift in the focus of analysis: fron indi- vidual to dyads, cliques, subgroups, or larger systems. The pmpose of the present chapter is to denrxxstrete has the matrix multiplication approach can be used to arrive at indicators of one specific process variable , nanely , camunication integration . For illustrative pm'poees, data are drawn from two Brazilian camunities. The Selection of the Two Cammnities The data used in the present study were obtained in two agpi- mltural camunities selected from a sample of 20 camunities in the state of Minas Gersis, Brazil. This sample derives fran ancriginal selection of 80 camunities initially included in Phase I of the Project "Diffusion of Innovations in Rural Societies.“ *See Rogers (1961+) for a description of the Project "Diffusion of Innovaticns in Rural Societies." N2 M3 In brief, these 80 cammxities were selected from a propcr— tional stratified sample of '40 mmicipios (counties) in which the Agricultlmal Extension Agency of the State of Minas Gerais (HEAR) had local offices. The local MAR agents in each of these 100 mudcipios were then requested to designate the two communities with- in their respective nunicipios in which they had most and least access in their programs. This procedure resulted in a selection of 80 calamities, HO "nore successful" and #0 "less successful.“ A discussion of the criteria that dictated the selection of the 20 calamities included in Phase II of the Brazil study is found in PM and others (1968). In essence, they had to be suitable sites fa‘ eaq>erimnts to be carried out in Phase III of the Brazil study. Since these experiments involved mainly literacy training and radio farm forums, the camunities had to be within reach of a single broadcast station, as well have some pre—deternu'ned place where the residents could neet to participate in one of the two Wu treatnerrts carried out (literacy training or radio farm forun). Also, they had to be relatively easily assessible fran Belo Horizmte, the Project Headquarters , in view of the anticipated need to travel to each connunity to carry out the Phase III treatments. furthermore, half of the oommnities should be of "greater success" and half of "less success." Lists of IVESILJE‘IIIS in each of these 20 canmmities were made in _.,...-..—.—---a More detailed descriptim of the sanpling procedure used in Phase I of the Bmle Study may be found in Whiting and others (1967). an advance, so that virtually all persons who were major decision-makers, fcr their respective households, and who owned at least part of the land they worked, were interviewed. The calamities used in the present study are the two, out of the 20 indicated previously, with the E *‘nest and the m mean com- nnnity inmtiveness score.* The selection of these two camunities was guided by two assumptions: 1. Provisionally, at least, we can assume that the wumnity with the highest irmovativeness score is relatively nore 'mrn," while the me with the lowest innovativeness score is relatively nore "traditicnal." These two tonns——nodem and traditiaxal--a.re hence- forth attmhed to each of the two camunities. 2. The selection of a "modern" and a "traditional" camlunity ms based on the assunrtion that these two types of social systems ex- hibit miderable dif f ere-1 aces in their internal cmuunicatim patterns, especially men a variable such as camunicatim integration isconcerned. -{ l'efir-zitim; of Conmmication Integration As previously defined (‘Efipter I), a camnnficatim system, which may be a subsystem of a social system (in our case, a camunity), unbreces such ccmmi'dcatim subsystem a8 <21in88. 311331091389 chains, and SR3“: I‘dr’t‘lefm'm ~ C" cumwhicaticn systen curtains such elements '--‘ ' -‘WW * - a ‘ ..‘r- (1') a. ' . image's—v» "j 14““ In terms of earliness or lateness in adapting an uu;<,)v;xtiuxx (infers, 1962), was measured as the normalized Of adopt-10“ "f 1" . " 12 Innovations, especially selected for each Of the 20 Cambrltlvn. us as cummioatim leaders, liaisons, and isolates. his degree of integratim of a camunicatim system can be viewed has at least two major perspectives: external and interval. mutual mmicadm integetion refers to the degree to which the cranial. available to the systan members are interconnected via ex- posure to these clumels.‘ Internal camunicatim integratim is de- fir-d as the degree to which the elemznts and the subsystems of a Win) system are intercormected via interpersonal channels. The internal and external aspects of a cannmicatim system scan to be closely interrelated. Using the two-step flow hypothesis (unfold and others, 19108) as an analogy, we may am, for ex- mph, that a cmmmication system which exhibits a relatively high degree of internal camulication integration is also likely to be W by a relatively high degree of external Minimisatim integratim. Conversely, a system with a relatively low degree of internal contamination integration may also show a relativelylow de- gree of WI munication integraticn. Orr major mm in the mt study is, however. with intemal cmmnicatim integratim, which his refer generally to CWSEEQQ integration , to facilitate dimssion.“ Within our frwmmork, the degree of integmtim of a _ g... ...—I- oo— - - *mjmenwr (labu) uses the term "integratim of canmnication strucm’ to referessentrally to what we are calling "external com- smication inteilmt 10‘“ unaws (1967) study of two villages in India is the only available empirical investigation in “bi Ch pin tion integration.’ as here dos-rum, is e: . . ternal cammnica #5 cannunicatim systan involves at least two levels of analysis: (1) the patterns of interoonnecticns exhibited by each system element , in reference to each other and to each cammication subsystem; and (2) the patterns of interconnections shown by the subsystems. This, we are basically interested in determining the camunication links m individual members of the system, as well as the relationships m counmicatim systems. Operetiaulizatim of Oamunication Integration The patterns of interconnections among individual members and ammg subsystems of a caunmicatim systen may be analyzed on the basis of relatimal data, gathered fluough sociaretric~type questions. One specific type of relatimship dealt with in Phase II of the Brazil study is based m respcnses to the following questim: i "V010 are your three best friends with whom you talk the host?" Operationally, therefore , coununication integration is indicated by the socianetric choices received by the system numbers on a criterion explicitly concerned with interperscnal cammication arrong infaml friends.* The data thus obtained were fed into a canputer program (called —.- *Following Parsons (1959), we may view interpersmal caxmmica- tion as instrumental or answerer: . Instnmental cammicatim refers to thosefifnterlersmal relations initiated for the purpose of seeking certain apec1fic information , such as the advantages or disadvantages of irmvation. . Wamtoq oanmmicatim refer to those interperscnal relatims initiate? and maintained for the purpose of friendship. Adkins...“ A w Clique 18) to reproduce a two—valued (1—0) N by N matrix, with each row Wanting a nominating person, and each oolum designating a tundra! The 1-0 matrix was fed into mother canputer mm, called ICPC, wl'loae main features incilaide:M l. A distance matrix, which has in each of its cells either (1) a positive integer indicating the rather of chains in the sl‘1ortest coluunicatim link between element _i_ and i, or (2) a 9_ if such commun— icatim link between i and i does not occur. When raised to n—pcwcrs, the distance matrix will show in its cells values of : (a) 0 — meaning that no cmmricatim links occur betwr‘len i. and is A (b) l - indicating one-step ccnnections betwaen i and i (o) 2, 3 . . . n - showing 2, 3 . . . n-step connections betweniandi. TheClique prrogramprintsortaanmeatrixwith 1— a values, the row and colum sums, and a list of nanimtors-nminees. It perform nultiplication of the N by N matrix up to the 7th lower Yet its routine does not take care of redundant relationships, with. the result that the products appearing in each cell of the matrix ‘c not represmt the actual communication links at a given step (two three, etc.) MAs previously indicated, the ICPC program was written Ly DI. Nan Lin, of The Johns Hopkins University. Its main characteristic 3 are discussed in Lin (1968). Briefly, the present capacity of the ICPC version adapted for use at Michigan State University Computer Center is 80 elements. The 1-0 distance matrix can be raised to a nardnum of 50 powers. For the present study the two l—O matrices. corresponding to the trodern and traditional carmmities, were fin"C raised to the 10th power, but since very few elements qualified, in .1 second run they were raised to the lwth power. This second output m- vides the basic information discussed in the present chapter. I68 2. Mommaeetigndaminofeedielemntinthedistaxm matrix, defined as the number of individuals directly or indirectly linkedtoi. 3. Agmtrelityggegofeachelamt,definedasthes\mof allcheineintmoommrdoatimdaneindividedbytheoommicatim domain. to. AWMofeachelmt,definedasfl1eoommioa- umdcuindividedbyumpnoductormoenmutywexwtho umberofathn‘elanents (Bi-1). W of Cmuunicetim Integgtim Despite the relatively large mount of infomflim provided in its output, especially in terms of mechanical amputation, the ICPC progrenis stilllimited insofaras certain features areconcerned. Apparently, fiiisptog'emwesinitiallydesigned fmressarchinwhich individuals are the unit of analysis. This, the determizmtim of in- dicators foravariableMesoaummicetim intsg'atimrequires additional omtetimel operation. Formnetely, however, most of the infatuation needed fa the damnation of gable indicators 21: W01 Wenbeextmcted frontheICPCprogrunoxt- put. A unwary of these possible indicators, both for the "modem" . and the ,"treditimal" commities, is provided in Table 1. By first selecting the iniividuals with the highest commune- timdanein, ineechofthetwocanmnities,andtha1trecinghis direct and indirect camtims we were able to determine the following indioents of columnioetion integration: PEPE”. of isolates (time who 119 Rimmerm‘mediosenby anyone); WQEWSW 391$ 92 ch__c_3_i_c_e_, but chose at least another person; m of liaiscn individuals (those who interlink two ormore NW); 939-; (two persons with mutual choices); and w (two ormore individuals linked mainly-but not necessarily exclusively-W unreciprocated relations). Comunicaticn leaders were determined by selecting those in- dividuals who obtained at least ten percent of the naxixmrn possible Table l . Possible Indicators of Ommmicatim Integration in a Modern and in a 'Draditional Oomunity in Mines Semis, Brazil. Modern Conrmnity Traditional Cormmity (N a 60) (N 8 77) Indicators NurrBer Percent Number Percent l. Isolates l 1.7 12 15.6 2. Received No Choices 26 23.3 5‘4 70.]. 3. 0amunicatim Leaders 13 21.6 8 10.3 1:. Liaison Individuals It 6.6 3 11.0 5. Rescind in Two-Step Cmnectims 59 98.3 29 37.7 60 was 12 -" l .- 7. Subgroups u - 3 -- 8. Cliques 0 -.. o -- 9. Mean Number of Choices Re- ceived by Individuals in the Comunity 1.3 -- 0.7 --- 10. Mean Ooummicatim Danain Received by Individuals in the Camunity 3.6 -- 1.11 -— 11. Mean Oenu'elity Index keeived by IIIdiViduals in the Comunity 0.9 -- 0J1 .. 50 oummioa‘tim daxain (N-l). The umber 93 individuals reached _ip_ two-step oonnectims was determined by saluting in each of the two distanoematrioes (raised to the fourth power) those cells which showed a two in them. The other three indicants (mean number 9}: choices, mean can-- uuficatim darein, and green centrality index) were determined (re- spectively) by dividing the sum of all the scores or treasures by N-l (since self-nominatims were not considered in the present stuiy) . Cmclusims The indioants shown in Table 1 are rather unrefined measures of mmicatim integraticn. Nevertheless, they serve to show that refined differences do exist between the modern and the treditimal oamunities in terms of their micatim patterns . By examining thevalues foreaohofthellindicantsshowninTablelwecminfer that the modern oowunity exhibits relatively more integraticn in its oamlnioatim system than does the treditianl oamunity. The faegoing oonclusim lends support to two assmnptims stated in an earlier sectim of the present chapter. We assured that the oammity with the highest irmovativeness score is relatively more modern, while the oamunity with the lowest imovativeness score is relatively mare traditia'xal. We further assuned that a "Inodsrn" and a "traditialal" odmunity exhibit considerable differences in their internal oouuunication patterns , especially when a variable such as camunication integration is considered. 51 “her: defining internal and external cannmioation integretim we proposed that these two camepts are interrelated. Table 2 shows fan-indicesofmassmdiaezqaosmeforeachofthetmcamwxities.‘ Table2. Massriedialbqnsmeinalbdernandina'lreditiomlCan- nunityofMinasGereis, Brazil. Modern Oaxuunity Traditional Camunity Pbdium (N I 60) (N I 77) 1. mm Readership .35 * .06 2. Radio aqua-me .75 .3u 3. Tunisia: W .78 .21 n. ma. Attendance .17 .05 Byirupectimofthevaluesin'l‘able2wenayconcludethatthe modern calamity elm relatively higher indices of exposure to mass mdiatlnntlntreditimaloammity. Ifmaocepttmseindicesas one type of indicants of external camunicatim integration, at least mapmvisimalbasis,wemaycmcludethatthennderncmuunityis relatively more integrated than the treditional community in terms of its external cammication system. As a general conclusim we may say, therefore, that innovative-— ngsg, external oammicatim integration , and internal carmmicatim *‘mese indices were derived as follows: (I) nwspapgr reader- ship, the percent who regularly read a newspaper; radio eggposurefflm percent who listen to me hour per day; televisim m. the per— cent who watch television movie expoane, the percent who ever see movies . 52 integration are positively interrelated , as shown in Figure 13 . mal Camunication Integration 4» + 4. Internal Camunication _ Integration g we Innovativeness Figure 13. Possible relaticnships ammg external camunica- tion integratim , internal cannmicatim inte- gration , and innovativeness . This general cmclusim is by no means definite. It is possible, for exanple , that internal cmmmication integration mediates external camunicatim integration and irlwvativeness. In that case we would have a situatim analogous to that found in Iazarsfeld and others (19%), i.e., a two—step flow of conmmicatim. 0n the other hand, it is also possible that internal cammication integration is in itself a primary factor in the innovativeness process. Both of thee questions can be answered mly through additional investigations, in which more refined measurements and statistical procedures (such as partial ccrrelatim) could be employed. CHAPTERV SUIMARY, C(NCLUSIWS, AND SUGGES'I'IWS FOR MURE RESEARCH Summary and Cmclusims A major argument of the present thesis is that camunicatim research has overemphasized individual behavior, and neglected __;_cel_1_1;- Wm interestim processes. are alternative to focusing on individuals as separate units, is to change to networks of relations mg individuals as units of analysis. Under the latter perspective, finindividualistreatedaspartofalargersystem,retherthanas an isolated or independent unit. Pleas in favor of relaticnal studies have received cmspic- uously little attentim. One explanation for this neglect lies in the data-gathering techniques of past my research. Recently, how- ever, various techniques of measurement, data gathering, and data analysis have been utilized to provide focus on relatimships rather than a: individuals. Sccianetric-type questions, as a technique of measurement , allows the identification of netwoflcs of ccunmicatim surmding each respmdent. Tho major data-gathering techniques are appropriate for relational studies: (1) the "srmballirg" technique, and (2) the ”saturatim" sanple. The analysis of relatimal data has two interdependent aspects: (1) the unit of analysis, and (2) the techniques of analysis. The unit of analysis may be any of the folloaing system: a dyad, a chain. 53 . 51+ aclique, aeubgmup, oracaunmioatim systemasawhole. Acon- mmicatimsystannaybepartofalargu‘systsm(i.e., acamunity). As such, it unbreces subsystem as dyads, chains, cliques, and sub- groups. In addition it contains such elements as cmmmicatim leaders, liaisons, and isolates. The analysis of relational data, with focus on any of the sub— systm indicated in the preceding paragraphs, may be performed with theusaof(l) clurtscrdiagram, smhassociogrems,_d_m, and socianatrices, or (2) by mans of Wurltiplicatim. The major objective of the present study was to ermine the relative writs of the matrix nultiplication technique, as canpued toflusodogrumthedigmph, mdtlresocicmaufix. Another objective of the present study was to illustrate the use of the matrix wltiplicatim approach with relational data fran two Brazilim cammities. As regards the first objecdve, me majcr carcbxsion that can bedrum franthestudyis thatthematrixmltiplicatim technique has obvious advantages over merely diagrmuutic presentations, and impatantly, itsusedoesnotnecessarilyexclndetheuseofmeor more of the other three techniques. . A major feature of the matrix nultiplicatim ted'mique is the fact that different investigators can manipulate the ...... data and tleresultsyieldwilltendtobesimilar. Sociograms, ornerediagram- matic presentatims, m the other hand, may provide different visual images,dependingmfi\ewayfl1eyareconstructed. 55 'lheinterpretatimoffileresultsyieldedbythemtrixmxlti- plicatimteclmiqueisrelativelysimple,mereasdiagmnsmybecane (interstate md difficult to interpret, especially whm a relatively large ssnpla is involved. N1 iuportmt characteristic of the natrix nultiplioatim ap- proach is objectivity in interpretaticn. The representational devices, thyhxiltmatrialbasis,mightnotbeas freefrunem. mele, wortlueesociogrumnaylookalike, ormightevenbe identical, but it is often difficult to determine their actual dif- feranes (r similarities. 'lhe matrix nultiplicatim tedmiqus, on finotlwhmd,psrudtsthecmstructimofindices, onthebssiscf whim (partitative carparebility became possible. Still. anofiner feature of the matrix nultiplication approach is its flaadbilitytodealwithlargesmples. Andperhapsminportant, it has been prognannsd for couputer use. The applicatim of the matrix nultiplicatim technique to data obtained in a "mdem" and a "traditional" camunity in Minus Genais, Brazil, lands W to the foregoing conclusions. ‘Ihe method allows the identificatim of formal defined structures of the commioation system, as well as the analysis of indirect relatiaxs. In addition, the formation of such indices as cammication danain, n—step connec- ticns, etc., would be more difficult and less acanete if derived on the basis of merely diagrammtic techniques. It is clear, however, that for certain situations (i.e., visual effects), the combinatim of the natrix nultiplication approach arrl diagram is desirable. 56 filggestions for further Research There are at least two broad (and interrelated) research We which deserve attention. One is methodological in nature, and the other conceptual. Under methodology we can distinguish two major (lamina: (1) additional applications of the matrix multiplica- tion approach, and (2) the statistical measuremnt of indicators de- rived fran the application of the matrix multiplicatim technique (as used in the present study). further Qpplioatims of the Matrix Multiplication Amroach The netrix nmltiplioatim technique applies to problems other thanthosedisoussedinflnpresmt study. Katz (1953) and, in nodified form, Hubbell (1965), have used matrices to determine such indices as "sociazetric stems" or "col'xesiveness." The procedure con- sists of nultiplying each entry of the natrix by a coefficimt, "a," representing the atenuatim of influence or informticn at each step orchainofthestnlc‘mre. Onthis basis, several othsrresults can be derived. Fm example, the n-power of the mau‘ix can represent the anamt of influence orinformation flowing, say, frmitoitlumgh exactlyn-steps. 'Iheswnofthematricestothe l, 2, . . . , npcwers represents the total influence or information from i to i at n-steps or less. In additim, the sun of the infinite series may be either con- vergent or divergent for a given value of "a." If it is convergent, this means that the influence flow dies out, if divergent, it means that the influence increases as it circulates through the structure. It may be divergent in some portions of the structure , cmvergent in others. 57 Matrix mltiplicatim has also been used for the analysis of two or nae different structures, or for. different relations. For exanple, ifmehastwogroups,61and62, thmthestrmtmeGl-GQ isaG bmeatrix. mltiplyingthisbytherbyGlmatrixwillre— sult in a matrix with 51;) entries. Other similar operatims may be carried out; the interpretation of their results will, of course, rest on their mderlying assunptims. There are still other potential areas of applicatim of the netrix nultiplieatim approach. me of then applies , for instance , to the analysis of roles and status relations, within different types of social system. The cell entry 1 could represent the existertce of role—status relationships, and the cell entry 0 the absence of such a relationship.* As the areas of application of these techniques are extended, it is likely that they will prove increasingly valuable to social research. ' Irriicators Derived from the Matrix Multiplication Approach As shown in Chapter IV, the matrix multiplication approach pro- duces a series of irriicators of a ammunicaticn system These in- dicators, as previously emphasized, are unrefined estimates of the patterns of interoormectims exhibited by the systan. Sane of the indicators of communication integration dealt with inthe present study are so interrelated that it is difficult to determine, at this point, -‘I _. ...—"..-- ”--.—“flu... ......“ * White (1963) Studied kinship structures trueugh a similar type of approach. 58 whether they are really independent estimates or just a slightly dif- ferent aspect of are or note other dmecteristics. An important task fcm future research is therefore to further examine these indi- cators with the purpose of reducing than to valid and reliable indices. One way of accormlishing the task referred to in the previcus paragraph is through factor analysis . Another alternative is to con- struct ideal connunication systems, with types ranging from a "caxpletely integrated" system to one in which the patterns of com- mlnicatim are "entirely spread out." These two polar types of can- Inmicatim systems may then be treated by matrix nultiplicatim, and the indicators derived from then can perhaps be used in determining indicators for camunication integration of empirical systems, such as the two systems amlyzwd in Chapter IV. Camptual Problems Another research realm that requires attention relates to con- ceptual and theoretical problems. A major variable that needs further theoretical (and methodological) consideration is camunication integration. CommutiCation integration was measured in the present study in terms of ccnsumtcry (merely social) interpersonal relations. The neasuremext should he exp'mded to ixnlude, for exmlple, instru- nnntal interjoer-izozzal correct“. as well (i.e., those relatims mintaincd to seek speC‘if‘iC‘ in? ="Eltion. such as the adoption or rejection of irmovations) . The i"‘"- ’- “3 ‘9’“ iiVemr': ,.arts of a communication system wally C(J-3102}\‘ in ‘cm- wateruinatc fashicn may prove useful in cii - ... , 7‘ v' —... . V, _ _ ' e fercnt Conn :1 . . ..- , ten. to explain, for exanple, now menbers of 59 a social system accept, reject or modify innovations which are dif- fused from other systems. Adninistrstore and change agents may be guided by the camcept in their efforts toward introducing innovations into "less dewIlOped system." Cannmicatim integration has not been systematically studied as a najcr variable; but recent developnents in modern society and inbeluvianlreseamhpointtothesalienoeoftheconceptfi 'Ihe paradigm presented in Figure 1n Wins a series of provisional hypotheses that deserve further consideration. The position intended is namely to state possible antecedent and cmsequent caiditicns of interval cummioatim integration. The anticipated relationships of the variables do not necessarily imply cause and effect. , ~. .- ‘Anamg those who have shown interest in cannmication inte- gration are Wirth (19%), Shils (1962), and Deutsch (1953). ...H vaE gggfiflflngmoga “338338238278: 33% #53 0958 .9. 335.39% E \3 98980 .9. w p . .SdEFwofi: 833% 5w: ego n8 BIBLICBRAPHY Aranson, B. andJ.M.Carsmith. 1963 ”Effect of the Severity of Threat on the Devaluation of Forbidden Behavior." Journal of Social Psychology 66: 589-588 Bales, Robert F. 1960 Interaction Process Analysis: A Method fcr the Study of Small Groups. Cambridge, Massachusetts: Addison-Wesley Publishing Canpany, Inc. Barge, Claude. 1962 ‘Ihe Theay of Graphs and Its Applications. ('I‘nansl. Alison Doig). New York: John Wiley 6 Sons, Inc. Bean, C. 0. Jr. and E. G. Brundage. 1950 "A Method for Analyzing the Socicmatrix." Socianetry Birdwhistell, Ray L. 1959 "Cmu‘ihrtim of linguistic-Kinesic Studies to the Under- standing of Schizophrenia. Pp. 109-161 in Alfred Auerback (ed.), Schizophrenia. An Integrated Approach. New York: The Rmald Press. Borgatta, Edgard P. 1951 "A Diagnostic Note a: the Construction of Sociograms and Action Diagram." Gruxp Psychotherapy 3: 300-308. 1968 "Socianetry," V01. 15, pp. 53-57 in Sills, David L. (och), International Encyclopedia of the Social Sciences. New York: 'meMcl‘iillanCo. EThePreePress. Bcrgatta, Edgard P. and Walter Stoltz. 1963 "A Note on Canmter Program for Rearmgenent of Matrices." 26: 391-392. Brel'm, J. W. andA. R. Cohen. 1962 Explmations in Cognitive Dissonance. New York: Wiley. Bisacker, RobertG. andThanasL. Saaty. 1965 Finite Graphs and Networks: An Introductim with Applications . New York: leraw—Hill. Cartwright, D. and '1‘. C. Gleasm. 1966 "The mmber of paths and cycles in a digraph." PsychmeUiJca 31: 179-199. Chabot, James. 1950 "A Simplified Maple of the Use of Matrix Multiplication for the Analysis of Socionetric Data." Socicmetry 13: 131-1u0. Coleman, James S. 1958 "Relational Analysis: The Study of Social Organizations with Survey Methods. " Human Organization 17: 28-36. 1960a "The Mathematical Study of Small Groups," Part I, pp. 1- 11:9 in Solonon, H. (ed. ) Mathematical Thinking in the Measurement of Behavior. Glencoe, 111.: The Free Press. 61 62 Coleman, James S. 19698. "Mathmntioal Models and Oauplter Simulations." Pp. 1027- 1062 in Paris, Robert E. L. (ed.), Handbook of Modern Sociology. Rand McNally. 1969b Intromctim to Phflmatical Sociology. Glencce, 111.: The Free Press. Coleman, J. S. and Duncan McRae, Jr. 1960b "Electronic Processing of Sociometric Data fcr Large Groups up to 1000 in Size." American Sociological Review . 25: 722-727. Carghenour, C. Milton. 19616 "The Rate of Technological Diffusion Mmg locality Groups," The Amrican Journal of Sociology 6”: 329-339. Deutsch, Karl W. 1953 Natia'alism and Social Ccmmnicaticn: An Inquiry Into the Famdations of Natimality. Cambridge, Mass.: MIT Press, New York, Wiley. Pestinger, lam, Stanley Schachter and Kurt Back . 1950 Social Pressures in Informal Groups: A Study of Human Factors in Housing. Stanford, Ca1.: Stanford University Press. Pestinger, L. and J. M. Carlsmith. 1959 "Cognitive cmsequences of forced compliance." Journal of Abnormal Social Psychology 58: 203-210. nanent, C. 1958a "La performance des groupes de travail. Rapports entre la structure de 1'activité et cells do reseau de commi- oatim." Amée Psychologique 58: 71-89. 1958b ”L'etude niafllenetique des structures psychosociales. " Annee Psychologique 58: 119-131. , 1963 Applicatim of Graph Theory to Group Structure. (Transl. Maurice Pinard, Raymari Breton, Fernand Fontaire.) Inglewood Cliffs, N.J.: Praltice Hall. Forsyth, Elaine and lac Katz. 1996 "A Maui): Approach to the Analysis of Sociometric Data: Preliminary Report." Sociouetry 9: sue-3w. 1960 "A Matrix Approach to the Analysis of Socicmetric Data: Preliminary Report." Pp. 229-235 in Moreno, J. 1.. (ed.). The Sociametry Reader. Glenooe, 111.: The Ree Press. Harary, Rank. 19515 "On the Notim of Balance of a Signed Graph." Michigan Mathematical Journal 2: 193-196. 1955 ”On Local Balance and N-Balance in Signed Graphs." Michigan Mathematical Journal 3: 37-91. 1959a "On the Measurement of Structural Balance." Behavioral Science u: 316-323. 1959b "Graph Theoretic Methods in the Management Sciences." Managemnt Science 5: 387—1403. Harary, Frank and Ian C. Ross. 1957 "A Procedure for Clique Detection Using the Group Matrix. " Sociometry 20: 205-215. 63 Harery, Frank, Robertz. NmIenandDorwinCartwright. 1965 Structural Models: An Introducticn to the Theory of Directed Graphs. New York: John Wiley 6 Sons, Inc. Herzog, William A. and others. 1968 "Patterns of Diffusim in Rural Brazil." Diffusion Research Report 10. Department of Caunmicatim, Michigan State University, East Lansing, Michigan. Horst, Paul. ' 1963 Matrix Algebra for Social Scientists. New York: Pblt , Rinehart and Winston, Inc. Hubbell, Carlee H. 1965 "An Input-Output Approach to Clique Identification . " Socianatry 25: 377-399. Jacobson, B. and S. Seashore. 1951 "Connmication Patterns in Couple): Organizations." Journal of Social Issues 7: 28-100. Janis, I. L. and S. Feshbach. 1953 "Effects of Pew Aroming Ommmications." Journal of Alnoruel and Social Psychology I+8: 78-92. Janis, I. L. and W. Milholland. 195“ "The Influence of Threat Appeals a: Selective learning of the Content of a Permissive Cannmioation." Journal of Psychology 37: 75-80. . Janis, I. L. and J. B. Gilmore. 1965 "The Influence of Incentive Cmditims on the arccess of Role Playing in Modifying Attitudes." Journal of Persmality and Social Psychology 1: 17-27. Katz Dec. 1953 "A New Status Index Derived from Socionetric Aralysis." trike 18: 394:3. ' 1960 "A New Status Index Derived from Socianetric Analysis." Pp. 266-271 in harem, J. L. The Sociaxetry Reader. Glencoe, 111.: The Free Press. , Kemeny, John 6., J. Barrie Snell andGerald L. Thomson. 1966 Introductim to Finite Mathematics. 2nd Edition. [Inglewood Cliffs, N.Y.: Prentice-Hall, Inc. Kbnig, D. 1936 Theorie dar mdlichan und mendlichen Graphen. Leipzig: Akademische Verlagsgesellschaft M.B.H. (Reprinted in 1950 by Chelsea Publ. Co., New York.) Lazarsfeld, Paul F. , Bernard Berelson and Hazel Gaudet. 1998 The People's Choice. New York: Columbia University Press. Leighton, Alexander H. and others. 1963 Psychiatric Disorder Among the Yoruba. Ithaca, New York: Cornell University Press. lewin, Kurt. 19143 "Forces Behind Food Habits and Methods of Change." Billetin of the National Research Council, 108, pp. 35-65. 6“ Lin, Nan. 1968 "Innovative Methods for Studying Innovatim in Education and an Illustrative Analysis of Structural Effects on Innovation Diffusion Within Schools . " Paper presented at the National Conference on the Diffusion of Edmational Ideas, Michigan State University, East Lansing, Mich. 26-28,Mard1. Luce, R. Dmcan and Albert D. Perry. 19:49 "A Method of Matrix Analysis of Group Structure. " 1966 "A Method of Phtrix Analysis of Group Structure." Readings in Mathenatical Social Science. Chicago: Science Research Associates. Md‘lirm, S. J. ‘ 1962 Matrices for Structtmal Analysis. New York: Wiley. McRae, .Jr., Dmcan. 1960 "Direct Pasta: Analysis of Socianetric Data." Socianetry 23: 360-371. hem, Jacob L. .1953 Who Shall Survive? Foundatims of Socianetry, Group Psyclotherepy and Sociodrema. Rev. 8 enl. ed. Beacon, N.Y.: Beacon House. Moreno, Jacob L. and others (eds.). 1960 The Sociometry Reader. Glencoe, Ill.: The Free Press. Ncrthway, M. L. 1990 "A Method for Depicting Social Relationships Obtained by Socicnetric Testing." Sociouetry 3: 199-150. 1960 "A Method for Depicting Social Relationships Obtained by Sociouetric Testing." Pp. 221-226 in Moreno, J. L. The Socianetry Reader. Glencoe, Ill.: The Free Press. Nuttin, J. M. 19616 "Dissmance Evidence About Dissonance Theory." Paper readatthe2nd. Conf. ofExp. Soc. Psychologistsin Drops, Hescati, Italy, 1961:. Ore, Oystein. 1962 Theory of Graphs. Providence: Amer. Math. Soc. Colloquium Publs., Vol. 38. 1963 Graphs and Their Uses. New York: Randan House. Par-sons, Talcott. 1959 "Carmel Theory in Sociology." Pp. 3-38 in R. K. Merton and others (eds.), Sociology Today: Problems and Prospects. New York: Basic Book. Parthasarethy, K. R. 196" "D'nmeretion of paths in digraphs. " Psychcmetrika 29: 153-165. Powell, Reed M. 1951 "A Carparetive Social Class Analysis of San Juan SUP, and Attire, Costa Rica." Socianstry 1n: 182-2-2. Proctor, Charles H. and Charles P. Loanis. 1951 "Atalysis of Sociometric Data." Part 2, pp. 561-585 in Jahoda, Marie and others. Research Methods in Social Relations, with ESpecial Reference to Prejudice. New York: Dryden. 65 Rogers, Everett M. 1962 Diffusion of Innovations. New York: The Free Press of Glencoe. 196': "Diffusion of Innovatims in Rural Societies." Resume of a research project conducted by Michigan State University under contract with the U.S. Agency fm Internaticnal Development. Department of Camlmication , Michigan State University, East Lansing, Michigan. 1967 Bibliography m the Diffusion of Innovations. Diffusion of Imovations Research Report No. 6 Department of Camunication, Michigan State University , East Lansing , Rogers, Everett M. and Nemi C. Jain. 1968 "Needed Research a: Diffusion Within Educational Organizatims . " Paper presented at the Natimal Conference on the Diffusion of Educational Ideas, East Lansing, Michigan 26-28. March. Ross, I.C. mxd Ptemc Harery. 1952 "On the Determination of Redundancies in Socianetric Chains." Psychometrika 7: 195-208. Sabidmsi, G. 1966 "The Centrelity Index of a Graph." Psychane'trika u: 581-60“. Schwartz, Donald F. 1968 Liaison Cmumicadon Role in a Formal Organization. Unpublished Ph.D. thesis, Department of Carmmication, Michigan State University, East Lansing , Michigan. Shils, Edward. 1962 The Thea'y of Mass Society. Diogenes 39: tt5-66. Spilerman, S. 1966 "Structural Analysis and the Generation of Sociogrcms." Behav. Sci. 11: 312-318. Watzlawick, Paul and others. 1967 Pragmatics of Hunen Camnmication: A Study of Inter- actional Patterns , Pathologies , and Paradoxes . New York: W. W. Norton and Conpany. Westley, Bruce H. and Malcolm Maclean, Jr. 1957 "A Conceptual Model for Camunioatims Research." Journalism Qnrterly (Winter): 31-38. 1965 In Campbell, J. H. and Kepler, H. W. Dimensions in Camunication: Readings, Belmont. California: Wadsworth Publishing Co. Weiss, Robert S. and Eugene Jacobean 1955 "A Method for the Analysis of the Structure of Couple): Organizations." American Sociological Review 20: 661-668. 19614 Pp. ass-Just: in Etzioni, Nnatai (ed.). Complex Organiza- tions: A Sociological Reader. New York: Holt , Pineflxam and Winston. White, A. 1963 An Anatomy of Kinship. Englewood Cliffs, N.J.: Prentice Hall, Inc. 68 Whiting, Gordon C. and others. 1967 Innovatim in Brazil: Success and Failure of Agrimlltural Programs in 76 Minas Gerais Carmunities. Diffusicn of Irmovatims Research Report 7. Department of Carmmication, Michigan State University, East lensing, Michigan. Wirth, Iouis. 191:8 "Consensus and Mass Cmmmicatim. " American Sociological Review. 13: 1-15. Yadav, Dharem P. 1967 Camunioation Structure and Innovatim Diffusion in 'I‘wo Indian Villages. Unpublished Ph.D. thesis, Department of Camunication, Michigan State University, East Lansing. a a 39:, _ . l i‘.‘ "Ic‘rflifllilflljflfikflfllflflifllfliflfs