Network Sampling: Some First Steps Author(s): Mark Granovetter Source: The American Journal of Sociology, Vol. 81, No. 6 (May, 1976), pp. 1287-1303 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/2777005 . Accessed: 16/01/2011 09:58 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=ucpress. 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This paperdescribes a practicalmethod for sampling averageacquaintance volume (the averagenumber of people known by each person) fromlarge populations and derivesconfidence limits on the resultingestimates. It is shownthat this averagefigure also yieldsan estimateof what has been called "networkdensity." Ap- plicationsof the procedureto communitystudies, hierarchical struc- tures,and interorganizationalnetworks are proposed.Problems in developinga generaltheory of networksampling are discussed. Sociologistsand anthropologistshave discussedand studiedcommunities sincetheir disciplines began. As the communitiesstudied have increasedin size, the fact that not all communitymembers have social relationswith one anotherhas become a matterof prominenttheoretical focus. The metaphormost consistently chosen to representthis situation is thatof the "social network"-a device forrepresenting social structurewhich depicts personsas points and relationsas connectinglines. (Good generaldis- cussionsare foundin Barnes 1969; Bott 1957; Mitchell 1969; White, Boorman,and Breiger1976). Most discussionsof networkideas, however, have had practicalapplica- tiononly to smallgroups. Inability to apply the ideas effectivelyto larger structureshas stemmedin part fromthe lack of a theoreticalframework in whichto place the networkmetaphor and in part fromthe absence- and perceiveddifficulty-of methods applicable to and statisticalunder- standingof large networks.In an earlierpaper (1973) I suggestedsome theoreticalleads forthe applicationof networkideas to macrosociology; here I exploresome statisticaland methodologicalavenues which,when morefully developed, should help to bringthe networkperspective more squarelyinto the mainstreamof sociologicalresearch. It is clear why networkmethods have been confinedto small groups: existingmethods are extremelysensitive, in theirpracticality, to group 1 An early version of this paper was deliveredat the Mont Chateau conferenceon the anthropologicalstudy of social networks,sponsored by the MathematicalSocial Science Board, Morgantown,West Virginia,May 16-19, 1974. Discussions begun at that con- ferenceled to crucial improvements.In particular,the progressreported here would not have been possible without the collaboration and stimulationof Paul Holland; remarksby Samuel Leinhardt triggeredimportant parts of the work. I am also in- debted to Harrison White, Stanley Wasserman,and Ove Frank for valuable criticism. AJS Volume 81 Number 6 1287 AmericanJournal of Sociology size because they are populationrather than samplingmethods. In a groupof size N, the numberof potential(symmetric) ties is [N (N 1)72] (i.e., proportionalto N2), so that any methodmeant to deal with the total populationfaces insuperableobstacles for groups larger than a fewhundred. A groupof 5,000,for instance-which we mightthink of as a small town-contains over 12 millionpotential lines in its network. Yet mostAmericans live in muchlarger aggregates, which analysts never- theless,in communitystudies, persist in thinkingrelevant as social units. Implicitly,these studies oftenmake argumentsabout the community's total network,but theyrarely do so explicitly,because no methodsexist forinvestigating such an object.Implicitly, again, what all suchstudies do, and mustdo, is to sample fromthat network.But because the procedure is not explicitand no statisticaltheory guides it, we are leftguessing about the representativenessof the patterns of social relationsfound. This uncer- taintyis particularlynoticeable when the "sampling"procedure is one of participantobservation, but representativenessis problematiceven if the procedureconsists of asking a randomsample of the communitysome sociometricquestions. Just as an enormousadvance in sociologicalwork ensued when the generaltheory of randomsampling was developedand appliedto sociologicalproblems, so the fulldevelopment of networkideas in macrosociologicalperspective must await a comparabletheory of net- worksampling. At present,only a fewanalysts have attackedthis problem (Goodman 1961; Bloemena 1964; Capobianco 1970; Frank 1971), and only Frank attemptsa comprehensivestatistical treatment. In this paper, I show that for one simplebut importantproperty of social networks,"density," a straightforwardand practicalmethod can provideacceptable sampling estimates even forvery large populations.I then suggestapplications of the methodand discuss the more general problemsof samplingfrom networks.2 Networkdensity is the ratioof the numberof ties actuallyobserved to the numbertheoretically possible. In small groups,density is usually treatedas a measureof group"cohesion" (Festinger,Schacter, and Back 1950, chap. 5) and as a partialindication of the extentto whicha group 2 I should stressthat the basic resultshere are made possible by the pathbreakingwork of Ove Frank (1971), professorof statistics,University of Lund, Sweden. Even more important than his actual results is Frank's demonstrationthat network sampling problems can be attacked with relatively standard methods of statistical inference (e.g., the use of indexingvariables), although their application requires a good deal of imagination.Another important breakthrough which deserves to be followed up is Goodman's paper on "snowball sampling" (1961). Snowball samplingis not appropri- ate in the present paper, however, because its practicalityis limited to cases where respondentsmake a fairlysmall number of sociometricchoices. I mean to develop methodsrelevant to respondents'entire friendship networks, including the many people they know whom it would not occur to them to choose in a limited-choicesituation. On the general significanceof "weak ties," see my 1973 paper in this Journal. 1288 NetworkSampling is "primary"or "closed" (see Homans 1974; Bott 1957). In communities or largersettings, density has been used to indicatelevels of "moderniza- tion" (see Mayer 1961; Tilly 1969). A good generaldiscussion of density can be foundin Barnes (1969). DENSITY AND THE "HOW-MANY-PEOPLE" PROBLEM Beforediscussing the samplingmethod, I want to make a detourto show that findingthe densityin networksis actually,given certain limitations, equivalentto answeringthe question "How manypeople do peopleknow?" That question,though one mightsuppose its answerto be a fundamental social fact,has actuallybeen studiedvery little,and no systematicin- formationexists for representative populations. Initially,the problemmay seem straightforward:If we want to know howmany people someone knows, why not ask him?To be quite frank,no direct evidenceshows that this procedurewould give poor results.In- direct evidence and everydayexperience, however, suggest that most individualscould give only a very rudimentaryestimate. The obvious methodwould be to ask a respondentto writeout a list of all the people he knowsand countthe names.But such a substantialproportion of one's contactsare seen infrequentlythat theywould come to mind only with some difficulty,particularly during the limitedtime one could allow or expectfor the schedule to be filledout. Gurevitch(1961) used an ingeniousextension of this method,which insuredfar greateraccuracy. He asked each respondentto keep a daily diaryover a periodof 100 days,listing, each day, all the personshe came intocontact with who also knewhim by thiscriterion (p. 1, n). This time periodwas chosenbecause "the net incrementduring the tail end of this periodwas small enoughto justifytermination of the procedure"(p 43). The method,a variantof time-budgettechniques, gives excellent results but has seriousdrawbacks. The most serious and obvious is that such sustainedcommitment of respondentscan probablyonly be securedon a paid basis. Gurevitch'ssample consisted of 15 individualswho responded to a noticeoffering pay forthis activity and