Network Analysis in the Social SciencesStephen P. Borgatti, Ajay Mehra, Daniel J. Brass, Giuseppe Labianca

Over the past decade, there has been an explosion of interest in network research across thephysical and social sciences. For social scientists, the theory of networks has been a gold mine,yielding explanations for social phenomena in a wide variety of disciplines from psychology toeconomics. Here, we review the kinds of things that social scientists have tried to explain usingsocial network analysis and provide a nutshell description of the basic assumptions, goals, andexplanatory mechanisms prevalent in the field. We hope to contribute to a dialogue amongresearchers from across the physical and social sciences who share a common interest inunderstanding the antecedents and consequences of network phenomena.

One of the most potent ideas in the socialsciences is the notion that individuals areembedded in thick webs of social rela-

tions and interactions. Social network theoryprovides an answer to a question that has pre-occupied social philosophy since the time ofPlato, namely, the problem of social order: howautonomous individuals can combine to createenduring, functioning societies. Network theoryalso provides explanations for a myriad of socialphenomena, from individual creativity to corpo-rate profitability. Network research is “hot” today,with the number of articles in the Web of Scienceon the topic of “social networks” nearly triplingin the past decade. Readers of Science are alreadyfamiliar with network research in physics andbiology (1), but may be less familiar with whathas been done in the social sciences (2).

HistoryIn the fall of 1932, there was an epidemic ofrunaways at the Hudson School for Girls in up-state New York. In a period of just 2 weeks, 14girls had run away— a rate 30 times higher thanthe norm. JacobMoreno, a psychiatrist, suggestedthe reason for the spate of runaways had less todo with individual factors pertaining to the girls’personalities and motivations than with the po-sitions of the runaways in an underlying socialnetwork (3). Moreno and his collaborator, HelenJennings, hadmapped the social network at Hudsonusing “sociometry,” a technique for eliciting andgraphically representing individuals’ subjectivefeelings toward one another (Fig. 1). The links inthis social network, Moreno argued, providedchannels for the flow of social influence and ideasamong the girls. In a way that even the girls them-selvesmay not have been conscious of, it was theirlocation in the social network that determinedwhether and when they ran away.

Moreno envisioned sociometry as a kind ofphysics, complete with its own “social atoms”and its laws of “social gravitation” (3). The idea

of modeling the social sciences after the physicalones was not, of course, Moreno’s invention. Ahundred years before Moreno, the social philos-opher Comte hoped to found a new field of“social physics.” Fifty years after Comte, theFrench sociologist Durkheim had argued thathuman societies were like biological systems inthat they were made up of interrelated compo-nents. As such, the reasons for social regularitieswere to be found not in the intentions of individ-uals but in the structure of the social environ-ments inwhich theywere embedded (4).Moreno’ssociometry provided away ofmaking this abstractsocial structure tangible.

In the 1940s and 1950s, work in social net-works advanced along several fronts. One frontwas the use of matrix algebra and graph theory toformalize fundamental social-psychological con-cepts such as groups and social circles in network

terms, making it possible to objectively discoveremergent groups in network data (5). Anotherfront was the development of a program of lab-oratory experimentation on networks. Researchersat the Group Networks Laboratory at the Massa-chusetts Institute of Technology (MIT) beganstudying the effects of different communicationnetwork structures on the speed and accuracywith which a group could solve problems (Fig.2). The more centralized structures, such as thestar structure, outperformed decentralized struc-tures, such as the circle, even though it could beshown mathematically that the circle structurehad, in principle, the shortest minimum solutiontime (6). Why the discrepancy? Achieving the

mathematically optimal solutionwould have required the nodes toexecute a fairly complex sequenceof information trades in which nosingle node served as integrator ofthe information. But the tendency inhuman networks seemed to be forthe more peripheral members of anetwork (i.e., the nodes colored bluein the “Star,” “Y,” and “Chain” net-works in Fig. 2) to channel infor-mation to themost central node (i.e.,the nodes colored red in Fig. 2),who then decided what the correctanswer was and sent this answerback out to the other nodes. Thefastest performing network struc-tures were those in which the dis-tance of all nodes from the obviousintegrator was the shortest (7).

The work done by Bavelas andhis colleagues at MIT captured theimagination of researchers in a num-ber of fields, including psychology,political science, and economics. Inthe 1950s, Kochen, amathematician,and de Sola Pool, a political scien-tist, wrote a highly circulated paper,eventually published in 1978 (8),which tackled what is known today

as the “small world” problem: If two persons areselected at random from a population, what arethe chances that they would know each other,and,more generally, how long a chain of acquaint-anceship would be required to link them? On thebasis of mathematical models, they speculatedthat in a population like the United States, at least50% of pairs could be linked by chains with nomore than two intermediaries. Twenty years later,Stanley Milgram tested their propositions empir-ically, leading to the now popular notion of “sixdegrees of separation” (9).

During this period, network analysis was alsoused by sociologists interested in studying thechanging social fabric of cities. The common con-viction at the time was that urbanization destroyedcommunity, and that cities played a central role inthis drama. These sociologists saw concrete rela-tions between people—love, hate, support, and so

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LINKS Center for Network Research in Business, Gatton Collegeof Business and Economics, University of Kentucky, Lexington,KY 40506–0034, USA. E-mail: sborgatti@uky.edu (S.P.B.),ajay.mehra@uky.edu (A.M.), dbrass@uky.edu (D.J.B.), andjoe.labianca@uky.edu (G.L.)

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Fig. 1. Moreno’s network of runaways. The four largest circles(C12, C10, C5, C3) represent cottages in which the girls lived.Each of the circles within the cottages represents an individualgirl. The 14 runaways are identified by initials (e.g., SR). Allnondirected lines between a pair of individuals represent feelingsof mutual attraction. Directed lines represent one-way feelingsof attraction.

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on—as the basic stuff of community, and theyused network analysis to represent communitystructure. For example, researchers interviewed1050 adults living in 50 northern Californiancommunities with varying degrees of urbanismabout their social relations (10). The basic pro-cedure for eliciting network data was to get re-spondents (egos) to identify people (alters) withwhom they had various kinds of relationshipsand then to also ask ego about the relationshipsbetween some or all of the alters. They found thaturbanism did in fact reduce network density,which, in turn, was negatively related to psycho-logical measures of satisfaction and overall well-being. A similar study of 369 boys and 366 girlsbetween the ages of 13 and 19 in a Midwesterntown of about 10,000 residents found that theadolescents’ behaviors were strongly influencedby the “cliques” to which they belonged (11).The representation and analysis of communitynetwork structure remains at the forefront of net-work research in the social sciences today, withgrowing interest in unraveling the structure ofcomputer-supported virtual communities that haveproliferated in recent years (12).

By the 1960s, the network per-spective was thriving in anthropol-ogy. Influenced by the pioneeringwork of Radcliffe Brown (13), therewere three main lines of inquiry.First, at the conceptual level, an-thropologists like S. F. Nadel beganto see societies not as monolithicentities but rather as a “pattern ornetwork (or ‘system’) of relation-ships obtaining between actors intheir capacity of playing roles rel-ative to one another” (14). Second,building on the insights of the an-thropologist Levi-Strauss, scholarsbegan to represent kinship systemsas relational algebras that consistedof a small set of generating relations (such as“parent of” and “married to”) together with binarycomposition operations to construct derived re-lations such as “in-law” and “cousin.” It was soondiscovered that the kinship systems of such peoplesas the Arunda of Australia formed elegant math-ematical structures that gave hope to the idea thatdeep lawlike regularities might underlie the ap-parent chaos of human social systems (15, 16).

Third, a number of social anthropologists beganto use network-based explanations to account fora range of outcomes. For example, a classic eth-nographic study by Bott (17) examined 20 urbanBritish families and attempted to explain the con-siderable variation in the way husbands and wivesperformed their family roles. In some families,there was a strict division of labor: Husband andwife carried out distinct household tasks sepa-rately and independently. In other families, thehusband and wife shared many of the same tasksand interacted as equals. Bott found that thedegree of segregation in the role-relationship ofhusband and wife varies directly with the con-

nectedness (or density) of the family’s socialnetwork. The more connected the network, themore likely the couple would maintain a tradi-tional segregation of husband and wife roles,showing that the structure of the larger networkcan affect relations and behaviors within the dyad.

In the 1970s, the center of gravity of networkresearch shifted to sociology. Lorrain and White(18) sought ways of building reduced models ofthe complex algebras created when all possiblecompositions of a set of relationswere constructed(e.g., the spouse of the parent of the parent of…).By collapsing together nodes that were structurallyequivalent—i.e., those that had similar incomingand outgoing ties—they could form a newnetwork(a reduced model) in which the nodes consistedof structural positions rather than individuals.This idea mapped well with the anthropologists’view of social structure as a network of rolesrather than individuals, and was broadly applica-ble to the analysis of roles in other settings, suchas the structure of the U.S. economy (19). It wasalso noted that structurally equivalent individualsfaced similar social environments and therefore

could be expected to develop similar responses,such as similar attitudes or behaviors (20).

Another key contribution was the influentialstrength of weak ties (SWT) theory developed byGranovetter (21). Granovetter argued that strongties tend to be “clumpy” in the sense that one’sclose contacts tend to know each other. As aresult, some of the information they pass along isredundant—what a person hears from contact Ais the same as what the person heard from B. Incontrast, weak ties (e.g., mere acquaintances) caneasily be unconnected to the rest of one’s net-work, and therefore more likely to be sources ofnovel information. Twenty years later, this workhas developed into a general theory of socialcapital—the idea that whom a person is connectedto, and how these contacts are connected to eachother, enable people to access resources that ulti-mately lead them to such things as better jobs andfaster promotions (22).

By the 1980s, social network analysis hadbecome an established field within the socialsciences,with a professional organization (INSNA,

InternationalNetwork forSocialNetworkAnalysis),an annual conference (Sunbelt), specialized soft-ware (e.g., UCINET), and its own journal (SocialNetworks). In the 1990s, network analysis radiatedinto a great number of fields, including physicsand biology. It also made its way into severalapplied fields such as management consulting(23), public health (24), and crime/war fighting(25). In management consulting, network analysisis often applied in the context of knowledgemanage-ment, where the objective is to help organizationsbetter exploit the knowledge and capabilities dis-tributed across its members. In public health, net-work approaches have been important both instopping the spread of infectious diseases and inproviding better health care and social support.

Of all the applied fields, national security isprobably the area that has most embraced socialnetwork analysis. Crime-fighters, particularly thosefighting organized crime, have used a networkperspective for many years, covering walls withhuge maps showing links between “persons ofinterest.” This network approach is often creditedwith contributing to the capture of SaddamHussein.In addition, terrorist groups are widely seen asnetworks rather than organizations, fueling researchon how to disrupt functioning networks (26). Atthe same time, it is often asserted that it takes anetwork to fight a network, sparking militaryexperiments with decentralized units.

Social Network TheoryPerhaps the oldest criticism of social networkresearch is that the field lacks a (native) theo-retical understanding—it is “merely descriptive”or “just methodology.” On the contrary, there issomuch of it that one of themain purposes of thisarticle is to organize and simplify this burgeoningbody of theory. We will give brief summaries ofthe salient points, using comparisons with thenetwork approach used in the physical sciences(including biology).

Types of ties. In the physical sciences, it is notunusual to regard any dyadic phenomena as anetwork. In this usage, a network and a mathe-matical graph are synonymous, and a commonset of techniques is used to analyze all instances,from protein interactions to coauthorship to in-ternational trade. In contrast, social scientiststypically distinguish among different kinds ofdyadic links both analytically and theoretically.For example, the typology shown in Fig. 3 dividesdyadic relations into four basic types—similarities,social relations, interactions, and flows. Much ofsocial network research can be seen as workingout how these different kinds of ties affect eachother.

The importance of structure. As in the studyof isomers in chemistry, a fundamental axiom ofsocial network analysis is the concept that struc-ture matters. For example, teams with the samecomposition of member skills can perform verydifferently depending on the patterns of relation-ships among the members. Similarly, at the levelof the individual node, a node’s outcomes and

YWheel

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Fig. 2. Four network structures examined by Bavelas andcolleagues at MIT. Each node represents a person; each linerepresents a potential channel for interpersonal communication.The most central node in each network is colored red.

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future characteristics depend in part on its posi-tion in the network structure. Whereas traditionalsocial research explained an individual’s outcomesor characteristics as a function of other character-istics of the same individual (e.g., income as afunction of education and gender), social networkresearchers look to the individual’s social environ-ment for explanations, whether through influenceprocesses (e.g., individuals adopting their friends’occupational choices) or leveraging processes (e.g.,an individual can get certain things done becauseof the connections she has to powerful others). Akey task of social network analysis has been toinvent graph-theoretic properties that characterizestructures, positions, and dyadic properties (suchas the cohesion or connectedness of the structure)and the overall “shape” (i.e., distribution) of ties.

At the node level of analysis, the most widelystudied concept is centrality—a family of node-level properties relating to the structural impor-tance or prominence of a node in the network.For example, one type of centrality is Freeman’sbetweenness, which captures the property of fre-quently lying along the shortest paths betweenpairs of nodes (27). This is often interpreted interms of the potential power that an actor mightwield due to the ability to slow down flows or todistort what is passed along in such a way as toserve the actor’s interests. For example, Padgettand Ansell (28) analyzed historical data on mar-riages and financial transactions of the powerfulMedici family in 15th-century Florence. The studysuggested that the Medici’s rise to power was afunction of their position of high betweennesswithin the network, which allowed them tobroker business deals and serve as a crucial hubfor communication and political decision-making.

Research questions. In the physical sciences,a key research goal has been formulating univer-sal characteristics of nonrandom networks, suchas the property of having a scale-free degree distri-bution. In the social sciences, however, researchershave tended to emphasize variation in structureacross different groups or contexts, using thesevariations to explain differences in outcomes. Forexample, Granovetter argued that when the cityof Boston sought to absorb two neighboringtowns, the reason that one of the towns was ableto successfully resist was that its more diffusenetwork structure wasmore conducive to collectiveaction (21).

A research goal that the social and physicalsciences have shared has been to explain the

formation of network ties and, more generally, topredict a host of network properties, such as theclusteredness of networks or the distributions ofnode centrality. In the social sciences, most workof this type has been conducted at the dyadiclevel to examine such questions as: What is thebasis of friendship ties? How do firms pick alli-ance partners? A host of explanations have beenproposed in different settings, but we find theycan usefully be grouped into two basic categories:opportunity-based antecedents (the likelihoodthat two nodes will come into contact) and benefit-based antecedents (some kind of utility maximi-zation or discomfort minimization that leads to tieformation).

Although there are many studies of networkantecedents, the primary focus of network researchin the social sciences has been on the consequencesof networks. Perhaps themost fundamental axiomin social network research is that a node’s positionin a network determines in part the opportunitiesand constraints that it encounters, and in this wayplays an important role in a node’s outcomes. Thisis the network thinking behind the popular con-cept of social capital, which in one formulationposits that the rate of return on an actor’s invest-ment in their human capital (i.e., their knowledge,skills, and abilities) is determined by their socialcapital (i.e., their network location) (29).

Unlike the physical sciences, a multitude ofnode outcomes have been studied as conse-

quences of social network variables. Broadlyspeaking, these outcomes fall into two main cat-egories: homogeneity and performance. Nodehomogeneity refers to the similarity of actorswith respect to behaviors or internal structures.For example, if the actors are firms, one area ofresearch tries to predict which firms adopt thesame organizational governance structures (30);similarly, where the nodes are individuals, a key

research area has been the pre-diction of similarity in time-to-adoption of an innovation forpairs of actors (31). Performancerefers to a node’s outcomes withrespect to some good. For exam-ple, researchers have found thatfirm centrality predicts the firm’sability to innovate, as measuredby number of patents secured (32),as well as to perform well finan-cially (33). Other research has

linked individual centrality with power andinfluence (34).

Theoretical mechanisms. Perhaps the mostcommon mechanism for explaining conse-quences of social network variables is some formof direct transmission from node to node.Whetherthis is a physical transfer, as in the case of mate-rial resources such as money (35), or a mimetic(imitative) process, such as the contagion of ideas,the underlying idea is that something flows alonga network path from one node to the other.

The adaptation mechanism states that nodesbecome homogeneous as a result of experiencingand adapting to similar social environments.Much like explanations of convergent forms inbiology, if two nodes have ties to the same (orequivalent) others, they face the same environ-mental forces and are likely to adapt by becomingincreasingly similar. For example, two highlycentral nodes in an advice network could developsimilar distaste for the telephone and e-mail,because both receive so many requests for helpthrough these media. Unlike the case of trans-mission, the state of “distaste for communicationmedia” is not transmitted from one node toanother, but rather is similarly created in eachnode because of their similar relations to others.

The binding mechanism is similar to the oldconcept of covalent bonding in chemistry. Theidea is that social ties can bind nodes together insuch a way as to construct a new entity whose

properties can be different fromthose of its constituent elements.Binding is one of the mechanismsbehind the popular notion of theperformance benefits of “structur-al holes” (Fig. 4). Given an ego-network (the set of nodeswith directties to a focal node, called “ego,”together with the set of ties amongmembers of the ego network), astructural hole is the absence of a tieamong a pair of nodes in the egonetwork (22). A well-established

proposition in social network analysis is thategos with lots of structural holes are better per-formers in certain competitive settings (19). Thelack of structural holes around a node means thatthe node’s contacts are “bound” together—theycan communicate and coordinate so as to act asone, creating a formidable “other” to negotiatewith. This is the basic principle behind the ben-efits of worker’s unions and political alliances. In

Similarities

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Fig. 3. A typology of ties studied in social network analysis.

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Fig. 4. Two illustrative ego networks. The one on the leftcontains many structural holes; the one on the right contains few.

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contrast, a node with many structural holes canplay unconnected nodes against each other, divid-ing and conquering.

The exclusion mechanism refers to com-petitive situations in which one node, by forminga relation with another, excludes a third node. Toillustrate, consider a “chain” network (Fig. 5) inwhich nodes are allowed tomake pairwise “deals”with those they are directly connected to. Node dcan make a deal with either node c or node e, butnot both nodes. Thus, node d can exclude node cby making a deal with node e. A set of exper-iments (36) showed that nodes b and d have highbargaining power, whereas nodes a, c, and e havelow power. Of special interest is the situation ofnode c, which is more central than, and has asmany trading partners as, nodes b and d. How-ever, nodes b and d are stronger because eachhave partners (nodes a and e) that are in weakpositions (no alternative bargaining partners).

Having only strong nodes to bargain with makesnode c weak. In this way, a node’s power be-comes a function of the powers of all other nodesin the network, and results in a situation in whicha node’s power can be affected by changes in thenetwork far away from the node. An example ofthe exclusion mechanism occurs in business-to-business supply chains. When a firm intentionallylocks up a supplier to an exclusive contract,competitor firms are excluded from accessingthat supplier, leaving them vulnerable in themarketplace.

In quantum physics, the Heisenberg uncer-tainty principle describes the effects of an observeron the system being measured. A foreseeable chal-lenge for network research in the social sciences isthat its theories can diffuse through a population,influencing the way people see themselves andhow they act, a phenomenon that Giddens de-scribed as the double-hermeneutic (37). For exam-ple, there has been an explosion in the popularity ofsocial networking sites, such as Facebook andLinkedin, which make one’s connections highlyvisible and salient. Many of these sites offer usersdetailed information about the structure and con-tent of their social networks, as well as suggestionsfor how to enhance their social networks. Will thisenhanced awareness of social network theoriesalter theway inwhich people create, maintain, andleverage their social networks?

Final ObservationsA curious thing about relations among physicaland social scientists who study networks is thateach camp tends to see the other as merely de-scriptive. To a physical scientist, network researchin the social sciences is descriptive because mea-sures of network properties are often taken at face

value and not compared to expected values gen-erated by a theoretical model such as Erdos-Renyirandom graphs. For their part, social scientistshave reacted to this practice with considerable be-musement. To them, baseline models like simplerandom graphs seem naïve in the extreme—likecomparing the structure of a skyscraper to a randomdistribution of the same quantities of materials.

More importantly, however, social and physi-cal scientists tend to have different goals. In thephysical sciences, it has not been unusual for aresearch paper to have as its goal to demonstratethat a series of networks have a certain property(and that this property would be rare in randomnetworks). For social scientists, the default expec-tation has been that different networks (and nodeswithin them) will have varying network proper-ties and that these variations account for differ-ences in outcomes for the networks (or nodes).Indeed, it is the relating of network differences to

outcomes that they see as constitutingtheoretical versus descriptive work.

Social scientists have also beenmore concerned than the physicalscientists with the individual node,whether an individual or a collec-tive such as a company, than with

the network as a whole. This focus on node-leveloutcomes is probably driven to at least someextent by the fact that traditional social sciencetheories have focused largely on the individual.To compete against more established social sci-ence theories, network researchers have had toshow that network theory can better explain thesame kinds of outcomes that have been the tra-ditional focus of the social sciences.

Some physicists argue that direct observationof who interacts with whom would be preferableto asking respondents about their social contacts,on the grounds that survey data are prone to error.Social scientists agree that survey data containerror, but do not regard an error-free measurementof who interacts with whom to be a substitute for,say, who trusts whom, as these are qualitativelydifferent ties that can have different outcomes. Inaddition, social scientists would note that evenwhen objective measures are available, it is oftenmore useful for predicting behavior to measure aperson’s perception of their world than to measuretheir actual world. Furthermore, the varying abil-ity of social actors to correctly perceive the net-work around them is an interesting variable initself, with strong consequences for such outcomesas workplace performance (38).

It is apparent that the physical and socialsciences are most comfortable at different pointsalong the (related) continua of universalism toparticularism, and simplicity to complexity. Froma social scientist’s point of view, network researchin the physical sciences can seem alarmingly sim-plistic and coarse-grained. And, no doubt, froma physical scientist’s point of view, network re-search in the social sciences must appear oddlymired in the minute and the particular, using tinydata sets and treating every context as different.

This is one of many areas where we can each takelessons from the other.

References and Notes1. M. Newman, A. Barabasi, D. J. Watts, Eds., The Structure

and Dynamics of Networks (Princeton Univ. Press,Princeton, NJ, 2006).

2. For a thorough history of the field, see the definitive workby Freeman (39).

3. J. L. Moreno, Who Shall Survive? Nervous and MentalDisease Publishing Company, Washington, DC, 1934).

4. E. Durkheim, Suicide: A Study in Sociology(Free Press, New York, 1951).

5. R. D. Luce, A. Perry, Psychometrika 14, 95 (1949).6. H. Leavitt, J. Abnorm. Soc. Psychol. 46, 38 (1951).7. Later experiments suggested that this result was

contingent on other factors. For example, severalexperiments showed that, as the complexity of puzzlesincreased, decentralized networks performed better (40).

8. I. de S. Pool, M. Kochen, Soc. Networks 1, 1 (1978).9. S. Milgram, Psychol. Today 1, 60 (1967).

10. C. S. Fischer, To Dwell Among Friends (Univ. of ChicagoPress, Chicago, IL, 1948)

11. C. E. Hollingshead, Elmtown’s Youth (Wiley, London, 1949).12. B. Wellman et al., Annu. Rev. Sociol. 22, 213 (1996).13. R. Brown, Structure and Function in Primitive Society

(Free Press, Glencoe, IL, 1952).14. S. F. Nadel, The Theory of Social Structure

(Free Press, Glencoe, IL, 1957).15. H. White, An Anatomy of Kinship: Mathematical Models

for Structures of Cumulated Roles (Prentice Hall,Engelwood, NJ, 1963).

16. J. P. Boyd, J. Math. Psychol. 6, 139 (1969).17. E. Bott, Family and Social Network (Tavistock, London,

1957).18. F. P. Lorrain, H. C. White, J. Math. Sociol. 1, 49 (1971).19. R. S. Burt, Corporate Profits and Cooptation (Academic

Press, NY, 1983).20. R. S. Burt, Am. J. Sociol. 92, 1287 (1987).21. M. S. Granovetter, Am. J. Sociol. 78, 1360 (1973).22. R. S. Burt, Structural Holes: The Social Structure of

Competition (Harvard Univ. Press, Cambridge, MA. 1992).23. R. Cross, A. Parker, The Hidden Power of Social Networks

(Harvard Business School Press, Boston, MA, 2004).24. J. A. Levy, B. A. Pescosolido, Social Networks and Health

(Elsevier, London, 2002).25. M. Sageman, Understanding Terror Networks (Univ. of

Pennsylvania Press, Philadelphia, 2004).26. S. P. Borgatti, in Dynamic Social Network Modeling and

Analysis: Workshop Summary and Papers, R. Breiger,K. Carley, P. Pattison, Eds. (National Academy of SciencesPress, Washington, DC, 2003), p. 241.

27. L. C. Freeman, Sociometry 40, 35 (1977).28. J. F. Padgett, C. K. Ansell, Am. J. Sociol. 98, 1259 (1993).29. R. S. Burt, Brokerage and Closure (Oxford Univ. Press,

New York, 2005).30. G. F. Davis, H. R. Greve, Am. J. Sociol. 103, 1 (1997).31. T. W. Valente, Soc. Networks 18, 69 (1996).32. W. Powell, K. Koput, L. Smith-Doerr, Adm. Sci. Q. 41,

116 (1996).33. A. V. Shipilov, S. X. Li, Adm. Sci. Q. 53, 73 (2008).34. D. J. Brass, Adm. Sci. Q. 29, 518 (1984).35. N. Lin, Annu. Rev. Sociol. 25, 467 (1999).36. T. Yamagishi, M. R. Gilmore, K. S. Cook, Am. J. Sociol.

93, 833 (1988).37. A. Giddens, The Constitution of Society (Univ. of

California Press, Berkeley and Los Angeles, 1984).38. D. Krackhardt, M. Kilduff, J. Pers. Soc. Psychol. 76, 770 (1999).39. L. C. Freeman, The Development of Social Network

Analysis: A Study in the Sociology of Science (EmpiricalPress, Vancouver, 2004).

40. M. E. Shaw, in Advances in Experimental SocialPsychology, L. Berkowitz, Ed. (Academic Press, New York,1964), vol. 1, p. 111.

41. We thank A. Caster, R. Chase, L. Freeman, and B. Wellman fortheir help in improving this manuscript. This work was fundedin part by grant HDTRA1-08-1-0002-P00002 from theDefense Threat Reduction Agency and by the Gatton Collegeof Business and Economics at the University of Kentucky.

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a b c d e

Fig. 5. A five-person exchange network. Nodes representpersons; lines represent exchange relations.

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www.sciencemag.org SCIENCE ERRATUM POST DATE 24 APRIL 2009 1

CORRECTIONS &CLARIFICATIONS

Reviews: “Network analysis in the social sciences” by S. P. Borgatti et al. (13 February, p. 892).

On page 892, the final sentence in the legend for Fig. 1 was missing. The sentence should read:

“Dashed lines represent mutual repulsion.”

Post date 24 April 2009