testing multitheoretical, multilevel hypotheses about ... · testing multitheoretical, multilevel...

TESTING MULTITHEORETICAL, MULTILEVELHYPOTHESES ABOUT ORGANIZATIONAL

NETWORKS: AN ANALYTIC FRAMEWORK ANDEMPIRICAL EXAMPLE

NOSHIR S. CONTRACTORUniversity of Illinois at Urbana-Champaign

STANLEY WASSERMANIndiana University and

Visible Path Corporation

KATHERINE FAUSTUniversity of California, Irvine

Network forms of organization, unlike hierarchies or marketplaces, are agile and areconstantly adapting as new links are added and dysfunctional ones dropped. Wereview some of the theoretical and methodological accomplishments and challengesof contemporary research on organizational networks. We then offer an analyticframework that can be used to specify and statistically test simultaneously multilevel,multitheoretical hypotheses about the structural tendencies of organizational net-works. We conclude with an empirical study illustrating some of the capabilities ofthis framework.

The past decade has witnessed considerablescholarly interest in conceptualizing twenty-first-century organizational forms as “networkorganizations” (Miles & Snow, 1995; Monge &Fulk, 1999; Nohria, 1992; Poole, 1999; Powell,1990). The network organization, these advo-cates argue, will supplant bureaucracies (andtheir descendants, the multidivisional form andthe matrix form) as the twenty-first-century or-ganizational coin of the realm. Network forms oforganization are neither vertically organized hi-erarchies like their bureaucratic predecessorsnor unorganized marketplaces governed by sup-ply and demand (Powell, 1990; Williamson,1991). Rather, network organizational forms useflexible, dynamic communication linkages to

connect multiple organizations and people intonew entities that can create products or ser-vices. These new forms are agile and are con-stantly adapting as new links are added anddysfunctional ones dropped. Thus, the evolving,emerging network form is the organization.

The changes looming in the organizationallandscape signal the need for a new generationof organizational theory and research that re-sponds to the assumptions, aspirations, and ad-versities that will characterize these twenty-first-century organizational forms. While therehas been a long-standing interest in the study oforganizations from a social network perspective(for reviews, see Krackhardt & Brass, 1994; Mizru-chi & Galaskiewicz, 1994; Monge & Eisenberg,1987), the fundamental changes outlined abovesuggest that the research agenda needs toevolve from studying networks in (or between)organizations to grappling with the notion thatthe network is the organization. This nuancedyet significant change in perspective has sub-stantial—and substantive—implications for thedeployment of a comprehensive network ana-lytic framework to specify and statisticallymodel the structural tendencies of networkforms on the basis of multiple theories and at

National Science Foundation Grant Nos. IIS-9980109, ECS-9427730, and SBR-9630754 and Office of Naval ResearchGrant No. N00014-02-1-0877 supported preparation of thismanuscript. We express our appreciation to Peter Monge forhelping develop many of the ideas presented here and laterpublished in Monge and Contractor (2003), Jon Templin forcomputational assistance, and two anonymous reviewersfor helpful comments. We presented an earlier version ofthis paper in a Top Paper session at the 2000 annual con-vention of the International Communication Association inAcapulco, Mexico.

� Academy of Management Review2006, Vol. 31, No. 3, 681–703.

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multiple levels of analysis. Toward that goal,we begin by reviewing some of the theoreticaland methodological accomplishments and chal-lenges of contemporary research on organiza-tional networks. We then offer an analyticframework that can be used to specify and sta-tistically test simultaneously multilevel, multi-theoretical hypotheses about the structural ten-dencies of organizational networks. Weconclude with an empirical study that illus-trates some of the capabilities of this frame-work.

RECONCEPTUALIZING ORGANIZATIONS ASNETWORKS

A social network consists of a set of actors andone or more relations between the actors. Thenetwork perspective is flexible in its applicabil-ity to different kinds of actors and to differentkinds of relations. Actors may be any kind ofmeaningful social unit, including individuals,collective entities, firms, organizations, and di-visions within organizations, as well as nonhu-man agents, such as knowledge repositories(Carley, 2002; Contractor, 2002; Contractor &Monge, 2002). The relations may be any kind oflinkage between actors, including formal rolerelations, affective expressions (friendship, re-spect), social interactions, workflows, transfersof material resources (money, goods), publish-ing and retrieval of knowledge, flows of nonma-terial resources (information, advice), and busi-ness alliances, to name but a few.

The social network approach to organizationsis entirely fitting, since, as O’Reilly observes,“Organizations are fundamentally relationalentities” (1991: 446). The focus on relations natu-rally leads to representation and analysis oforganizations as social networks. Indeed, Noh-ria asserts, “All organizations are in importantrespects social networks and need to be ad-dressed and analyzed as such” (1992: 4). More-over, this claim holds whether the focus is oninteracting individuals within a single organi-zation, divisions within a firm, or networks ofinteracting firms. Again, Nohria notes these dif-ferent levels of foci: “The premise that organiza-tions are networks of recurring relationships ap-plies to organizations at any level of analysis—small and large groups, subunits of organiza-tions, entire organizations, regions, industries,

national economies, and even the organizationof the world system” (1992: 4).

As we enter the new millennium, the new net-work forms of organizing, precipitated by tech-nological developments, are eroding the distinc-tion between formal and emergent structuralcategories that traditionally have been used tocharacterize organizations. Contrary to tradi-tional views, contemporary organizations are in-creasingly constructed out of ephemeral com-munication linkages, where the

networks of relations span across the entire orga-nization, unimpeded by preordained formalstructures and fluid enough to adapt to immedi-ate technological demands. These relations canbe multiple and complex. But one characteristicthey share is that they emerge in the organiza-tion, they are not preplanned (Krackhardt, 1994:218).

These developments offer new challenges forfuture research on organizational networks bothfrom a theoretical and a methodological stand-point.

THEORETICAL AND METHODOLOGICALCHALLENGES

Theoretically, the increasing irrelevance of re-search contrasting formal and emergent struc-tures has prompted researchers to advocate ashift in focus from examining “emergent” (i.e.,informal) networks to understanding the “emer-gence” of organizational networks. In otherwords, the focus has shifted toward modelingthe dynamics through which flexible organiza-tional forms emerge. Based on a review of theempirical literature, Monge and Contractor(2001) identify nine families of theoretical mech-anisms that have been used to explain the cre-ation, maintenance, dissolution, and reconstitu-tion of organizational networks. These are (1)theories of self-interest, (2) theories of mutualinterest and collective action, (3) cognitive theo-ries, (4) cognitive consistency theories, (5) conta-gion theories, (6) exchange and dependency the-ories, (7) homophily theories, (8) proximitytheories, and (9) theories of network evolutionand coevolution. The theoretical mechanismsare summarized in Table 1.

Monge and Contractor’s review demonstratesfour theoretical implications for studying theemergence of organizational networks. First, awide array of social theories are amenable to

682 JulyAcademy of Management Review

network formulations. Second, in some cases,different theories, using similar theoreticalmechanisms, offer similar explanations but atdifferent levels of analysis. Third, different the-oretical mechanisms sometimes offer comple-mentary as well as contradictory explanationsat the same level of analysis. Fourth, there isconsiderable variation in the depth of concep-tual development and empirical research acrossthe different theories and theoretical mecha-nisms. Thus, their review highlights the need fornetwork research that is not only theoreticallymotivated but also cognizant of incorporatingmultiple theoretical mechanisms at multiplelevels of analysis.

Methodologically, the shift in focus from ex-amining emergent networks to explaining emer-gence has challenged network analysts to makethree moves: from (1) exploratory and descrip-tive techniques to confirmatory and inferential

techniques, (2) single-level, single-theoreticalnetwork analyses to multitheoretical, multilevelanalyses, and (3) purely network explanations tohybrid models that also include attributes of theactors. These are discussed in greater detailbelow.

Confirmatory Network Analysis

In the past two decades there has been con-siderable progress in the development of de-scriptive network metrics. Since network dataare, by definition, relational, nonindependentobservations, “standard” statistical methodsthat assume independent units simply are notappropriate. The efforts to develop statisticalmodels for network processes have been rela-tively sparse, disparate, and esoteric, therebymaking them inaccessible to the larger researchcommunity (see Part V of Wasserman & Faust,

TABLE 1Selected Social Theories and Their Theoretical Mechanisms

Theories Theoretical Mechanisms

Self-interest theories Individual value maximizationSocial capital Investments in opportunitiesStructural holes Control of information flowTransaction costs Cost minimization

Mutual self-interest and collective action theories Joint value maximizationPublic good Inducements to contributeCritical mass Number of people with resources and interests

Cognitive theories Cognitive mechanisms leading toSemantic/knowledge networks Shared interpretations/expertiseCognitive social structures Similarity in perceptual structures

Cognitive consistency theories Choices based on consistencyBalance Drive to avoid imbalance and restore balanceCognitive dissonance Drive to reduce dissonance

Contagion theories Exposure to contact leading toSocial information processing Social influenceSocial learning Imitation, modelingInstitutional Mimetic behaviorStructural theory of action Similar positions in structure and roles

Exchange and dependence theories Exchange of valued resourcesSocial exchange Equality of exchangeResource dependence Inequality of exchangeNetwork exchange Complex calculi for balance

Homophily theories Choices based on similaritySocial comparison Choose comparable othersSocial identity Choose based on own group identity

Proximity theories Choices based on proximityPhysical proximity Influence of distanceElectronic proximity Influence of accessibility

Network evolution and coevolution theories Variation, selection, retentionOrganizational ecology Competition for scarce resourcesComplex adaptive systems Network density and complexity

2006 683Contractor, Wasserman, and Faust

1994). For instance, there are measures that canbe used to describe the level of reciprocity in anetwork—that is, the extent to which communi-cation links from actor A to actor B are recipro-cated, for all pairs in the network, and there arestatistical tests of whether the level of reciproc-ity in a network is more than one would expectby chance (Wasserman & Faust, 1994: Chapter13). However, standard statistical procedurescannot be applied to determine if the number oftriangles in the network (a property of triples ofactors, all of whom are tied to each other) isgreater than expected, given the number of two-stars (an actor connected to two others). Testingsuch a hypothesis is problematic, because thetriads are not independent of one another.

Multilevel Network Analysis

One of the key advantages of a network per-spective is the ability to collect, collate, andstudy data at various levels of analysis (actor,dyadic, triadic, group, organizational, and inter-organizational). However, for the purposes ofanalysis, most network data are either trans-formed to a single level of analysis (e.g., theactor or the dyadic level), which necessarilyloses some of the richness in the data, or areanalyzed separately at different levels of anal-ysis, thus precluding direct comparisons of the-oretical influences at different levels. For in-stance, social exchange theory suggests that thetendency to have a communication tie from ac-tor A to actor B is predicated on the presence ofa communication tie from actor B to actor A.However, balance theory suggests that the ten-dency to have a communication tie from actor Ato actor B is predicated on the configuration ofties the two actors have with third actors, Cthrough, say, Z.

While social exchange theory makes a predic-tion at the dyadic level, balance theory makes aprediction at the triadic level. Jones, Hesterly,and Borgatti extend this dilemma even beyondthe triadic level, noting that although many or-ganizational studies adopt a network perspec-tive, “these studies most often focus on ex-change dyads, rather than on the network’soverall structure or architecture” (1997: 912). Yet,by limiting attention to dyads and ignoring thelarger structural context, “these studies cannotshow adequately how the network structure in-fluences exchanges” (Jones et al., 1997: 912). This

is the problem of “dyadic atomization” noted byGranovetter (1992).

Gnyawali and Madhavan (2001) propose amultilevel network model for capturing compet-itive dynamics phenomena. At the actor level,they propose firm network centrality and struc-tural autonomy; at the dyadic level, they pro-pose structural equivalence; and at the globallevel, they propose network density as influenc-ing “(1) the likelihood of a firm’s initiating acompetitive action . . . and (2) the likelihood of acompetitor responding to that action” (Gnyawali& Madhavan, 2001: 434). However, as they ac-knowledge, while network analysis offers inde-pendent statistical tests for theoretical predic-tions at each of these levels of analysis,combining and comparing effects simulta-neously necessitates an analytic frameworkthat offers multilevel hypothesis testing. In fact,it is often difficult to determine the appropriatelevel at which a network property applies. Twoactors are structurally equivalent if they occupyidentical structural positions; thus, structuralequivalence might be viewed as a dyadic prop-erty, yet determining the nature and identity ofthe positions requires information about globalproperties of the network. Indeed, the opportu-nities and challenges of multilevel theory build-ing extend beyond just the study of organization-al networks (Klein, Tosi, & Cannella, 1999).

Hybrid Network Attribute Models

There has been a long-standing debateamong structural scholars about the merits andfeasibility of incorporating information about anactor’s attributes (e.g., an individual’s organiza-tional affiliation in an interorganizational net-work) into studies examining the actor’s network(Wellman, 1988). Setting aside the “Simmeliansensibility” (Wellman, 1988: 25) of the formalists,who dismiss the utility of looking at actors’ at-tributes, the majority of network scholars em-brace the idea but are deterred by the feasibilityof creating hybrid models that incorporate infor-mation about actors’ attributes to explain theirnetwork patterns. Although there has been con-siderable empirical network research that incor-porates data on actors’ attributes, these studiesare often limited, as described previously, to onelevel of analysis. For instance, theories of ho-mophily would suggest that in an interorgani-zational network actors with similar organiza-


tional affiliations are more likely to havecommunication ties with one another than withactors from other organizations. In a potentiallyconflicting prediction, theories of collective ac-tion would argue that actors with similar orga-nizational affiliations are more likely to bestructured in centralized networks among them-selves than with actors across different organi-zations. Thus, theories of collective action leadto the expectation that ties will not be morelikely between actors with similar characteris-tics. Simultaneously combining and contrastingthese two predictions involving actors’ at-tributes goes beyond the capabilities of mostcontemporary network analytic methods.

In summary, there is a pressing need for or-ganizational network analyses to extend the fo-cus from descriptive network metrics to statisti-cal approaches. These statistical techniquesneed to simultaneously incorporate multipletheoretical explanations at all relevant levels ofanalysis—the actor, dyadic, triadic, and, possi-bly, even the global level. Further, techniquesneed to incorporate theoretical explanationsthat are based on information about the actors’attributes.

We now describe an analytic model that con-siders the genres of multitheoretical, multilevelhypotheses that might influence the structuraltendencies of a network. This model has threepotential benefits. First, it serves as a templateto stimulate a conscious attempt to specify hy-potheses grounded in multiple theories and atmultiple levels. Second, it seeks to make theappropriate selection and deployment of net-work statistical techniques more accessible tothe larger research community, rather than re-maining in the hands of the network methodol-ogists. Finally, it serves network methodologistsby highlighting attention on the theoreticallychallenging areas where there remains a needto develop new statistical techniques.

MULTITHEORETICAL, MULTILEVEL MODELS

We adopt the position that network organiza-tional forms need to be studied as relationalsystems; consequently, we now introduce a sta-tistical vocabulary for investigating hypothesesabout the relational properties of organizationsas social networks. The focus is on hypothesesthat are explicitly relational and, thus, makeclaims about the patterns or structures of orga-

nizational networks. The problem is that sincethese hypotheses concern interdependencies(relations) among actors, they are not testableusing “standard” statistical methods that as-sume independent observations. To overcomethis obstacle, in this section we frame thesehypotheses in terms of the probabilities of graphrealizations with specific structural tendencies.The section begins by introducing the notion ofgraph realization and the logic of statisticalmodeling of social networks using randomgraph models.

Graph theorists use the term graph to de-scribe a network. Here we assume that thegraph under consideration is random; hence, theobserved network (i.e., the empirical data) isonly one graph realization among (usually)many theoretical possibilities. Consider an in-terorganizational consortium of 17 members rep-resenting various industry and government or-ganizations. The observed communicationnetwork (i.e., the data collected) is one realiza-tion of a graph consisting of 17 nodes and thepossible ties (or edges) among them.

Theoretically, there are many possible graphsthat could arise on communication ties amongthe 17 members. All of these are possible graphrealizations. The number of possible graph real-izations can be quite large. In a network of 17individuals, each individual can have ties to 16other individuals. Hence, the network of 17 indi-viduals can have a total of 272 (17 times 16) ties.If the ties are dichotomous (i.e., ties to individu-als are either present or absent) and the relationis directed (the graph is a directed graph), eachof the 272 ties can be in one of two states. Hence,there are 2272 possible configurations of the net-work, or approximately 7.5885 � 1081—that is,the number of configurations is over 7 followedby 81 zeros! The set of possible configurations ofthe network is referred to as the sample space(Wasserman & Faust, 1994).

The observed network is only one of thesepossible graph realizations. It is worth notingthat we are interested in graphs with a fixednumbers of nodes. So, in the example above, thesample space only comprises graphs on 17nodes. This distinguishes the focus of our re-search from sections of mathematical graph the-ory where node numbers are allowed to in-crease with a view to determining asymptoticresults or phase transitions as networks reach acertain size.


The probability of the observed graph relatesto the probability distribution across the samplespace. For instance, the probability of the ob-served graph is vastly different in the uniformdistribution of graphs (in which case it is verysmall indeed!) compared to certain other distri-butions. Hypotheses about network properties ineffect pick out different types of graphs as moreprobable within the sample space. There isnothing unusual about this: it is exactly thesame logic for statistical inference regardingindividuals, the only difference being that wehave a distribution of graphs, rather than a dis-tribution of individual scores. The question ofinterest in statistical modeling of social net-works is whether the observed graph realizationexhibits certain hypothesized structural tenden-cies. The extent to which these tendencies areexhibited is captured by parameters, which areestimated by quantifying the effects of the hy-pothesized structural property on the probabilityof ties being present or absent in the network.These parameters describe a distribution ofgraphs with the hypothesized properties, inwhich the observed graph is the most typicalrepresentative. If a parameter is statisticallysignificant, then the hypothesized property isstatistically important for understanding thestructural tendencies of the observed network.

This logic is central to random graph modelsand to statistical models including Markov ran-dom graph models (Frank & Strauss, 1986;Strauss & Ikeda, 1990) and the p* family of mod-els (Anderson, Wasserman, & Crouch, 1999; Pat-tison & Robins, 2002; Pattison & Wasserman,1999; Robins, Elliott, & Pattison, 2001; Robins,Pattison, & Wasserman, 1999; Wasserman & Pat-tison, 1996). In many of these models, nodes areassumed to be homogeneous—that is, they donot have distinguishing labels. As a conse-quence, graphs of the same type may have rel-atively large probabilities if graphs that are iso-morphic are considered to be equivalent.

Table 2 summarizes various genres of networkhypotheses in terms of the probabilities graphrealizations will exhibit the hypothesized rela-tional property. In each case, the hypothesis isthat graph realizations with the hypothesizedproperty have larger probabilities of being ob-served. In other words, the probability of tiesbeing present or absent in the graph reflects thehypothesized relational property. Consistentwith the multilevel focus of the hypotheses that

we investigate, these models allow conclusionsboth about global network properties (the prob-ability of the graph or, more precisely, the na-ture of the graph distribution) and about theprobability of network ties, given properties oftheir surrounding network (a local property).

Table 2 begins by distinguishing endogenousand exogenous variables that influence theprobability of ties being present or absent in thefocal network. It should be noted that the exog-enous-endogenous distinction being made hereis not equivalent to similar terminology used inthe development of causal models in generaland structural equation models in particular.Unlike their use in causal modeling, endoge-nous variables here are not predicted by exog-enous variables. Rather, both explain structuraltendencies of the network. Structural tendenciesbased on configurations of the focal relation it-self—in this case, the communication relation—are defined as endogenous variables. In con-trast, structural tendencies that incorporatefactors other than the focal relation itself—forinstance, the attributes of actors in the net-work—are defined as exogenous variables.Hence, all variables “outside” the focal commu-nication relation are defined as exogenous vari-ables.

Endogenous variables (rows 1 through 4 inTable 2) refer to various relational properties ofthe focal network itself that influence the prob-ability ties will be present or absent in the samenetwork. From a metatheoretical perspective,these endogenous variables capture the extentto which relational properties of the networkinfluence its self-organization. It is important toclarify that, as in any attempt to explain self-organization, endogenous variables do not rep-resent a tautology or circularity in argument.Instead, they suggest that the configuration ofties in the observed realization reflects an un-derlying structural tendency that is consistentwith the hypothesized network property. Exoge-nous variables (rows 5 through 10 in Table 2)refer to various properties outside the focal net-work that influence the probability ties will bepresent or absent in the focal network. Hence,exogenous variables include the attributes ofthe actors in the network and additional net-work relations among the actors, as well as thesame network relation at previous points intime. Within each of these two categories (i.e.,endogenous and exogenous variables), the table


offers a further subclassification based on theextent to which the probability of ties beingpresent or absent in the network is influencedby properties at the actor, dyadic, triadic, andglobal levels.

In the remainder of this section, we review theinfluence of endogenous variables and discussthe exogenous variables at each of the actor,dyadic, triadic, and global levels. We make aconcerted effort to illustrate each of these cate-gories and subcategories by using hypothesesderived from the nine families of theoreticalmechanisms for the emergence of organization-

al networks identified by Monge and Contractor(2001).

Endogenous Influences on Network StructuralTendencies

Actor level. The actor level refers to variousactor-level network properties that influence theprobability ties will be present or absent in thenetwork. In the case of endogenous variables(row 1 in Table 2), these actor-level propertiescould include network metrics, such as an ac-tor’s centrality, prestige, or structural autonomy

TABLE 2Summary of a Multilevel, Multitheoretical Framework to Test Hypotheses

About Organizational NetworksNull Hypothesis: All Ties Are Independent with Equal Probability

Independent VariableExamples ofSpecific Measures Hypotheses: Graph realizations where . . .

1. Endogenous (same network):actor level

Actor structuralautonomy

. . . high structural autonomy has a higherprobability of occurring (e.g., theory ofstructural holes)

2. Endogenous (same network):dyadic level

Mutuality,reciprocation

. . . high mutuality has a higherprobability of occurring (e.g., socialexchange theory)

3. Endogenous (same network):triadic level

Transitivity,cyclicality

. . .high cyclicality has a higherprobability of occurring (e.g., balancetheory)

4. Endogenous (same network):global level

Networkcentralization

. . . high centralization has a higherprobability of occurring (e.g., collectiveaction theory)

5. Exogenous (shared actorattributes): actor level

Age, gender,organization type,education

. . . ties between actors with similarattributes have a higher probability ofoccurring (e.g., theories of homophily)

6. Exogenous (shared actorattributes): dyadic level

Differentialmutuality andreciprocation

. . . mutual ties between actors withsimilar attributes have a higherprobability of occurring (e.g., exchangetheory)

7. Exogenous (shared actorattributes): triadic level

Differentialtransitivity andcyclicality

. . . transitive (or cyclical) ties betweenactors with similar attributes have ahigher probability of occurring (e.g.,balance theory)

8. Exogenous (shared actorattributes): global level

Differential networkcentralization

. . . network centralization among actorswith similar attributes has a higherprobability of occurring (e.g., collectiveaction theory)

9. Exogenous (network): otherrelations

Advice, friendshipnetwork

. . . communication ties co-occuring withties on a second relation have a higherprobability of occurring (e.g., cognitivetheories)

10. Exogenous (network): samerelation at previous point in time

Communicationnetwork

. . . ties between actors co-occurring withties at preceding points in time have ahigher probability of occurring (e.g.,evolutionary theories)


in the network. These are actor-level propertiesbecause they characterize the position of an in-dividual actor in the network. For instance, thetheory of structural holes (Burt, 1992) suggeststhat actors seek to enhance their structural au-tonomy by forging ties with two or more uncon-nected others, thus creating indirect ties be-tween the people with whom they are linked.This hypothesis would be supported if therewere greater probabilities for graph realizationsin which actors had a high degree of structuralautonomy. In other words, this hypothesis wouldbe supported if the probability of ties beingpresent or absent in the network reflected ac-tors’ tendencies to exhibit structural autonomy.

Figure 1 shows a hypothetical six-person net-work. If there is a tendency for actors to abide bythe theory of structural holes, actor A is lesslikely (shown with a negative sign) to have a tiewith actor C, because it would be redundantwith the indirect tie actor A has with actor C viaactor B. However, there will be a greater ten-dency (represented with a positive sign) for ac-tor A to have a tie with actor D, since this wouldrepresent a nonredundant tie.

It is worth noting here, and in the discussionsaccompanying Figures 2 through 10, that we aredescribing probabilistic tendencies for ties to bepresent or absent. Therefore, in Figure 1, theremay well be some occasions where a tie existsfrom A to C. However, the probability of theseties will diminish if there are ties from actor A toactor B and from actor B to actor C.

Dyadic level. The dyadic level refers to vari-ous dyadic counts that influence the probabilityties will be present or absent in the network. In

the case of endogenous variables (row 2 in Ta-ble 2), these dyadic-level properties could in-clude mutuality and reciprocation. For instance,theories of social exchange (Blau, 1964; Homans;1958), network exchange (Willer & Skvoretz,1997), and resource dependence (Emerson,1972a,b; Pfeffer & Salancik, 1978) suggest thatactors (individuals or organizations) forge tiesusing a calculus of exchange of material or in-formation resources. In its most elemental form,this hypothesis would be supported if therewere greater probabilities for graph realizationsin which pairs of actors had a high degree ofreciprocated (or mutual) ties. In other words, thishypothesis would be supported if the probabil-ity of ties being present or absent in the networkreflected actors’ tendencies to exhibit mutualityor reciprocity.

In Figure 2, social exchange theory would sug-gest a positive tendency for a tie from actor F toactor A, since it would reciprocate the tie fromactor A to actor F. However, social exchangetheory would posit a negative tendency for a tiefrom actor D to actor C, since it would not recip-rocate a tie from actor C to actor D.

This example also offers a simple illustrationof the cross-level implication of a dyadic-leveltheoretical mechanism. By increasing the ten-dency of reciprocity at the “local” dyadic level,we observe a graph with a large proportion ofreciprocated ties, with implications for globaloutcomes.

Triadic level. The triadic level refers to vari-ous triadic network configurations that influ-ence the probability ties will be present or ab-sent in the network. In the case of endogenous

FIGURE 1Endogenous Actor Level: Structural Hole

Theory

FIGURE 2Endogenous Dyadic Level: Social Exchange

Theory


variables (row 3 in Table 2), these triadic-levelproperties include transitivity or cyclicality. Atriad is transitive if, when actor A has a tie toactor B and actor B has a tie to a third actor, C,actor A has a tie to actor C. Tendencies for tran-sitivity can be interpreted in a number of ways,depending on the substance of the relation un-der study. If the relation is one of sentiment(such as liking or friendship), then theories ofcognitive balance (Heider, 1958; Holland & Lein-hardt, 1975, 1981) suggest a tendency towardconsistency in relations. Colloquially, a friend’sfriend should be one’s own friend, and oneshould like one’s friend’s friends. In contrast,transitivity in formal relations, such as exerciseof authority, reflects a hierarchical tendency—one’s boss’s boss is also one’s boss. Hypothesesabout transitive behavior would be supported ifthere were greater probabilities for graph real-izations in which triads of actors in the networkexhibited a high degree of transitivity.

Cyclicality in triads occurs when there is a tiefrom actor A to actor B, a tie from actor B to actorC, and a tie from actor C to actor A, completingthe cycle. Interpretation of cyclicality dependson the substance of the relation. When the tie isone of flow of resources (such as doing favors orproviding information), then cyclicality can bethought of as illustrating the theory of general-ized exchange (Bearman, 1997). Actor A does afavor for B, and B, rather than return the favordirectly to A, does a favor for C, who, in turn,does a favor for A, returning A’s favor to B indi-rectly. Hypotheses about cyclical behaviorwould be supported if there were greater prob-abilities for graph realizations in which triads ofactors in the network exhibited a high degree ofcyclicality.

In Figure 3, theories of balance would posit agreater tendency for actor A to have a tie to actorC, because actor A has a tie to actor B and actorB has a tie with actor C. However, theories ofbalance would posit less tendency for a tie fromactor A to actor E, because it does not completea triad.

Global level. The global level refers to overallnetwork measures that influence the probabilityties will be present or absent in the network. Inthe case of endogenous variables (row 4 in Ta-ble 2), these global properties include the net-work’s degree of centralization. A network has ahigh degree of centralization when some actorsin the network have a much higher degree of

centrality than other actors in the network. Forinstance, theories of collective action (Coleman,1973, 1986; Marwell & Oliver, 1993) and publicgoods theories (Fulk, Flanagin, Kalman, Monge,& Ryan, 1996; Monge et al., 1998) suggest thatactors in a network are more likely to obtain acollective good if the network is centralized(Marwell, Oliver, & Prahl, 1988). This hypothesiswould be supported if there were greater prob-abilities for graph realizations in which net-works had a high degree of centralization. Inother words, this hypothesis would be supportedif the probability of ties being present or absentin the network reflected the network’s tenden-cies to exhibit a high degree of centralization.

In Figure 4, theories of collective action wouldsuggest that actor A has a greater tendency toforge a tie with actor E, since the tie enhancesthe relative centrality of actor E and thereby theoverall network’s centralization.

FIGURE 3Endogenous Triadic Level: Balance Theory

FIGURE 4Endogenous Global Level: Collective Action

Theory


Exogenous Influences on Network StructuralTendencies

In addition to the influence of actor, dyadic,triadic, and global properties of the endogenousvariable (i.e., the focal network itself), exoge-nous variables (i.e., various properties outsidethe focal network) also influence the probabilityties will be present or absent in the focal net-work. As mentioned earlier, these exogenousvariables include attributes of the actors in thenetwork (rows 5 through 8 in Table 2), as well asadditional networks of relations among the ac-tors (row 9 in Table 2) and the same network ofrelations at previous points in time (row 10 inTable 2). These cases are discussed below.While rows 1 through 4 consider structural ten-dencies for the formation of network ties be-tween any two actors, rows 5 through 8 considerthe structural tendency for differential networktie formation specifically among actors whoalso share common attributes, such as organi-zational affiliation. It is worth noting that, insome cases, the differential network tie forma-tion may be privileged among actors who do notshare common attributes—for instance, buyersand sellers. While our illustration here focuseson theories of homophily that posit ties amongsimilar actors, theories of exchange might wellposit ties among actors who differ in certainattributes.

Actor level. The actor level for exogenous vari-ables (row 5 in Table 2) refers to various actorattributes that influence the probability ties willbe present or absent in the network. These actor-level properties include such attributes as age,gender, membership in an organization, and thetype of organization. For instance, theories ofhomophily suggest that individuals have ties toothers with whom they share similar attributes.Homophily has been studied on the basis ofsimilarity in age, gender, education, prestige,social class, tenure, and occupation (e.g.,Coleman, 1957; Ibarra, 1992, 1993, 1995; McPher-son, Smith-Lovin, & Cook 2001). Hypothesesbased on homophily would be supported if therewere greater probabilities for graph realizationsin which actors with shared attributes weremore likely to have ties with one another. Inother words, these hypotheses would be sup-ported if the probabilities of ties being presentor absent in the network reflected actors’ ten-dencies to choose others with similar attributes.

Figure 5 indicates that theories of homophilywould posit a greater tendency for a tie fromactor A to actor C, since they both share a com-mon attribute (both being from government), anda lower tendency for a tie from actor A to actor E,because they do not share a common attribute(actor F being from industry).

Dyadic level. The dyadic level for exogenousvariables (row 6 in Table 2) refers to variousshared attributes that influence the probabilityties will be present or absent in the network.These dyadic-level properties include mutualityand reciprocation (defined previously in the dis-cussion of row 2 in Table 2). In an extension ofthe theories of social exchange and resource de-pendence, the argument proposed here is thatthere is a greater tendency for exchange ties(i.e., mutual or reciprocated ties) to occur amongpairs of actors who share similar attributes. Hy-potheses based on this differential mutuality orreciprocation would be supported if there weregreater probabilities for graph realizations inwhich actors with shared attributes were morelikely to have mutual (or reciprocated) ties withone another. In other words, these hypotheseswould be supported if the probability of tiesbeing present or absent in the network reflectedactors’ tendencies to reciprocate ties with otheractors sharing similar attributes.

Figure 6 shows how theories of resource de-pendence would posit a greater tendency formutual ties between government actors A and B

FIGURE 5Exogenous Attribute Actor Level: Homophily

Theories


and a lower tendency for mutuality betweengovernment actor A and industry actor F.

Triadic level. The triadic level for exogenousvariables (row 7 in Table 2) refers to variousshared triadic attributes that influence the prob-ability ties will be present or absent in the net-work. These triadic-level properties includetransitivity and cyclicality (defined previouslyin the discussion of row 3 in Table 2). In anextension of the theories of cognitive balanceand generalized exchange, the argument pro-posed here is that there is a greater tendency fortransitive and cyclical ties, respectively, amongactors who share similar attributes. Hypothesesbased on this differential transitivity and cycli-cality would be supported if there were greaterprobabilities for graph realizations in which ac-tors with shared attributes were more likely tohave transitive and cyclical ties with one an-other. In other words, these hypotheses wouldbe supported if the probability of ties beingpresent or absent in the network reflected ac-tors’ tendencies to engage in transitive or cycli-cal relations with other actors sharing similarattributes.

Figure 7 indicates that theories of cognitivebalance would posit a greater tendency for a tiefrom actor A to actor C, since it completes atransitive triad among government actors. How-ever, there is a lower tendency for a tie fromactor A to actor E, since it completes a triad thatincludes both government and industry actors.

Global level. The global level for exogenousvariables (row 8 in Table 2) refers to variousshared global attributes that influence the prob-ability ties will be present or absent in the net-work. These global properties include networkcentralization (defined previously in the discus-sion of row 4 in Table 2). In an extension of thetheories of collective action and public goods,the argument proposed here is that there is agreater tendency for network centralization tooccur among subgroups of actors who sharesimilar attributes. Hypotheses based on differ-ential network centralization would be sup-ported if there were greater probabilities forgraph realizations in which actors with sharedattributes were more likely to have higher levelsof subgroup network centralization. In otherwords, these hypotheses would be supported ifthe probability of ties being present or absent inthe network reflected actors’ tendencies to forgemore centralized subgroup networks with otheractors sharing similar attributes.

In Figure 8, theories of collective action wouldsuggest a greater tendency for a tie from actor Ato fellow government actor C, since it wouldenhance the centralization within governmentactors, but a lower tendency for a tie from actorA to industry actor E, since it would enhancecentralization between government and indus-try actors.

Other relations in the network. In addition toattributes of the actors, additional relations

FIGURE 6Exogenous Attribute Dyadic Level: Resource

Dependence Theory

FIGURE 7Exogenous Attribute Triadic Level: Balance

Theory


among the actors represent a second set of ex-ogenous variables that influence the probabilityties will be present or absent in the focal net-work (row 9 in Table 2). For instance, the conver-gence theory of communication (Richards &Seary, 1997; Rogers & Kincaid, 1981), cognitivetheories (Carley, 1986; Carley & Krackhardt,1996; Krackhardt, 1987a; Stohl, 1993), and trans-active memory theory (Hollingshead, 1998; Mo-reland, 1999; Wegner, 1995) offer arguments thatcan be used to map the influence of actors’ cog-nitive or semantic networks (Monge & Eisen-berg, 1987) onto their communication networks.These theories argue that the presence or ab-sence of a cognitive or semantic tie betweenthese actors is associated with the presence orabsence of a communication tie between theactors. Hypotheses based on the influence ofexogenous networks would be supported if therewere greater probabilities for graph realizationsin which the actors’ ties in the focal networkcorresponded to their ties in the exogenous net-works. In other words, these hypotheses wouldbe supported if the probability of ties beingpresent or absent in the focal network reflectedthe presence or absence of ties in the exogenousnetworks.

It may appear that the objective sought herecould be obtained far more easily by computinga simple correlation between the two relationsin the network. While that is indeed the case, thelack of independence among the observations

and the fact that the individual variables understudy are usually dichotomous preclude the useof standard statistical techniques to assess thesignificance of this correlation. Techniques in-troduced by Hubert (Hubert 1978; Hubert &Schultz 1976) based on permutation tests (one ofthe solutions to the Quadratic Assignment Prob-lem) have been used to test the significance ofassociation between two relations in a network.While organizational network researchers haveused such permutation tests extensively (Krack-hardt, 1987b), the technique does not generalizeto the multirelational, multilevel framework pro-posed here. Recently, these situations havebeen viewed as multivariate networks (Wasser-man & Pattison 1999) and the relations modeledsimultaneously.

Figure 9 indicates that there is a greater ten-dency for a friendship tie from actor A to actor B,because they communicate with one another,and a lower tendency for a friendship tie fromactor C to actor D, because they do not commu-nicate with one another.

Relations at previous points in time. Finally,the probability ties will be present or absent inthe primary relation can also be influenced bythe presence or absence of ties in that samerelation at previous points in time (row 10 inTable 2). In their most primitive form, theories ofevolution (McKelvey, 1997) would argue that in-ertia alone would predict that a tie betweenactors at a previous point in time would in-crease the tendency of the tie to be maintained

FIGURE 8Exogenous Attribute Global Level: Collective

Action Theory

FIGURE 9Exogenous Other Relations: Cognitive Theories


at a subsequent point in time. For instance, Gu-lati hypothesizes that “the higher the number ofpast alliances between two firms, the morelikely they are to form new alliances with eachother” (1995: 626). Hypotheses based on the influ-ence of the same network at previous points intime would be supported if there were greaterprobabilities for graph realizations in which theactors’ ties in the focal network corresponded totheir ties in the preceding networks.

Figure 10 indicates that evolutionary theorieswould posit a greater tendency for a future tiefrom actor A to actor B because of an existing tiefrom actor A to B, and a lower tendency for afuture tie from actor A to actor D because of thelack of an existing tie from actor A to actor D.

The treatment of exogenous variables de-scribed here is intentionally attenuated to re-flect the lack of statistical techniques address-ing the plethora of hypotheses that can bestudied by considering the interactions amongthe exogenous variables described above. Twoscenarios are worth considering. First, the influ-ence of exogenous networks (either of differentrelations in the same network of actors or thesame network at previous points in time) on thefocal network can be moderated based on athird set of exogenous variables: the attributesof the actors. In other words, the tendency tobuild on preexisting ties may be different foractors with different shared attributes. An illus-tration of this situation is represented in Steven-

son and Gilly’s study of organizational problem-solving networks, where they note that“managers are more likely than non-managersto use preexisting ties when forwarding organi-zational problems” (1993: 103).

A second scenario would be the influence onthe focal network of an exogenous network(which is a different relation in the same net-work of actors and at a previous point in time).This is the case when new kinds of ties might beestablished against the backdrop of existing re-lationships of a different type. For example, asGranovetter (1992) has argued, economic trans-actions are often “embedded” in social rela-tions. This would suggest that economic rela-tionships between actors might be more likelywhen they have a prior social relationship.While the statistical models, including the p*family of models, have incorporated techniquesto test hypotheses in the ten situations de-scribed in this section, additional efforts are be-ing made to address the more complicated sce-narios, such as the two illustrated above(Pattison & Robins, 2002; Snijders, 2001).

In summary, we have introduced an integra-tive analytic framework that seeks to examinethe extent to which the structural tendencies oforganizational networks are influenced by multi-theoretical hypotheses operating at multiplelevels of analysis. The exigencies of noninde-pendence in relational data preclude the use ofstandard statistical testing procedures. Hence,we introduced the notion of graph realizationsand described how the hypothesized propertiesof networks influence the probabilities of graphrealizations. In the next section we illustratehow some of these hypotheses can be tested inan empirical study.

EMPIRICAL EXAMPLE: THE CRADA NETWORK

Sample

The example here is based on a subset of datafrom a larger research project examining thesocial and organizational issues surroundingthe creation of “virtual work communities” (Fulk,Lu, Monge, & Contractor, 1997). The communityunder study was composed of representativesfrom three agencies of the U.S. Army and fourprivate corporations, who forged a CooperativeResearch and Development Agreement(CRADA). The goal of this CRADA, a network

FIGURE 10Exogenous Prior Relations: Evolutionary

Theories


organization, was the commercial production ofsoftware for improving the building design pro-cess for large institutional facilities. The fourprivate companies were a CAD operating sys-tems developer, a construction software firm, asoftware development company, and an archi-tectural firm. The U.S. Army partners included aresearch laboratory, a district office, a unit of thearmy reserves, and members from headquar-ters. The software to be produced through thisCRADA would offer advanced “virtual” coordi-nation capabilities through its object-orientedtechnology and modular design system.1

CRADAs, which were first authorized by the1986 Technology Transfer Act, enable govern-ment and industry to negotiate patent rights androyalties before entering into joint R&D projects.They were conceived as an incentive for indus-try, to facilitate investment in joint research byreducing the risk that the products of the re-search would fall into the public domain and beexploited by both domestic and internationalcompetitors. Since 1989, there has been an expo-nential growth in the creation of CRADAs,reaching over 2,200 by 1993. The Departments ofEnergy, Commerce, Agriculture, and Defenseinitiated a large proportion of these. CRADAsinvolve large, medium, and small businesses ina wide variety of industries, including computersoftware, materials, agricultural chemicals, bio-medical research, and electronic networking.

Unlike most other CRADAs, which are dyadicarrangements involving only one partner fromprivate industry and one from government, theCRADA studied here involved multiple privateand government organizations. As a result, theprivate organizations needed not only to ham-mer out an agreement with the multiple govern-ment agencies but also to work through the dif-ficult process of negotiating an agreement forhow their own private partnership was to func-tion and how the benefits of the alliance were tobe distributed among the partners. After a com-plex set of negotiations, a partnership frame-work was developed among the business partic-ipants, and the CRADA agreement was signedin a formal ceremony. Hence, the structure andpractices of this CRADA reflect many of the fea-

tures of the new network forms of organizingdescribed in the introduction.

Data

The network being analyzed in this examplewas the communication that occurred in themonth prior to the signing of the CRADA agree-ment among the seventeen members represent-ing the various private and government organi-zations. In this network a tie was directed from amember in one organization to a member in thesame or another organization if the member re-ported communication during the month ofstudy—a dichotomous relationship (eitherpresent or absent).

Hypotheses

We test eight hypotheses derived from fourtheories at three levels (dyadic, triadic, global).The first four hypotheses being tested here positthat the probabilities of graph realizations (ofwhich the observed network is but one realiza-tion) are influenced by endogenous properties ofthe network itself at the dyadic, cyclical triadic,transitive triadic, and global levels. Exchangeand dependence theories would suggest a struc-tural tendency toward mutuality among the ac-tors at the dyadic level (Hypothesis 1). Cognitiveconsistency theories would suggest a structuraltendency toward transitivity and cyclicalityamong the actors at the triadic level (Hypothe-ses 2 and 3). And collective action theorieswould posit a structural tendency towardgreater network centralization—variance in out-degrees (Hypothesis 4a)—and prestige—vari-ance in indegrees (Hypothesis 4b).

The remaining four hypotheses examine theinfluence of one exogenous attribute of themembers in the network—whether they repre-sented a government agency or industry. Thesefour hypotheses posit that the probabilities ofgraph realizations are influenced by the exoge-nous attribute at the actor, dyadic, transitivetriadic, and global levels. Homophily theorieswould suggest a structural tendency for actorswith the same attribute (belonging to govern-ment or industry) to exhibit greater communica-tion (Hypothesis 5), mutuality (Hypothesis 6),transitivity (Hypothesis 7), and centralization/prestige (Hypothesis 8a and b) with others shar-ing their attribute. The hypotheses shown in Ta-

1 Additional information about this project can be ob-tained from http://impact.usc.edu/impact/JIVE/contents.htm.


ble 3 are presented so that they map directlyonto the framework summarized in Table 2 anddescribed previously. As is evident, the eighthypotheses tested in this empirical illustrationmap directly onto seven of the ten cells de-scribed in Table 1.

As discussed below, we test these multitheo-retical, multilevel hypotheses by statistically es-timating the extent to which structural tenden-cies implied by these hypotheses influence theprobabilities of observing certain realizations ofthe network.

p* Statistical Models for TestingMultitheoretical, Multilevel Hypotheses

The hypotheses tested here use the p* familyof statistical models. This family was first intro-duced in the mid 1980s (Frank & Strauss, 1986;Strauss & Ikeda, 1990) and popularized in thelate 1990s by a number of researchers (e.g., Pat-tison & Wasserman, 1999; Robins et al., 1999;Wasserman & Pattison, 1996).2 In brief, these

models are based on the fact that the Hammers-ley-Clifford theorem (Besag, 1974) provides ageneral probability distribution for a socioma-trix X from a specification of which pairs of tierandom variables are conditionally dependent,given the values of all other random variables.These conditional dependencies express hy-pothesized structural tendencies in the network.Specifically, a dependence graph D with nodeset N(D) � {Xij: i, j � N, i � j} and edge set E(D) �{(Xij, Xkl): Xij and Xkl} is assumed to be condition-ally dependent, given the rest of X. We can useD to obtain a model for Pr(X � x), denoted p*, interms of parameters and substructures corre-sponding to cliques of D. The model has the form

Pr(X � x) � p*(x) � (1/c)exp��P�N(D)�PzP(x)�

where

1. the summation is over all cliques P of D(with a clique of D defined as a nonemptysubset P of N(D) such that �P� � 1 or (Xij, Xkl)� E(D) for all Xij, Xkl � P);

2 A thorough history of this family can be found in thechapters on p* in Carrington, Scott, and Wasserman (2003),

especially in the Wasserman and Robins (2003) chapter. Werefer readers to these chapters for further mathematical andstatistical details about p*.

TABLE 3Multitheoretical, Multilevel Hypotheses About the Structural Tendencies of an Interorganizational

Network

Independent Variable Hypotheses: Graph realizations where. . .

Endogenous (same network): actor levelEndogenous (same network): dyadic level H1: . . . actors have a high degree of reciprocated (or mutual) communication

tiesEndogenous (same network): triadic level H2: . . . triads of actors in the network exhibit a high degree of cyclicality

H3: . . . triads of actors in the network exhibit a high degree of transitivityEndogenous (same network): global level H4: . . . the network has a high degree of outdegree centralization (4a) and

prestige (or indegree) centralization (4b)

Exogenous (actor attributes): actor level H5: . . . actors in the network who belong to the same type of organization(i.e., government or industry) are more likely to have ties with oneanother

Exogenous (actor attributes): dyadic level H6: . . . actors in the network who belong to the same type of organization(i.e., government or industry) are more likely to have mutual (orreciprocated) communication ties

Exogenous (actor attributes): triadic level H7: . . . actors in the network who belong to the same type of organization(i.e., government or industry) are more likely to be embedded in transitiveties with one another

Exogenous (actor attributes): global level H8: . . . actors in the network who belong to the same type of organization(i.e., government or industry) are more likely to have higher levels ofsubgroup (outdegree) centralization than the overall network’scentralization (8a) and higher levels of subgroup prestige (or indegree)centralization than the overall network’s prestige network centralization(8b)


2. zP(x) � �Xij�Pxij is the (observed) networkstatistic corresponding to the clique P of D;and

3. c � �xexp{�P�PzP(x)} is a normalizing quan-tity.

The quantities zP(x) are calculated from theobserved network and correspond to the hypoth-esized structural tendencies expressed in thedependence graph. The �P are parameters cor-responding to the cliques P of D. These param-eters express the importance of the associatedstructural tendency for the probability of thegraph.

One possible dependence assumption isMarkov, in which (Xij, Xkl) � E(D) whenever {i, j}� {k, l} � �. This assumption implies that theoccurrence of a network tie from one node toanother is conditionally dependent on the pres-ence or absence of other ties in a local neigh-borhood of the tie. A Markovian local neighbor-hood for Xij comprises all possible ties involvingi and/or j. We primarily make a Markov depen-dence assumption in our models. Many otherdependence assumptions are also possible, andthe task of identifying appropriate dependenceassumptions in any modeling venture poses asignificant theoretical challenge. The multi-level, multitheoretical hypotheses that we in-vestigate here illustrate the flexibility and gen-erality of this approach.

Analysis and Results

The p* family of models was used to simulta-neously test the eight hypotheses. We used lo-gistic regression to fit a series of nested modelswhere the response variable was the presenceor absence of a tie between each pair of actors.The explanatory variables were the changes inthe hypothesized network statistic when thatspecific tie changed from a 1 to 0.3 These vari-ables were computed using Prepstar (seeCrouch & Wasserman, 1998) and the MultiNetnetwork analysis software programs (Seary &Richards, 2001), and then fitted using standardlogistic regression techniques (see Crouch &Wasserman, 1998). This maximum pseudo-likelihood method of estimation is, at best, ap-proximate, and in particular provides standarderrors that may be too large. As such, this

method provides only an approximate basis fornull hypothesis statistical testing.

There have been considerable and promisingrecent efforts to develop Monte Carlo maximumlikelihood procedures, which produce reliablestandard errors more appropriate for formal sta-tistical testing (for a review, see Wasserman &Robins, 2003). Estimation procedures for five ofthe simpler models hypothesized here havebeen implemented in SIENA (Snijders, 2001,2002). Algorithms for the more complex modelsare expected to be available in the near future.Where possible, we estimated each model usingMonte Carlo maximum likelihood proceduresand compared the results with those obtainedfrom the maximum pseudo-likelihood proce-dures. In all cases, there were modest differ-ences in the values of the estimates, with thesimilarity of the estimates decreasing as thenumber of the parameters estimated increased.However, the estimates using the two proce-dures led to the same conclusions about support(or lack thereof) for the hypotheses. Again, weissue to the reader a cautionary note about mak-ing inferential decisions based on approximatetechniques.

The results for the fitted models using maxi-mum pseudo-likelihood are shown in Table 4.The first column indicates the variables in-cluded in the model. The second column indi-cates the number of parameters estimated in themodel. The number of parameters estimated cor-responds to the number of variables in themodel. The third column reports the fitness ofthe model. The fitness value is twice the nega-tive of the log pseudo-likelihood of the model,sometimes referred to as the pseudo-likelihooddeviance. Hence, the magnitude of this valueshould be interpreted as a “badness of fit” mea-sure. Models that have a lower deviance can beassumed to better predict the observed network.Pseudo-likelihood estimates are approximate;in particular, the standard errors may be toolarge. Although the decrease in the badness offit values between two nested models does notapproximate a chi-squared distribution (wherethe degrees of freedom are the difference in thenumber of parameters estimated in the twomodels), a large difference in fit may be evi-dence that an effect is present. As such, thesevalues can be used as an effective heuristicguide. The fourth column reports the mean of theabsolute residuals across all 272 (17 times 16)

3 Wasserman and Pattison algebraically derive the ration-ale for this approach (1996: 407).


ties. The residuals are the difference betweenthe observed ties and the probabilities for thoseties predicted by the model. The mean of theabsolute residuals, along with the pseudo-likelihood deviance, serves as a simple badnessof fit measure.

The first model (Model 1) is a baseline modelwhere the single explanatory variable, some-times referred to as choice, is always valued at1. This model estimates one parameter, for thevariable choice, and reflects the null hypothesisthat the probabilities for ties in the network area constant, given by the total number of ties inthe network, and there are no additional struc-tural effects. As such, it is the equivalent of anintercept term or a grand mean in regression orANOVA, respectively. The pseudo-likelihood de-viance or badness of fit value, 354.39, reportedfor this model was large, indicating a poor fit.Further, the mean of the absolute residuals wasquite high (0.459). Clearly, the probabilities forgraph realizations were not constant and weredependent on other structural properties of thenetwork, such as mutuality, transitivity, central-ization, and so on. The effects of these hypothe-sized structural properties are tested in the mod-els below.

Model 2 tests the first hypothesis that there isa greater probability for graph realizations in

which actors have a high degree of mutuality orreciprocation. The two parameters estimated inthis model include the parameter for the choice(the baseline) variable estimated in Model 1 andthe change statistic associated with the dyadicendogenous network property of mutuality. Alarge decrease in the badness of fit value fromModel 1 to Model 2 (354.39 � 254.25 � 100.04, d.f.� 1) indicates support for Hypothesis 1. Themean of the absolute residuals fell from 0.459 to0.294. Consistent with social exchange theory,given the number of other possible realizationsof the observed graph, there were more mutualcommunication ties than would be expected bychance. That is, there was a greater-than-chance probability for mutual ties in the CRADAnetwork. Substantively, this suggests that indi-viduals involved in this software collaborationwere more likely to be engaged in mutual inter-actions than in some form of a linear (or possiblyhierarchical) set of unidirectional interactions.

Models 3 and 4 test, individually, the secondand third hypotheses, which state, respectively,that there is a greater probability for graph re-alizations in which triads of actors are embed-ded in cyclical and transitive relations. Models 3and 4 incorporate the parameters specified inModel 2, in order to test the hypotheses abouttriads controlling for the influence of dyads. The

TABLE 4Goodness of Fit for the Hypothesized Models

ModelNumber ofParameters

Pseudo-likelihoodDeviance �2 (logpseudo-likelihood)

Mean of theAbsoluteResiduals

1. Choice (intercept term � uniform distribution of ties) 1 354.39 0.4592. Choice mutuality (H1) 2 254.25 0.2943. Choice mutuality cyclicality (H2) 3 241.97 0.2814. Choice mutuality transitivity (H3) 3 228.84 0.2665. Choice mutuality transitivity cyclicality 4 228.01 0.2656. Choice mutuality transitivity choice within

shared attribute (H5)4 222.75 0.259

7. Choice mutuality transitivity choice withinshared attribute mutuality with shared attribute(H6)

5 221.72 0.256

8. Choice mutuality transitivity choice withinshared attribute transitivity within sharedattribute (H7)

5 218.93 0.254

9. Model 6 degree centralization (H4a) degreeprestige (H4b)

6 211.66 0.241

10. Model 6 degree centralization degree prestige degree centralization within shared attribute (H8a) degree prestige within shared attribute (H8b)

8 202.21 0.232


large decrease in the badness of fit values fromModel 2 to Model 3 (254.25 � 241.97 � 12.28, d.f. �1) and Model 4 (254.25 � 228.84 � 25.41, d.f. � 1)lends evidence to the importance of both cycli-cality and transitivity. However, the mean of theabsolute residuals was higher for Model 3 withcyclicality (0.281) than it was for Model 4 withtransitivity (0.266). Consistent with balance the-ory, these findings support the hypotheses that,given the number of other possible realizationsof the observed graph, there were more transi-tive and cyclical structures in the CRADA com-munication network than would be expected bychance. Substantively, these findings suggestthat individuals involved in this software col-laboration had a tendency to work collectivelyin triads rather than to rely on unitary chain-of-command or independent dyadic links.

Model 5 tests, collectively, Hypotheses 2 and 3,regarding transitivity and cyclicality, respec-tively. There was a very small drop in the bad-ness of fit measure from Model 4 (which testedHypothesis 3, regarding transitivity) to Model 5(228.84 � 228.01 � 0.83, d.f. � 1). Likewise, themean of the absolute residuals fell marginallyfrom 0.266 (for Model 4 with transitivity) to 0.265(for Model 5 with cyclicality and transitivity).This indicates that when both transitivity andcyclicality effects are included (Model 5), littlegain in fit is realized over a model containingtransitivity alone (Model 4). This finding sug-gests that, in the CRADA network, the actors’tendency to engage in cyclical communicationtriads was not substantial after controlling fortheir tendency to engage in transitive communi-cation triads. In other words, after taking intoaccount the greater-than-chance probability oftransitive triads in the CRADA communicationnetwork, there was no greater-than-chanceprobability of finding cyclical triads in the net-work. Substantively, this would suggest that in-dividuals in the network did demonstrate somelevel of hierarchy. If actor A went to actor B andactor B went to actor C, there was a greatertendency for actor A to also seek communicationwith actor C (transitivity), rather than for actor Cto seek actor A (cyclicality).

From a statistical standpoint, the minimalgain in fit resulted in dropping the cyclicalityvariable in the estimation of subsequent nestedmodels. It is worth noting that our model did notestimate tendencies for other triadic structures,such as 2-in stars (where one actor receives a

link from two other actors), 2-out stars (where anactor sends links to two other stars), or mixedstars (where an actor receives a link from onestar and sends a link to another star). A strictlyhierarchical model should include those effects.However, we chose not to include them becausewe did not identify a sufficiently strong theoret-ical argument for their inclusion. Technically,even if these parameters were estimated, wewould expect to retain the triadic effects wereport here.

Models 6, 7, and 8 test Hypotheses 5, 6, and 7,which state, respectively, that there is a greaterprobability for graph realizations in which ac-tors in the network who belong to the same typeof organization (government or industry) aremore likely to have ties with one another, thatthese ties are mutual, and that these ties aretransitive. Model 6 results in an appreciablegain in fit over earlier models, suggesting indi-viduals were more likely to report ties to otherindividuals in their own organizational typethan to individuals in the other organizationaltype. The mean of the absolute residualsdropped further, to 0.259. In other words, aftercontrolling for the previously tested hypotheses(ceteris paribus), there was still a greater-than-chance probability that actors would have com-munication ties with others within their ownorganizational type (government or industry).This provides support for theories of homophily.It should be noted that this model posits that thedensities of ties within organizations are thesame. That is, the model does not posit a differ-ent propensity for actors within governmentagencies to form ties among themselves as com-pared to actors within industry to form tiesamong themselves.

Given only a minor decrease in fit from Model6 to Model 7 (222.75 � 221.72 � 1.03, d.f. � 1) andModel 8 (222.75 � 218.93 � 3.82, d.f. � 1), littleevidence exists for differential mutuality or dif-ferential transitivity effects over and above dif-ferential choice. The mean of the absolute resid-uals also dropped marginally, from 0.259 to0.256. Substantively, this suggests that individ-uals involved in this software collaborationwere not more likely to be engaged in mutualinteractions with individuals in their own typeof organization compared to individuals fromthe other type of organization. Further, it sug-gests that the tendency of individuals to interactin transitive triads was no more pronounced


within organizations of their own type (be it gov-ernment or industry) than it was in the othertype. Here again, the mean of the absolute re-siduals dropped minimally, from 0.256 to 0.254.In other words, ceteris paribus, there was not agreater-than-chance probability for actors inone organizational type to forge mutual ties ortransitive ties involving other actors from thesame organizational type. The lack of supportfor the hypothesized differential effects for mu-tuality and transitivity suggests that individu-als were not “ganging up” in dyads or triadswithin their respective government or industrysectors. Given the goal of the CRADA to collab-orate across these boundaries, this may be in-terpreted as a promising sign. From a statisticalstandpoint, the lack of improvement in fit im-plies that the exogenous variables associatedwith mutuality and transitivity should bedropped from subsequent nested models.

Model 9 tests Hypotheses 4a and 4b, whichstate that there is a greater probability for graphrealizations in which the network has a highdegree of centralization and prestige, respec-tively. The substantial improvement in the fit ofModel 9 over previous models indicates supportfor Hypothesis 4. The mean of the absolute re-siduals dropped substantially, to 0.241. In otherwords, ceteris paribus, there was a greater-than-chance probability for actors to forge tiesthat would enhance the overall centralization ofthe network. Substantively, this means that, con-sistent with theories of collective action, theCRADA communication network exhibited astrong structural tendency toward centraliza-tion. We acknowledge that adding centraliza-tion and prestige parameters to the model goesbeyond Markov dependence assumptions. Mod-els that incorporate non-Markov dependence as-sumptions can lead to estimation problems. Thisis an active area of research (see Carrington etal., 2004).

Finally, Model 10 tests Hypothesis 8, whichstates that there is a greater probability forgraph realizations in which actors in the net-work who belong to the same type of organiza-tion (government or industry) are more likely tohave higher levels of network centralizationthan the overall network’s centralization. Hereagain, the substantial improvement in the fit ofModel 10 over Model 9 (211.66 � 202.21 � 9.45, d.f.� 1) suggests a strong effect of differential cen-tralization on the probability for graph realiza-

tions. Further, the mean of the absolute residu-als dropped from 0.241 (for Model 9) to 0.232.However, before substantively interpreting thisfinding and concluding that this indicates sup-port for Hypothesis 8, it is important to examinethe individual parameter values associatedwith the variables fitted in Model 10.

While Table 4 reports global measures of fitfor each of the ten models, Table 5 reports theparameter estimates and the associated tests ofsignificance for the best-fitting model (Model10). The first column lists the variables includedin Model 10. The second column is the parameterestimate for the corresponding explanatory vari-able. A large positive value of a parameter sug-gests the presence of the associated networkstructural component, while a large negativevalue suggests its absence. One can also inter-pret the parameters in terms of log odds. Thus,for a unit increase in the explanatory variable,the odds ratio that the response equals 1 (i.e., atie is present) changes by a factor of exp(�1). (Themagnitude of this effect depends on a number ofpossibilities. For instance, there can only be onepossibility for mutuality, but an arc might beinvolved in several triads so that what appearsas a modest transitivity effect may actually besubstantial.)

The third column indicates the Wald statistic,which is defined as the {(parameter estimate)/Standard Error(parameter estimate)}2. It shouldbe noted that the pseudo-likelihood estimates ofthe standard errors used to compute the WaldStatistic are approximate. The fourth column inTable 5 indicates the extent to which each vari-able contributes to a change in the odds ratio of

TABLE 5Parameters for the Best-Fitting Model

(Model 10)

Variable BWaldStatistic Exp(B)

Choice (intercept term) �5.61 54.99Mutuality (H1) 2.11 32.21 8.25Transitivity (H2) .26 24.72 1.30Choice within shared attribute (H5) 2.48 15.37 11.94Degree centralization (H4a) 2.84 8.67 17.12Degree prestige (H4b) 2.33 6.46 10.28Centralization within shared

attribute (H8a)�5.50 4.53 0.004

Prestige within shared attribute(H8b)

�4.35 2.75 0.01


a tie being present. Consider Hypothesis 1,where, in the second column, the mutuality pa-rameter is estimated to be 2.11. The fourth col-umn indicates that if there is a tie from actor B toactor A, the odds of a mutually reciprocated tiefrom actor A to actor B will increase by a factorof exp(2.11), which is 8.25. Likewise, according toHypothesis 2, if actor A is connected to actor Cand actor C is connected to actor B, the odds of atie from actor A to actor B (which would com-plete a transitive triad) increases by a modestfactor of 1.30. Further, considering Hypothesis 3,if actor A and actor B both represent the sameorganization, the likelihood of a communicationtie between them increases by a factor ofexp(2.48), which is 11.94. In contrast, consideringHypothesis 8, since the parameter for centraliza-tion within a shared attribute (i.e., organizationtype) is �5.50, the odds of a tie that contributesto a more centralized network among govern-ment or industry organizations are substantiallydecreased by a factor of exp(�5.50), which is0.004. This is a strong effect, albeit not in thedirection hypothesized. Hence, despite the sub-stantial improvement of fit in Model 10 (reportedin Table 4), the negative coefficient associatedwith this variable indicates a significant effectin the direction opposite that proposed by Hy-pothesis 8.

These results indicate that there is a lower-than-chance probability that actors would forgeties that would enhance the centralization of thenetwork involving other actors within their owntype of organization. Given that the goal of theCRADA was to mobilize a collective agreementacross government and industry organizations,this finding is (in retrospect) plausible. It indi-cates a structural tendency to downplay central-ization within organizational type (governmentor industry). This finding, taken in conjunctionwith a tendency to centralize in the overallCRADA network (Model 9, Hypothesis 4), wouldsuggest that individuals’ propensity for collec-tive action across organizational types super-ceded any parochial attempts to centralizewithin their own organizational type.

The positive overall centralization/prestigeparameters and the negative subgroup central-ization/prestige parameters are best consideredtogether. The overall parameters counteract thesubgroup parameters in circumstances whenthe node has many ties to actors outside thesubgroup. One interpretation, then, is that ac-

tors are more likely to seek ties to popular actorswithin their organization if those actors havecross-organization ties. That is, actors who aremore popular within their organization tend tobe boundary spanners. However, from a statis-tical standpoint, the subgroup negative param-eters could also reflect the fact that the variancein outdegrees (indicating centralization) issmaller within subsets of similar organizations,simply because the actors are fewer in number.

In summary, the results of this empirical illus-tration suggest that there were structural ten-dencies in the CRADA network to reciprocatecommunication ties (Hypothesis 1, see Figure 2),engage in transitive communication triads (Hy-pothesis 2, see Figure 3), foster a centralizedoverall network (Hypothesis 4, see Figure 4), andcommunicate more with individuals in organi-zations of their own type, be it government orindustry (Hypothesis 5, see Figure 5). Further,contrary to Hypothesis 8, there was a structuraltendency to eschew centralization within thenetwork comprising members of their own or-ganizational type. The remaining three hypoth-eses were not supported. In addition to its sub-stantive implications, this empirical exampleoffers a modest illustration of how the frame-work for testing multitheoretical, multilevel hy-potheses introduced in the previous section canbe used to explain the emergence of an inter-organizational network. Specifically, Model 10nested variables at the dyadic, triadic, andglobal levels that were simultaneously esti-mated.

CONCLUSION

The advent of digital technologies has ush-ered in a radical reconceptualization of our con-ventional notions of organizing (Contractor,2002; Contractor & Monge, 2003). New networkforms of organizing are supplanting hierarchiesand markets that dominated the better part ofthe twentieth-century “workscape.” While net-work researchers have made substantialprogress in examining networks in organiza-tions, they are less well prepared to understandorganizing as networks. The characteristics oftwenty-first-century network organizationalforms challenge us to extend our efforts fromexamining emergent networks to a more theo-retically and methodologically sophisticated


approach to explaining the emergence of net-works.

Building on recent efforts to identify the mul-tiple theoretical mechanisms that contribute tothe emergence of organizational networks, wehave proposed, and illustrated empirically, ananalytic framework that has the potential to testmultitheoretical, multilevel hypotheses aboutthe structural tendencies of networks. Theframework, by its very organization, also re-veals the substantial theoretical and method-ological limitations in current research on or-ganizational networks. More important, theframework brings into focus the specific areaswhere new network methodologies need to re-spond to theoretical concerns and new theoreti-cal issues can leverage some of the methodolog-ical advances.

REFERENCES

Anderson, C., Wasserman, S., & Crouch, C. 1999. A p* primer:Logit models for social networks. Social Networks, 21:37–66.

Bearman, P. 1997. Generalized exchange. American Journalof Sociology, 102: 1383–1415.

Besag, J. E. 1974. Spatial interaction and the statistical anal-ysis of lattice systems. Journal of the Royal StatisticalSociety, 36(Series B): 192–236.

Blau, P. M. 1964. Exchange and power in social life. NewYork: Wiley.

Burt, R. S. 1992. Structural holes: The social structure of com-petition. Cambridge, MA: Harvard University Press.

Carley, K. 1986. An approach for relating social structure tocognitive structure. Journal of Mathematical Sociology,12(2): 137–189.

Carley, K. 2002. Smart agents and organizations of the future.In L. Lievrouw & S. Livingstone (Eds.), Handbook of newmedia: 206–220. London: Sage.

Carley, K., & Krackhardt, D. 1996. Cognitive inconsistenciesand non-symmetric friendship. Social Networks, 18: 1–27.

Carrington, P. J., Scott, J., & Wasserman, S. 2003. Models andmethods in social network analysis. New York: Cam-bridge University Press.

Coleman, J. S. 1957. Community conflict. New York: FreePress.

Coleman, J. S. 1973. The mathematics of collective action.Chicago: Aldine.

Coleman, J. S. 1986. Individual interests and collective ac-tion: Selected essays. New York: Cambridge UniversityPress.

Contractor, N. S. 2002. Introduction: New media and organiz-ing. In L. Lievrouw & S. Livingstone (Eds.), Handbook ofnew media: 201–205. London: Sage.

Contractor, N. S., & Monge, P. R. 2002. Managing knowledgenetworks. Management Communication Quarterly, 16:249–258.

Contractor, N. S., & Monge, P. R. 2003. Using multi-theoreticalmultilevel models to study adversarial networks. InR. Brieger, K. Carley, & P. Pattison (Eds.), Dynamic socialnetwork modeling and analysis: Workshop summaryand papers: 324 –344. Washington, DC: National Re-search Council.

Crouch, B., & Wasserman, S. 1998. A practical guide to fittingsocial network models via logistic regression. Connec-tions, 21: 87–101.

Emerson, R. M. 1972a. Exchange theory I: A psychologicalbasis for social exchange. In J. Berger, M. Zelditch, &B. Anderson (Eds.), Sociological theories in progress, vol.2: 38–57. Boston: Houghton Mifflin.

Emerson, R. M. 1972b. Exchange theory II: Exchange relationsand networks. In J. Berger, M. Zelditch, & B. Anderson(Eds.), Sociological theories in progress, vol. 2: 58–87.Boston: MA: Houghton Mifflin.

Frank, O., & Strauss, D. 1986. Markov random graphs. Journalof the American Statistical Association, 81: 832–842.

Fulk, J., Flanagin, A. J., Kalman, M. E., Monge, P. R., & Ryan,T. 1996. Connective and communal public goods in in-teractive communication systems. Communication The-ory, 6: 60–87.

Fulk, J., Lu, S. C., Monge, P. R., & Contractor, N. S. 1997.Interactive communication and computing for virtualwork communities: Interim report. Los Angeles: Univer-sity of Southern California, Annenberg Center for Com-munication.

Gnyawali, D. R., & Madhavan, R. 2001. Cooperative networksand competitive dynamics: A structural embeddednessperspective. Academy of Management Review, 26: 431–445.

Granovetter, M. 1992. Problems of explanation in economicsociology. In N. Nohria & R. G. Eccles (Eds.), Networksand organizations: Structure, form, and action: 25–56.Boston: Harvard Business School Press.

Gulati, R. 1995. Social structure and alliance formation pat-terns: A longitudinal analysis. Administrative ScienceQuarterly, 40: 619–652.

Heider, F. 1958. The psychology of interpersonal relations.New York: Wiley.

Holland, P. W., & Leinhardt, S. 1975. The statistical analysisof local structure in social networks. In D. R. Heise (Ed.),Sociological methodology, 1976: 1–45. San Francisco:Jossey-Bass.

Holland, P. W., & Leinhardt, S. 1981. An exponential family ofprobability distributions for directed graphs. Journal ofthe American Statistical Association, 76: 33–65.

Hollingshead, A. B. 1998. Communication, learning and re-trieval in transactive memory systems. Journal of Exper-imental Social Psychology, 34: 423–442.

Homans, G. C. 1958. Social behavior as exchange. AmericanJournal of Sociology, 19: 22–24.


Hubert, L. 1978. Evaluating the conformity of sociometricmeasurements. Psychometrika, 43: 31–41.

Hubert, L., & Schultz, L. 1976. Quadratic assignment as ageneral data analysis strategy. British Journal of Math-ematical and Statistical Psychology, 29: 190–241.

Ibarra, H. 1992. Homophily and differential returns: Sex dif-ferences in network structure and access in an advertis-ing firm. Administrative Science Quarterly, 37: 422–447.

Ibarra, H. 1993. Personal networks of women and minoritiesin management: A conceptual framework. Academy ofManagement Review, 18: 56–87.

Ibarra, H. 1995. Race, opportunity, and diversity of socialcircles in managerial networks. Academy of Manage-ment Journal, 38: 673–703.

Jones, C., Hesterly, W. S., & Borgatti, S. P. 1997. A generaltheory of network governance: Exchange conditions andsocial mechanisms. Academy of Management Review,22: 911–945.

Klein, K. J., Tosi, H., & Cannella, A. A., Jr. 1999. Multileveltheory building: Benefits, barriers, and new develop-ments. Academy of Management Review, 24: 243–248.

Krackhardt, D. 1987a. Cognitive social structures. Social Net-works, 9: 109–134.

Krackhardt, D. 1987b. QAP partialling as a test of spurious-ness. Social Networks, 9: 171–186.

Krackhardt, D. 1994. Constraints on the interactive organiza-tion as an ideal type. In C. Heckscher & A. Donnellon(Eds.), The post-bureaucratic organization: New perspec-tives on organizational change: 211–222. ThousandOaks, CA: Sage.

Krackhardt, D., & Brass, D. J. 1994. Intra-organizational net-works: The micro side. In S. Wasserman & J. Ga-laskiewicz (Eds.), Advances in social network analysis:Research in the social and behavioral sciences: 207–229.Thousand Oaks, CA: Sage.

Marwell, G., & Oliver, P. 1993. The critical mass in collectiveaction: A micro-social theory. Cambridge, MA: Cam-bridge University Press.

Marwell, G., Oliver, P. E., & Prahl, R. 1988. Social networksand collective action: A theory of the critical mass. III.American Journal of Sociology, 94: 502–534.

McKelvey, B. 1997. Quasi-natural organization science. Or-ganization Science, 8: 352–380.

McPherson, M., Smith-Lovin, L., & Cook, J. M. 2001. Birds of afeather. Homophily in social networks. Annual Reviewof Sociology, 27: 415–444.

Miles, R. E., & Snow, C. C. 1995. The new network firm: Aspherical structure built on a human investment philos-ophy. Organizational Dynamics, 23(4): 5–18.

Mizruchi, M. S., & Galaskiewicz, J. 1994. Networks of interor-ganizational relations. In S. Wasserman & J. Ga-laskiewicz (Eds.), Advances in social network analysis:Research in the social and behavioral sciences: 230–253.Thousand Oaks, CA: Sage.

Monge, P. R., & Contractor, N. S. 2001. Emergence of commu-nication networks. In F. M. Jablin & L. L. Putnam (Eds.),

New handbook of organizational communication: 440–502. Thousand Oaks, CA: Sage.

Monge, P. R., & Contractor, N. 2003. Theories of communica-tion networks. New York: Oxford University Press.

Monge, P. R., & Eisenberg, E. M. 1987. Emergent communica-tion networks. In F. M. Jablin, L. L. Putnam, K. H. Roberts,& L. W. Porter (Eds.), Handbook of organizational com-munication: 304–342. Newbury Park, CA: Sage.

Monge, P. R., & Fulk, J. 1999. Communication technology forglobal network organizations. In G. DeSanctis & J. Fulk(Eds.), Shaping organizational form: Communication,connection, and community: 71–100. Thousand Oaks,CA: Sage.

Monge, P. R., Fulk, J., Kalman, M., Flanagin, A. J., Parnassa,C., & Rumsey, S. 1998. Production of collective action inalliance-based interorganizational communication andinformation systems. Organization Science, 9: 411–433.

Moreland, R. L. 1999. Transactive memory: Learning whoknows what in work groups and organizations. InL. Thompson, D. Messick, & J. Levine (Eds.), Sharingknowledge in organizations: 3–31. Mahwah, NJ: Law-rence Erlbaum Associates.

Nohria, N. 1992. Is a network perspective a useful way ofstudying organizations? In N. Nohria & R. G. Eccles(Eds.), Networks and organizations: Structure, form, andaction: 1–22. Boston: Harvard Business School Press.

O’Reilly, C. A., III. 1991. Organizational behavior. Wherewe’ve been, where we’re going. Annual Review of Psy-chology, 42: 427–458.

Pattison, P., & Robins, G. 2002. Neighborhood-based modelsfor social networks. Sociological Methodology, 32: 301–337.

Pattison, P., & Wasserman, S. 1999. Logit models and logisticregressions for social networks. II: Multivariate rela-tions. British Journal of Mathematical and StatisticalPsychology, 52: 169–193.

Pfeffer, J., & Salancik, G. 1978. The external control of orga-nizations. New York: Harper & Row.

Poole, M. S. 1999. Organizational challenges for the newforms. In G. DeSanctis & J. Fulk (Eds.), Shaping organi-zational form: Communication, connection, and commu-nity: 453–471. Thousand Oaks, CA: Sage.

Powell, W. W. 1990. Neither market nor hierarchy: Networkforms of organization. Research in Organizational Be-havior, 12: 295–336.

Richards, W. D., & Seary, A. J. 1997. Convergence analysis ofcommunication networks. In G. A. Barnett & L. Thayer(Eds.), Organizational communication: Emerging per-spectives. V: The renaissance in systems thinking: 141–189. Greenwich, CT: Ablex.

Robins, G., Elliott, P., & Pattison, P. 2001. Network models forsocial selection processes. Social Networks, 23: 1–30.

Robins, G., Pattison, P., & Wasserman, S. 1999. Logit modelsand logistic regressions for social networks. III: Valuedrelations. Psychometrika, 64: 371–394.

Rogers, E. M., & Kincaid, D. L. 1981. Communication networks:


Toward a new paradigm for research. New York: FreePress.

Seary, A. J., & Richards, W. D. 2001. Fitting to p* models inMultiNet. Connections, 23(1): 84–101. Also available athttp://www.sfu.ca/insna/Connections-Web/Volume23/23-1Seary/Seary-web.html.

Snijders, T. A. B. 2001. The statistical evaluation of socialnetwork dynamics. In M. E. Sobel & M. P. Becker (Eds.),Sociological methodology—2001: 361–395. Boston & Lon-don: Blackwell. Also available at http://stat.gamma.rug.nl/snijders/socnet.htm.

Snijders, T. A. B. 2002. Markov chain Monte Carlo estimationof exponential random graph models. Journal of SocialStructure, 3. Available at http://zeeb.library.cmu.edu:7850/JoSS/snijders/Mcpstar.pdf.

Stevenson, W. B., & Gilly, M. C. 1993. Problem-solving net-works in organizations: Intentional design and emer-gent structure. Social Science Research, 22: 92–113.

Stohl, C. 1993. European managers’ interpretations of partic-ipation: A semantic network analysis. Human Commu-nication Research, 20: 97–117.

Strauss, D., & Ikeda, M. 1990. Pseudolikelihood estimation forsocial networks. Journal of the American Statistical As-sociation, 85: 204–222.

Wasserman, S., & Faust, K. 1994. Social network analysis:Methods and applications. Cambridge: Cambridge Uni-versity Press.

Wasserman, S., & Pattison, P. 1996. Logit models and logisticregressions for social networks. I: An introduction toMarkov graphs and p*. Psychometrika, 60: 401–426.

Wasserman, S., & Robins, G. 2003. An introduction to randomgraphs, dependence graphs, and p*. In P. J. Carrington,J. Scott, & S. Wasserman (Eds.), Models and methods insocial network analysis: 148–161. New York: CambridgeUniversity Press.

Wegner, D. M. 1995. A computer network model of humantransactive memory. Social Cognition, 13: 319–339.

Wellman, B. 1988. Structural analysis: From method andmetaphor to theory and substance. In B. Wellman & S. D.Berkowitz (Eds.), Social structures: A network approach:19–61. Cambridge: Cambridge University Press.

Willer, D., & Skvoretz, J. 1997. Network connection and ex-change ratios: Theory, predictions, and experimentaltests. Advances in Group Processes, 14: 199–234.

Williamson, O. E. 1991. Comparative economic organization:The analysis of discrete structural alternatives. Admin-istrative Science Quarterly, 36: 269–296.

Noshir S. Contractor ([email protected]) is a professor in the Department of SpeechCommunication at the University of Illinois at Urbana Champaign and has appoint-ments in Psychology, Library & Information Science, and the Center for AdvancedStudy. He received his Ph.D. from the University of Southern California. His researchinvestigates factors that lead to the formation, maintenance, and dissolution of dy-namically linked knowledge networks.

Stanley Wasserman ([email protected]) is the Rudy Professor of Sociology, Psy-chology, and Statistics and has appointments in the Departments of Sociology, Psy-chological and Brain Sciences, and Statistics at Indiana University. He is also chiefscientist of Visible Path Corporation. He received his Ph.D. in statistics from HarvardUniversity. His research centers on applied statistics.

Katherine Faust ([email protected]) is on the faculty in the Sociology Department andthe Institute for Mathematical Behavioral Sciences at the University of California,Irvine. She received her Ph.D. from the University of California, Irvine. Her researchfocuses on methods for comparative social structural analysis and relationshipsbetween population processes and social network structure.


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