How To Close a Hole: Exploring Alternative Closure Mechanisms in Interorganizational Networks

Alessandro Lomi and Francesca Pallotti

Mechanisms of Network Closure

One way to think about social networks is as social structures built from the bottom up through combinations of simpler components defined in terms of local configurations of ties, or “motifs” (Milo et al., 2002; Pattison & Robins, 2002). Local configurations of network ties may be interpreted as observable outcomes of specific social mechanisms such as reciprocity. Because organizations display a strong tendency toward forming ties with their partner’s partners, processes of tie maintenance and formation based on closure mechanisms have been of particular interest to scholars of interorganizational networks (Gulati & Gargiulo, 1999; Hallen, 2008; Laumann & Marsden, 1982; Lomi & Pattison, 2006). Closure has been found to shape the formation and maintenance of network ties between organizations operating in a variety of empirical settings ranging from manufacturing relations in the automotive industry (Lomi & Pattison, 2006), to strategic alliances in various industrial sectors (Gulati & Gargiulo, 1999), to equity relations between organizations belongingto thesame “keiretsu” (Lincoln, Gerlach, & Ahmadjian, 1996). The accumulation of empirical experiences in the study of interorganizational relations has given shape to the general expectation that partners of partners are (more likely to be) partners. What social mechanisms may be underlying such expectations?

In theoretical terms, the tendency toward transitive closure in interorganizational networks has been framed and interpreted as the direct

We gratefully acknowledge the financial support provided by the Schweizerische National- fonds (Swiss National Science Foundation Grant No. 124537). We thank the participants to the Quantitative Methods in the Social Sciences 2 (QMSS2) seminar “Networks, Markets and Organizations,” August 27-29, 2009, University of Groningen, for comments and discussion.

consequence of the costs and risks inherent in the formation and maintenance of network ties with partners whose quality, capability, and trustworthiness are only imperfectly observable (Baum et al., 2005; Sorenson & Stuart, 2008). To manage these different sources of uncertainty and reduce the exposure to opportunistic behavior of potential partners, organizations tend to form new ties with their partners’ partners based on referrals and shared information (Baker, 1990; Uzzi, 1996). Ties to common third parties also promote adherence to norms by promoting trust and by facilitating social monitoring and sanctioning of opportunistic behavior (Burt & Knez, 1995; Rousseau et al., 1998). In fact, fundamental third-party effects such as reputation and status affect the formation of network ties precisely because direct information about the quality of potential partners is not easily available (Gulati & Gargiulo, 1999; Podolny, 2001). As Coleman succinctly put it: “reputation cannot arise in an open structure” (1988, S107).

In analytical terms, the tendency toward network closure may be interpreted as the “outcome” of path-shortening behavior whereby indirect connectivity between organizations in the form of (possibly multiple) 2-paths leads to a direct tie. This particular type of path closure is represented graphically in Figure 15.1a, and discussed in greater detail in Snijders et al. (2006) and Robins et al. (2009). The configurations in Figure 15.1 are presented in Chapter 6.

The configuration of local network ties in Figure 15.1a embodies the expectation that “partners of my partner are my partners.” This specific closure mechanism, perhaps the most commonly encountered mechanism in studies of interorganizational networks, is described by Uzzi as resulting from the fact that “[expectations of trust and reciprocity between two economic actors could be ‘rolled over’ to a new third party, thereby establishing trust and reciprocal obligations between two parties that lacked a prior history of exchange” (1996, 490).

Mechanisms of “expectations rollover” are perfectly capable of producing direct ties between indirectly connected partners, but other possible mechanisms exist that may be responsible for closure in interorganizational networks. Although sketched by Laumann and Marsden (1982), to the best of our knowledge, these mechanisms have not been examined systematically in contemporary studies of interorganizational networks.

Two organizations may come to form a tie because they are both related in the same way to the same other. This may be viewed as a kind of structural homophily, whereby similarity in choice leads to the formation or maintenance of network ties (DiMaggio, 1986). As noted in Chapter 6, this mechanism is called “activity closure” and is represented in Figure 15.1b. Activity closure can be interpreted as structural equivalence in outgoing ties, or the outcome of joint dependence on common resources, information, and knowledge, or, possibly, of shared capacity

204 Exponential Random Graph Models for Social Networks

Local configurations of network ties representing different closure mechanisms

Figure 15.1. Local configurations of network ties representing different closure mechanisms: (a) path closure, (b) activity closure, (c) popularity closure, and (d) cyclic closure.

constraints. A clear example in which this interpretation is appropriate is offered by the study of technological innovation in interorganizational communities within which “common dependence on technological antecedents indicates substitutability and thus a competitive relation between two organizations” (Podolny, Stuart, & Hannan, 1996, 667). Of course, the extent to which common dependence on technological (or any other) resources generates competition rather than relational coordination remains an open empirical issue (Bothner, 2003). Depending on the specific relational context, a positive estimate of activity closure may indicate a general tendency toward cooperation among potential competitors.

Organizations may form a tie not only because they choose the same others as partners, or because they depend on resources controlled by the same others, but also because they are chosen as exchange partners by the same others. This situation is depicted in Figure 15.1c, and the corresponding mechanism is called “popularity closure.” To the extent that the unreciprocated flow of activity (or relations) received may be interpreted as a signal of deference, this particular closure mechanism is relevant to studies of status homophily because “status (direct ties) provides strong signals of quality” (Podolny et al., 1996, 669). This interpretation seems to be particularly apposite when the qualities of potential partners are difficult to ascertain - a situation in which status is typically interpreted as a signal of quality (Podolny, 1994). A positive estimate of the popularity closure parameter would provide some evidence that status homophily is an important uncertainty reduction mechanism underlying the selection of network partners.

A fourth distinct closure mechanism is based on generalized exchange, a triadic pattern of network ties that does not involve immediate needs for reciprocation (Bearman, 1997). Generalized exchange defines a situation in which “the recipient of benefit does not return benefit directly to the giver, but to another actor in the social circle. The giver eventually receives some benefit in return, but from a different actor” (Molm, Collet, & Schaefer, 2007, 207-208). In other words, in a system of generalized exchange, participants have to be “givers” before they may become “receivers.” Generalized exchange is associated with the cyclic closure configuration of network ties depicted in Figure 15.1d. It plays an important coordination role in interorganizational networks because “any particular exchange or transfer of resources occurs in a context of other exchanges and transfers, and regularities in patterns of exchange involving more than two members provide one possible means by which particular exchanges are integrated into a wider collaborative effort” (Lazega & Pattison, 1999, 68). A positive estimate of the cyclic closure parameter would be consistent with the presence of diffuse cooperation or, perhaps, “organic” solidarity among members of an interorganizational community (Ekeh, 1974).

In summary, triadic closure may result as an “outcome” of alternative mechanisms, but each mechanism implies that network ties arise for different reasons, and that they have different implications and interpretations. As explained in Chapter 6, exponential random graph models for directed social networks permit specification and empirical identification of these alternative closure mechanisms.

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