On Network Theory - Borgatti and Halgin (2011) - Article

Introduction

Social network analysis (SNA) is currently popular and increasingly exponential over time, as shown in figure 1 (p. 1169). Despite the popularity, there exists considerable confusion about network theorizing. The objectives of this paper are to clarify the concept of social network and to begin to identify the characteristic elements of social network theorizing. It is important to emphasize that the objective is not to define what should and should not be network theory. It should also be noted that SNA theorizing encompasses two (analytically) distinct domains, which is referred to as “network theory” proper and “theory of networks”. Network theory refers to the mechanisms and processes that interact with network structures to yield certain outcomes for individuals and groups. Theory of networks refers to the processes that determine why networks have the structures they do. In this paper, the focus is on proper network theory.

What is a network?

A network consists of a set of actors or nodes along with a set of ties of a specified type that link them. The ties interconnect through shared end points to form paths that indirectly link nodes that are not directly tied. The pattern of ties in a network yields a particular structure, and nodes occupy positions within this structure. The researcher defines a network. The choice of which nodes to include should not be regarded as an empirical question, but rather it should be dictated by the research question and one’s explanatory theory. Part of the angst involved in the boundary specification problem is due to confusing networks with “groups”. Groups have a natural existence of boundaries. Networks do not have “natural” boundaries. Networks also do not have to be connected. A disconnected network is one in which some nodes cannot reach certain others by any path, meaning that the network is divided into fragments known as components (see fig. 2, p. 1169). By allowing the network to be disconnected, the evolution of connectivity within it can be traced. So, we do not ask “under which circumstances network will emerge”, but rather “how specific properties of the network change over time”.

A closely related issue is what “counts” as a tie. The realist position would state that there is a “true” network of relationships out there, and the job of researchers is to discover it. Given this assumption, it is reasonable to ask which social network questions have proven effective at eliciting this network. However, the nominalist position holds that every network question generates its own network, and which to use is determined by the research question.

In practice, the kinds of ties that network theorists’ focus on can be categorized into two basic types: states and events (see table 1, p. 1170). States have continuity over time, so they have an open-ended persistence. They can be dimensionalized in terms of strength, intensity and duration. In contrast, an event-type tie has a discrete and transitory nature and can be counted over periods of time. Cumulated over time, event-type ties can be dimensionalized in terms of frequency of occurrence. When networks are defined as a recurring pattern of ties, it are these kinds of ties that researchers have in mind.

Both types can be seen as roads or pipes that enable (and constrain) some kind of flow between nodes. Flows are what actually pass between nodes as they interact, such as ideas or goods.

In empirical studies, researchers often make use of relational states and events that are not, properly speaking, social ties.

Network theorizing

Granovetter’s (1973) strength of network ties (SWT) theory is organized as a set of explicit premises and conclusions. The first premise is that the stronger the tie between two people, the more likely their social worlds will overlap, so that they have ties with the same third parties: if A and B and B and C have a strong tie, A and C have an increased change of having at least a weak tie (e.g., A and C are acquaintances). This is a kind of transitivity, and arises from homophily, meaning that people tend to have stronger ties with people who are similar to themselves. The second premise is that bridging ties are a potential source of novel ideas. A bridging tie is a tie that links a person to someone who is not connected to his or her other friends. Through a bridging tie, a person can hear things that are not already circulating among his close friends. In fig. 3 (p. 1171), A’s tie with G is a bridging tie.

Putting the two premises together, Granovetter reasons that strong ties are unlikely to be sources of novel information, because bridging ties are unlikely to be strong and because these bridging ties are the sources of novel information, it is the weak ties that are the best potential sources of novel information.

Another well-known theory is Burt’s (1992) structural holes theory (SH) of social capital. This theory is concerned with ego networks – the cloud of nodes surrounding a given node, along with all the ties among them. Burt argues that if we compare nodes A and B in fig. 3, the shape of A’s network is likely to afford A more novel information than B’s ego network, and as a result that A may perform better in a given setting. Both have the same number of ties, and we can stipulate that their ties are of the same strength. However, because B’s contacts are connected with each other, the information B gets from say X may well be the same information that he gets from Y. In contrast, A’s ties connect to three different pools of information (represented by the circles in fig. 4, p. 1171). As a result, A is likely to receive more non-redundant information at any given time than B.

Kilduff (2010) argues that the theories are significantly different from each other. Granovetter embraces a serendipitous world in which people only form ties incidentally prove useful, whereas Burt embraces a more strategic and instrumental view. However, it should be obvious that the theories are closely related; the concept is the same and so are the consequences: more novel information. The difference between the theorists is preferring the distal cause (strength of ties) as Granovetter does, or the proximal cause (bridging ties), as Burt does. In addition, Granovetter uses getting jobs as an outcome of having non-redundant information, whereas Burt uses getting promoted.

Characterizing network theory

There are two features of network theory that are highly characteristic if we look at SWT and SH. First, the twin notions of structure and position play fundamental roles. The general agenda of examining the consequences of network structure includes the examination of how structure and attributes interact to yield outcomes. But a piece of that investigation is the exploration of how structural differences alone have effects. Second, there is an implicit theory of network function; the network function is the flow or distribution of information. In effect, SWT and SH rely on an underlying model of a social system as a network of paths that act as conduits for information to flow: the flow or pipes model. Theoretical propositions from this model are for instance that nodes that are far from all others will, on average, receive flows later than nodes that are more centrally positioned and nodes that are embedded in locally dense parts of a network will often receive the same bits of flow from their various contacts, because the contacts are tied to each other as well.

For the flow model, different variations for how flows move through the network can be specified. For example, a dollar bill can never be in two places at the same time, while a virus duplicates itself when A passes it to B, so A retains a copy. Another example is the difference between a true path (you can only pass a node one time) and a trail (information can pass a node several times). A dollar bill illustrates a walk, which is unrestricted with respect to whether it reuses nodes or ties. Hypotheses that are actually tested in empirical studies relate to features of the observed network to outcomes such as performance in an organizational setting, and network theory consists of elaborating how a given network structure interacts with a given process to generate outcomes for the nodes or the network as a whole.

Another model of network theory studies power. After playing a game in which subjects had to make as many deals at the best possible terms as possible, Cook and Emerson (1978) found that the subject in position B was able to negotiate the best deals, even though subjects were not shown the structure of the network they were embedded in. The fundamental advantage that B enjoys is the independency of others. This positional advantage is very different from the concept of centrality, which largely emerges from the flow model. This can be seen in figure 6 , in which B and D emerge as high-power positions and A, C and E have very low power. C’s partners B and D both have better alternatives to C; the wholly dependent A and E. Thus, being connected to weak others makes one powerful, and being connected to powerful others make one weak. This differs from centrality, where being connected to well connected other implies greater centrality.

Another way to look at network power is in terms of coordination and virtual amalgamation. The principle behind unionization is shown in figure 7 and 8. In fig. 7, E has a strong position because the As are not working together, where in fig. 8 E has a less good negotiating position, because the As are converted into a single node that can deal with E on an equal basis: a mechanism of virtual amalgamation. By working together, they can accomplish more than they could alone.

This phenomenon is known as virtual capitalization, meaning that the bonds between the nodes enable the nodes to act as if they were transferring the capabilities of the other nodes to each other, but without actually doing so. The bonding function serves as the basis for the bond or coordination model.

An interesting question is whether the work on experimental exchange networks can be derived from the bond model. There is a point of commonality, which is that when a pair of nodes makes a deal in a given round, the nodes become, momentarily, a unit that excludes those not part of the deal. From this perspective, a node’s advantage derives from its inexcludability (see B and D in fig. 6). In the bond model, paths of an even length emanating from a node reduce its power, whereas paths of an odd length increase its power. Another derivation from the bond model is that isomorphic nodes will have similar outcomes even if they are not reachable from each other. For example, in figure 9, A and H are structurally isomorphic and therefore must have the same structural advantages and disadvantages. Another thing to note about network theory is that the network is not only a sociological construct, but also a mathematical object.

Goals of network theorizing

There are two generic types of outcomes that network research has sought to explain. The first is choice, and includes behaviours, attitudes, beliefs, and internal structural characteristics. The work in this area is often referred to as the social homogeneity literature. The second generic outcome is success, which includes performance and rewards, whether at the node or whole network level. Work in this area is known as the social capital literature. Combining the generic outcomes with the explanatory models, we get a simple typology of network theorizing. As shown in table 2, the top right quadrant, contagion, consists of flow-based explanations of choice. Diffusion is one reason that organizations have similar structures. The locus of agency can be used to distinguish four different types of diffusion, as shown in table 3.

Mimetic processes: the adopter actively seeks to copy a trait from a node in its environment. Coercive processes: the node is forced by a node in its environment to adopt a train. Apprentice processes: both the ego and its environment are actively trying to help the ego get what the alter has. Osmotic processes: neither party is actively expending energy to enable the transfer, but it happens anyway.

The bottom right quadrant of table 2, convergence, contains bond-based explanations of homogeneity and structural equivalence, which posits that nodes adapt to their environments, and as a result nodes with similar structural environments will demonstrate similarities. The top left quadrant, capitalization, contains flow-based explanations of achievement. The basic concept here is that social position in a network provides access to resources. Finally, the bottom left quadrant, cooperation, consists of bond-based explanations of achievement. Here, combinations of nodes act as a unit, excluding others and exploiting divisions among them.

Discussion

Model-based theorizing

In this paper, it is argued that at least some portions of the network theory can be described as model-based theorizing, and two fundamental models that underlie extant network theorizing have been outlined: the flow and bond models. In model-based theorizing, an observed state of affairs as the outcome of an unseen process can be imagined, which is what the model specifies. Given the model, you can derive testable implications. The implications are used to test the theory as well as to apply the theory to new situations.

One feature of model-based theorizing is the separation between the abstract elements of the model and the mapping of those elements to the real world. Object-oriented computer programming (OOP) can help to point the way toward dealing with issues of context and culture. Theory should be build at the level of abstract ties that have certain properties needed by the theory, instead of a particular definition of a tie (e.g., a friendship). This analogy also helps clarify the question of whether we can apply the same network theories to collective and/or non-human actors – such as firms – as we do to actors that are individual persons.

Endogeneity

In this paper, network theory has been separated from theory of networks. However, there are some concerns about the separation. First, it can be questioned if the distinction is “merely” analytical, because it might be expected that, in reality, the two kinds of processes occur together. Second, there is the concern that we cannot correctly predict outcomes of network structure if we have not taken account of how the network got there. Third, there is the question of endogeneity: factors causing the outcome in some part are dependent on the outcome. Finally, the issue of agency: if actors deliberately shape the networks around them for their benefit, can it really be said that it was network structure that led to the benefit?

To begin the discussion, let’s make clear that the consequences of network processes can include other network phenomena, in which case network theory is simultaneously theory of networks, which is to say we have a network theory of networks (see table 4). In a network theory of networks, both independent and dependent variables involve network properties. However, on closer inspection of whether network theory must include theory of networks, the answer seems to be “no”. If a model has been constructed that embodies the mechanisms that convert a given set of inputs at time T to an output at T + 1, then given that input, nothing else is needed to explain the outcome. In practice, however, it is a little more complicated.

It should be noted that the ability to theorize about consequences of networks independently of antecedents does not absolve the field from resolving issues of endogeneity in a given empirical inquiry. In every field study, we must be concerned about whether A causes B, or the other way around, or whether both are caused by an uncontrolled third variable.

Finally, the issue of agency: any theory of social networks must take into account actors’ agency in creating those networks, but the problem with this is that it is not the actors intentions and actions leading to occupying a certain position that creates the outcome, but the actual occupation of the position. Given the same conditions, the outcomes are the same. However, node attributes and contextual factors in network research are important.