The Blackwell Companion to Sociology (74 page)

examples. Consider the diffusion of innovations. If accepting some new thing

depends on attributes such as how adventurous people are or how much atten-

tion they pay to the media, then an innovation moves steadily from the faster to the slower kinds of potential adopters. But if adoption is a social process, the pattern will be different. Adoption occurs when someone who has already taken

up the innovation influences someone who has not, so the rate of adoption varies with the number who have adopted times the number who have not yet done so.

Thus the rate of new adoption is slow at first (when there are few innovators to emulate) and at last (when almost everyone is on the bandwagon), while fastest

in the middle of the process (when many innovators still have many holdouts to

influence). Many examples of diffusion show the characteristic network profile,

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and many more refined details of adoption are rooted in network structure

(Valente, 1995).

As still another example, consider social vacancies (Chase, 1991). White had

the original theoretical insights while studying careers in a large church, for

which he had records of people and positions over a long time. He realized that

careers did not really consist of what people did, since a person could only move into a post after someone had moved out of it by promotion or retirement. What

really drove the system was the empty spaces in it: a vacancy in one post

attracted someone from another post, which then had a vacancy, and so forth,

with vacancies flowing through the organizational structure. Looking at the

flows of vacancies proved to be more informative than looking at the flows of

people. The freshness of this idea, and the elegance of the models that White

developed around it, have encouraged people to successfully apply them to quite

different examples from empty apartments to empty hermit crab shells.

Again, consider what people think. Some people try to explain this through

individual attributes, such as relating the politics of the wealthy to their desire to protect their interests. This approach constantly runs into trouble generalizing: the wealthy, women, white, or whatever keep having different views in different

times and places. Structural analysis by-passes such difficulties by making an

entirely different kind of generalization, not about what particular things people think but about how much people agree on whatever it is that they think

(Erickson, 1988). The more that people are very strongly tied to each other in

tight cliques with little outside influence, the more they agree. Their strong,

frequent interaction, and their shared awareness of what everyone else is think-

ing, leads to strong conformity pressures. Note that this argument is indifferent to the content of people's beliefs, which can be anything their particular history, culture, and so on have generated, and equally indifferent to the contents of

people's relationships, since social influence occurs in all kinds of networks. The argument is formal sociology in Simmel's sense: the abstracted form of ideas

(amount of agreement) depends on the abstracted form of the structure (degree

of density). This formal approach can be extended to other structural patterns;

for example, if people are not in a clique but are exposed to the influence of the same third parties, they will also tend to agree, but not so much, because of

the lack of direct mutual influence. Of course, ideas have effects on social

structure too, since people are drawn to those they agree with or those they

share knowledge with, and there are some interesting models of the dynamic

duet between interpersonal similarity and interpersonal attraction over time (for example, Carley, 1991).

If social structure is so important, it is important to know how to identify it, and important to realize that special approaches are needed. Broadly there are

two kinds of structural approaches: studying an entire network of all the ties of interest among the actors in some bounded setting (whole networks) or studying

the ties among all the people tied in some way to particular actors (actor-

centered approaches). For example, one might study ties of trade, diplomacy,

war, and so on among all the countries of the world, or one might randomly

survey people and ask them to report on their ties to their intimates. Whole

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network analysis is always best if feasible, because it gives the overall structure of the network as a whole as well as the limited network surrounding each

individual actor.

Starting with whole networks, then, what has to be done to study one? First

comes the sticky problem of boundaries. Networks naturally spread out, so no

boundary is ever perfect. For example, Florentine elite families sometimes mar-

ried and did business with families outside their group. Some boundaries are

defined by populations of special interest, like the Florentine elite. Some are

based on social definition of separate social entities, as in looking at all the ties of advice and friendship within a corporation. Some researchers start with one of

these approaches, track ties to any social actor (whether in the initially selected group or not), and then add any actors with many ties to the initially

selected group. Whatever the strategy, one hopes to find a set of actors with

relatively good separateness from the rest of the world, separateness in the

network sense: more ties within the set than between those in it and those

outside it.

Second, what ties should one study? The best overall strategy is variety:

friendship and enmity, business alliances and competition, trade, diplomacy,

and war. Different kinds of ties have different causes and effects, and it is all of them together that makes up social structure. All too often we skip negative

ties, in part because these can be a real challenge for research. People happily report whom they like, but when asked whom they dislike, insist that they dislike no one at all. When companies engage in illegal conspiracies, they do their best not to let researchers know.

Third, how can one make sense of all this information? People routinely store

their relational data in matrices: rows for actors 1 through N, columns for actors 1 through N, and cell entries recording the tie from the row actor to the column actor. For example, a cell might record the number of times that the row actor

sent the column actor e-mail last month, or whether the row nation sent an

armed force to the column nation last year. Usually the order of the rows and

columns is based on something meaningless like the order in which people were

interviewed, so the information is unorganized and looks like visual static.

Organization is imperative.

One popular, classic approach with a long history is to look for sets of actors

who are relatively closely tied to each other, the small groups within the bigger networks. We recognize such groups in everyday life: cliques in a high school,

business groups, political factions. And such groups can be important; for

example, in encouraging similarity of thought among group members, as noted

above. It would be easy to identify such groups if they were ideal-typical in some way ± for example if all people had friendship ties only within their cliques and hostile ties only with outsiders ± but social reality is just not that neat. Thus people have developed a number of ways to define groupings that are approximately cliques, in some modified sense of cliqueness. Different options have

different theoretical rationales and suit different research issues. For example, conformity pressures are strongest when clique members have many ties to each

other (hence are under each other's influence), so a student of attitudes might

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want to look for cliques in the sense of high density groups (density is the

proportion of all possible linkages that actually exists). But information can

flow among all members of a group as long as they are interconnected, directly

or indirectly, even if many possible ties are missing; while at the same time the quality of the information tends to deteriorate if it is passed on many times. Thus students of information flow might want to look for groups such that everyone

in the group can reach everyone else directly or through at most one intermedi-

ary. See Erickson (1988) for a more extended discussion of possible interpreta-

tions of group-finding strategies, and Wasserman and Faust (1994) for the

procedures.

The search for groups has great intuitive appeal for most people, but it cannot

handle some important features of social networks. First, some crucial parts of

social structures are not groups in any sense, such as marginal actors whose

defining (and crippling) characteristic is their lack of connections. Actors may have a common location in a structure without having ties to each other. Second, most structures include a variety of ties, each with a different pattern, yet the search for groups can handle only one tie at a time. For example, if we want

groups in the sense of maximum density, we can maximize density on only one

kind of tie; the maximum density groupings for other ties will normally be

different. One may be involved in one cluster of co-workers while discussing

work problems, and another while discussing sports. Problems like these fueled

interest in a more general kind of search: the search for sets of actors who occupy the same kind of position in an overall social structure. Concern shifts from how well actors are connected to each other, to how similarly they are connected to

everyone. The key idea is structural equivalence, or the extent to which actors

have the same kinds of ties to the same third parties. Structurally equivalent

actors share the same social location, the same position in all the relationships in a network. The Florentine elite provides examples of the important difference

between the two ways to define groupings of actors. If we are looking for clique-like groupings, supporters of the oligarchs qualify because they were all inter-

connected by marriage and business ties, while supporters of the Medici do not

because they had ties to the Medici but not each other. Yet both groupings were

socially recognized and important. Structural equivalence includes both, since

the Medici supporters were all in the same structural position of dependence

on the Medici.

Structural equivalence includes more than one kind of relationship at a time.

Consider a greatly simplified version of world systems theory. There are two

structural locations: core and periphery. Core nations trade with each other at

high rates, while periphery nations trade little with each other but a good deal with core nations. Core nations never send armed forces into each other's

territory, but sometimes send them into peripheral nations, which never dare

to return the favor but do occasionally invade each other. The same way of

defining structural location organizes both trade relationships and attacks, even though each of these has a different pattern. (There are more detailed accounts

of the world network, beginning with Snyder and Kick, 1979.) Once we identify

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are together, it is easy to see the nature of the overall structure by direct visual inspection. Computers do the hard work (see Wasserman and Faust, 1994, for

details). But people always have to make some tough judgment calls. How many

structural locations should there be, and how alike do actors have to be to be in the same position? At present we have no convincing answers to such questions.

Moreover, we have no joy for fans of statistical tests, since we build our models of structure from the same relational data that are all we have to test whether the model fits or not.

Analysis of whole network structure raises some intriguing questions that will

take a long time to answer. What is the morphology of social structures: what

kinds of structure are there? Some kinds of structure recur often in quite different settings; when and why? For example, a center±periphery structure has dense

ties among central actors, few ties among peripheral ones, and a moderate

number between more and less central actors. Trade among world nations is

one example; so is recognition among members of a scientific specialty. Why

does such a pattern occur sometimes but not at other times? Further, what

difference does it make? The difference may be for actors; for example, peri-

pheral actors may be too poorly connected to profit much from their trades or to be on top of current scientific trends. Or the difference may be for groups; for example, the social structure of a social movement helps to determine how

effectively it can mobilize its membership for action.

Analysis of whole network structure also raises the problem of responsible

portraiture. We always have a choice of ways to represent the overall structure of a network: in terms of cliques or in terms of structural locations; in terms either as determined by different methods, or as including more or fewer subdivisions;

and so on. There is never a single, obviously right choice, but a series of

judgments that call on the researcher's wider knowledge (does this version

make sense in light of what the people in this structure think it is, or in light of what I have observed, or in terms of what structural location it is correlated