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Mathematics LibreTexts

1.1: Introduction - What's different about social network data?

On one hand, there really isn't anything about social network data that is all that unusual. Social network analysts do use a specialized language for describing the structure and contents of the sets of observations that they use. But, network data can also be described and understood using the ideas and concepts of more familiar methods, like cross-sectional survey research.

On the other hand, the data sets that social network analysts develop usually end up looking quite different from the conventional rectangular data array so familiar to survey researchers and statistical analysts. The differences are quite important because they lead us to look at our data in a different way -- and even lead us to think differently about how to apply statistics.

"Conventional" social science data consist of a rectangular array of measurements. The rows of the array are the cases, or subjects, or observations. The columns consist of scores (quantitative or qualitative) on attributes, or variables, or measures. A simple example is shown as figure 1.1. Each cell of the array then describes the score of some actor (row) on some attribute (column). In some cases, there may be a third dimension to these arrays, representing panels of observations or multiple groups.

Figure 1.1. Example of rectangular data array
Name Sex Age In-Degree
Bob Male 32 2
Carol Female 27 1
Ted Male 29 1
Alice Female 28 3

The fundamental data structure is one that leads us to compare how actors are similar or dissimilar to each other across attributes (by comparing rows). Or, perhaps more commonly, we examine how variables are similar or dissimilar to each other in their distributions across actors (by comparing or correlating columns).

"Network" data (in their purest form) consist of a square array of measurements. The rows of the array are the cases, or subjects, or observations. The columns of the array are -- and note the key difference from conventional data -- the same set of cases, subjects, or observations. In each cell of the array describes a relationship between the actors. A simple example is shown as figure 1.2, which describes the network of friendship relations among four people.

Figure 1.2. Example of square array of network data

Who reports liking whom?

  Choice:      
Chooser: Bob Carol Ted Alice
Bob --- 0 1 1
Carol 1 --- 0 1
Ted 0 1 --- 1
Alice 1 0 0 ---

We could look at this data structure the same way as with attribute data. By comparing rows of the array, we can see which actors are similar to which other actors in whom they choose. By looking at the columns, we can see who is similar to whom in terms of being chosen by others. These are useful ways to look at the data, because they help us to see which actors have similar positions in the network. This is the first major emphasis of network analysis: seeing how actors are located or "embedded" in the overall network.

But a network analyst is also likely to look at the data structure in a second way -- holistically. The analyst might note that there are about equal numbers of ones and zeros in the matrix. This suggests that there is a moderate "density" of liking overall. The analyst might also compare the cells above and below the diagonal to see if there is reciprocity in choices (e.g. Bob chose Ted, did Ted choose Bob?). This is the second major emphasis of network analysis: seeing how the whole pattern of individual choices gives rise to more holistic patterns.

It is quite possible to think of the network data set in the same terms as "conventional data." One can think of the rows as simply a listing of cases, and the columns as attributes of each actor (i.e. the relations with other actors can be thought of as "attributes" of each actor). Indeed, many of the techniques used by network analysts (like calculating correlations and distances) are applied exactly the same way to network data as they would be to conventional data.

While it is possible to describe network data as just a special form of conventional data (and it is), network analysts look at the data in some rather fundamentally different ways. Rather than thinking about how an actor's ties with other actors describes the attributes of "ego," network analysts instead see a structure of connections, within which the actor is embedded. Actors are described by their relations, not by their attributes. And, the relations themselves are just as fundamental as the actors that they connect.

The major difference between conventional and network data is that conventional data focuses on actors and attributes; network data focus on actors and relations. The difference in emphasis is consequential for the choices that a researcher must make in deciding on research design, in conducting sampling, developing measurement, and handling the resulting data. It is not that the research tools used by network analysts are different from those of other social scientists (they mostly are not). But the special purposes and emphases of network research do call for some different considerations.

In this chapter, we will take a look at some of the issues that arise in design, sampling, and measurement for social network analysis. Our discussion will focus on the two parts of network data: nodes (or actors) and edges (or relations). We will try to show some of the ways in which network data are similar to, and different from more familiar actor by attribute data. We will introduce some new terminology that makes it easier to describe the special features of network data. Lastly, we will briefly discuss how the differences between network and actor-attribute data are consequential for the application of statistical tools.