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Mathematics LibreTexts

17.1: Introduction to Two-Mode Networks


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For a classic study of the American south (Deep South, University of Chicago Press, 1941), Davis and his colleagues collected data on which of 18 women were present at each of the 14 events of the "social season" in a community. By examining patterns of which women are present (or absent) at which events, it is possible to infer an underlying pattern of social ties, factions, and groupings among the women. At the same time, by examining which women were present at the 14 events, it is possible to infer underlying patterns in the similarity of the events.

The Davis study is an example of what Rom Breiger (1974) called "The duality of persons and groups". Breiger is calling attention to the dual focus of social network analysis on how individuals, by their agency, create social structures while, at the same time, social structures develop an institutionalized reality that constrains and shapes the behavior of the individuals embedded in them.

The data used for social network analysis, most commonly, measure relations at the micro level, and use analysis techniques to infer the presence of social structure at the macro level. For example, we examine the ties of individuals (micro) for patterns that allow us to infer macro structure (i.e. cliques).

The Davis data is a bit different. It describes ties between two sets of nodes at two different levels of analysis. The ties that Davis identifies are between actors (the women) and events (the parties of the social season). Data like these involve two levels of analysis (or two "modes"). Often, such data are termed "affiliation" data because they describe which actors are affiliated with (present, or members of) which macro structures.

Two-mode data offer some very interesting analytic possibilities for gaining greater understanding of "macro-micro" relations. In the Davis data, for example, we can see how the choices of the individual women "make" the meaning of the parties by choosing to attend or not. We can also see how the parties, as macro structures, may affect the choices of the individual women.

With a little creativity, you can begin to see examples of these kinds of two-mode, or macro-micro social structures everywhere. The social world is one of "nesting" in which individuals (and larger structures) are embedded in larger structures (and larger structures are embedded in still larger ones). Indeed, the analysis of the tension between "structure and agency" or "macro and micro" is one of the core themes in sociological theory and analysis.

In this chapter we will take a look at some of the tools that have been applied (and, in some cases, developed) by social network analysts for examining two-mode data. We begin with a discussion of data structures, proceed to visualization, and then turn our attention to techniques for identifying quantitative and qualitative patterns in two-mode data.

For most of the examples in this chapter we will use a new 2-mode dataset from a problem that I happen to be working on in parallel with this chapter. The data describe the contributions of a small number of large donors (those who gave a total of at least $1,000,000) to campaigns supporting and opposing ballot initiatives in California during the period 2000 to 2004. We've included 44 of the initiatives. The dataset has two modes: donors and initiatives.

We will use two different forms of the data - one valued and one binary. The valued data describe the relations between donors and initiatives using a simple ordinal scale. An actor is coded as -1 if they gave a contribution opposing a particular initiative, 0 if they did not contribute, and +1 if they contributed in support of the initiative. The binary data describe whether a donor did (+1) or did not (0) contribute in the campaign on each initiative.