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Mathematics LibreTexts

8.1: Introduction

  • Page ID
    7693
  • [ "article:topic", "authorname:rhanneman" ]

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    In the previous chapter we looked at some tools for examining the ways that individuals are connected, and the distances between them. In this chapter we will look at the same issue of connection. This time, though, our focus is the social structure, rather than the individual. That is, we will adopt a more "macro" perspective that focuses on the structures within which individual actors are embedded.

    The "top down" perspective we'll follow in this chapter seeks to understand and describe whole populations by the "texture" of the relations that constrain its individual members. Imagine one society in which extended kin groups live in separate villages at considerable distances from one another. Most "texture" of the society will be one in which individuals have strong ties to relatively small numbers of others in local "clusters". Compare this to a society where a large portion of the population lives in a single large city. Here, the "texture" of social relations is quite different - individuals may be embedded in smaller nuclear families of mating relations, but have diverse ties to neighbors, friends, coworkers, and others.

    Social network analysts have developed a number of tools for conceptualizing and indexing the variations in the kinds of structures that characterize populations. In this chapter, we'll examine a few of these tools.

    The smallest social structure in which an individual can be embedded is a dyad (that is, a pair of actors). For binary ties (present or absent), there are two possibilities for each pair in the population - either they have a tie, or they don't. We can characterize the whole population in terms of the prevalence of these dyadic "structures". This is what the density measure does.

    If we are considering a directed relation (A might like B, but B might not like A), there are three kinds of dyands (no tie, one likes the other but not vice versa, or both like the other). The extent to which a population is characterized by "reciprocated" ties (those where each directs a tie to the other) may tell us about the degree of cohesion, trust, and social capital that is present.

    The smallest social structure that has the true character of a "society" is the triad - any "triple" {A, B, C} of actors. Such a structure "embeds" dyadic relations in a structure where "other" is present along with "ego" and "alter". The analysis of triads, and the prevalence of different types of triads in populations has been a staple of sociometry and social network analysis. In (directed) triads, we can see the emergence of tendencies toward equilibrium and consistency - institutionalization - of social structures (balance and transitivity). Triads are also the simplest structures in which we can see the emergence of hierarchy.

    Most of the time, most people interact with a fairly small set of others, many of whom know one another. The extent of local "clustering" in populations can be quite informative about the texture of everyday life. Actors are also embedded in "categorical social units" or "sub-populations" defined either by shared attributes or shared membership. The extent to which these sub-populations are open or closed - the extent to which most individuals have most of their ties within the boundaries of these groups - may be a telling dimension of social structure.

    There are many approaches to characterizing the extent and form of "embedding" of actors in populations. There is no one "right" way of indexing the degree of embedding in a population that will be effective for all analytic purposes. There are, however, some very interesting and often useful approaches that you may wish to explore.