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In this chapter we will examine how relaxing this assumption has enabled structural analysts to open this area to rigorous analysis in ways which have called into question some of the conventional literature. , an adult male, an adult female, and their children) to the exclusion of other aspects of kinship systems. , nurturance, socialization), and with a form of methodological individualism in which actors create a 2: Kin, Friends, and Community 27 stage upon which they act out a series of sociodramas based upon generalized conscious and unconscious motives and interests.

14 Source: Harrison C. White, An Anatomy of Kinship © 1963, p. 8. J. " The directions given by the arrowheads indicate possible role compounds. Note that cyclic or repetitive role sequences are possible, for example, FWFWFW. The upwardly looping and downwardly looping arrows defined onto the father (F) and son (S) roles indicate possible paths between generations—for example, FF = ego's grandfather. 43 Individuals would have a great deal of difficulty navigating in societies in which kinship is seen as the focal aspect of social order, White continues, unless some principle existed for creating classes of equivalent relations.

Simple visual inspection of these graphs, however, can be deceptive: network B is far less dense than it appears to be at first sight. By creating a formal density measure, as this example indicates, structural analysts were able to significantly improve upon the more intuitive notions of "dense" and "sparse" patterns of interaction which had been common before it was introduced. KIN AND COMMUNITY AS SYSTEMS While each of these properties of graphs and their associated matrices—reachability and compactness, duality, and density—had clear implications for studies of networks of interpersonal ties, social scientists, as a whole, were relatively slow to adopt them for use in empirical work.

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