Biased networks and social structure theorems: Part II

It was shown in a previous paper (Fararo 1981) that the part of Peter Blau's theory of social structure bearing on heterogeneity could be embedded within the framework of biased net models, providing a conceptual and mathematical basis for its central theorems. This paper continues this project. It begins by indicating certain revisions of the earlier work and then turns to the part of Blau's theory that deals with inequality and shows how the simplest inbreeding bias model, through a series of derivations and constructive generalizations, permits the derivation of basic theorems that relate the Gini inequality (of a population) to what we term the relational Gini (of a network). The central idea is to construct theoretical models that yield specific forms of transformation of the population Gini into the relational Gini.