Biased networks and social structure theorems

It is shown that the part of Peter Blau's theory of social structure bearing on heterogeneity can be imbedded within the framework of biased networks, thereby clarifying conceptual aspects of the theory as well as providing a mathematical proof of the most central heterogeneity theorem for a class of networks. The key step is the postulation of a mathematical concept of salience, called an ‘inbreeding bias’ in prior work, which corresponds to Blau's fundamental axiom. In addition, there are derivations and discussions bearing on related topics in the analysis of social structure.