Positional analyses of sociometric data
One of the major goals of social network analysis is to discern fundamental structure(s) of networks in ways that: (i) allow us to know these structures and (ii) facilitate our understanding of network phenomena. One of the most used tools for doing this is blockmodeling, a collection of methods for partitioning networks according to well specified criteria. Initially, we use the term ‘blockmodeling’ for ‘conventional blockmodeling’ to characterize the usual approach to blockmodeling, one based on the concepts of structural equivalence (Lorrain and White, 1971) and regular equivalence (White and Reitz, 1983)1. Our intent here is to use an optimizational approach to blockmodeling to generalize blockmodeling to consider indefinitely many types of blockmodels. See Batagelj et al. (1992a,b) for an account of optimizational methods applied to blockmodeling, Doreian et al., (1994) for the extension to generalized blockmodeling, and Batagelj et al., (1998) for pre-specified blockmodeling. Integral to this approach is the use of a built-in measure of the adequacy of the fit of a blockmodel.