ECOLOGICAL AND PERFECT COLORINGS

A recent study (Hummon and Carley 1992) has indicated that one of the main research paths in the discipline of social networks is the study of roles and positions. Several key positional concepts have been elucidated, including regular colorings (White and Reitz 1983), automorphic colorings (Everett 1985), and structural colorings (Lorrain and White 1971). Regular colorings in particular have been seen as formalizations of the intuitive concept of social role. However, in this paper we suggest that regular colorings only incorporate one half of the intuitive role concept. The other half, which we formalize as ecological colorings, is equally important. We therefore introduce perfect colorings, which are both regular and ecological, and are consequently more complete models of the role concept. Perfect colorings have a number of interesting mathematical properties, which we describe briefly.