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 eluc idated, including regular colorings (White and Reitz 1983), automorphi c colorings (Everett 1985), and structural colorings (Lorrain and Whit e 1971). Regular colorings in particular have been seen as formalizati ons of the intuitive concept of social role. However, in this paper we suggest that regular colorings only incorporate one half of the intui tive role concept. The other half, which we formalize as ecological co lorings, is equally important. We therefore introduce perfect coloring s, which are both regular and ecological, and are consequently more co mplete models of the role concept. Perfect colorings have a number of interesting mathematical properties, which we describe briefly.