TRANSITIVITY IN STRUCTURAL MODELS OF SMALL GROUPS

Our purpose here is to show how various deterministic models for the structure of interpersonal relations in small groups may all be viewed as special cases of a single model: namely, a transitive graph (t-graph). This exercise serves three purposes. First, the unified approach renders much of the mathematical discussion surrounding these various models quite transparent. Many of the arguments boil down to nothing more than defining certain equivalence relations and looking at the resulting equivalence classes. Second, our focus on the general model may stimulate the search for other useful specializations besides those indicated here. We discuss two ways of specializing the model-restrictions on edges and