On the structural form of human social groups : a social network perspective
Linton C. FREEMAN
In 1977, Winship demonstrated that if the social proximities linking a collection of individuals satisfy the properties of an ultrametric, then the social structure giving rise to those proximities is a nested hierarchy in which collections of actors overlap only by containment. Since this structural form corresponds very well to the traditional sociological conception of groups, it is important to assess the degree to which social proximities meet the requirements of an ultrametric. In 1992, Freeman showed that observed data on social proximities do not satisfy these requirements. Despite this failure, he conjectured that proximities in human groups tend toward satisfying the ultrametric requirements. The current paper proposes a stochastic model to address this question. Using the same data sets as the 1992 study, it is shown that the patterning of interaction comes close to the ultrametric form.