Who is collaborating with whom? Part I. Mathematical model and methods for empirical testing

There are two versions in the literature of counting co-author pairs. Whereas the first version leads to a two-dimensional (2-D) power function distribution; the other version shows three-dimensional (3-D) graphs, totally rotatable around and their shapes are visible in space from all possible points of view. As a result, these new 3-D computer graphs, called “Social Gestalts” deliver more comprehensive information about social network structures than simple 2-D power function distributions. The mathematical model of Social Gestalts and the corresponding methods for the 3-D visualization and animation of collaboration networks are presented in Part I of this paper. Fundamental findings in psychology/sociology and physics are used as a basis for the development of this model.