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. The application of these new methods to male and to female networks is shown in Part II. After regression analysis the visualized Social Gestalts are rather identical with the corresponding empirical distributions (R 2 >0.99). The structures of female co-authorship networks differ markedly from the structures of the male co-authorship networks. For female co-author pairs’ networks, accentuation of productivity dissimilarities of the pairs is becoming visible but on the contrary, for male co-author pairs’ networks, accentuation of productivity similarities of the pairs is expressed. 
Who is collaborating with whom? Part I. Mathematical model and methods for empirical testing