Who Is Collaborating with Whom in Science? Explanation of a Fundamental Principle

Hildrun Kretschmer,Theo Kretschmer

doi:10.4236/sn.2013.23011

Abstract

Since many decades power functions are well-known in counting single scientists or co-author pairs in social networks. However, in this paper a developed procedure for visualizing a bivariate distribution of co-author pairs’ frequencies hence producing three-dimensional graphs is presented. This distribution is explained by a fundamental principle of social group formation and described by a mathematical model. This model is applied to 52 co-authorship networks. For 96% of them the squared multiple R is larger than 0.98 and for 77% of the 52 networks even larger than 0.99. The visualized social Gestalts in form of three-dimensional graphs are rather identically with the corresponding empirical distributions. Question: Can we expect a general validity of this mathematical model for co-authorship networks?

Highlights

What does it mean: “Fundamental Principles of Social Group Formations?” There are both visible formations and non-visible
In this paper a developed procedure for visualizing a bivariate distribution of co-author pairs’ frequencies producing three-dimensional graphs is presented. This distribution is explained by a fundamental principle of social group formation and described by a mathematical model
For 96% of the 52 distributions the squared multiple R is larger than 0.98% and for 77% even equal or larger than 0.99

Summary

Introduction

What does it mean: “Fundamental Principles of Social Group Formations?” There are both visible formations and non-visible. The visualization of a special non-visible fundamental principle of social group formations in co-authorship networks is presented in our paper. In this connection a mathematical model for the intensity function of interpersonal attraction (Social Gestalt) will be explained. Group formations of fishes or birds are well-known. These kinds of group formations can be observed by our own eyes (cf Figures 1 and 2). The shapes of these group formations can be changed depending on the changing environment (cf Figure 2)

Methods

Results

Conclusion