Lotka's distribution and distribution of co-author pairs’ frequencies

Abstract

The original Lotka's Law refers to single scientist distribution, i.e. the frequency of authors A i with i publications per author is a function of i: A i = f( i). However, with increasing collaboration in science and in technology the study of the frequency of pairs or triples of co-authors is highly relevant. Starting with pair distribution well-ordered collaboration structures of co-author pairs will be presented, i.e. the frequency of co-author pairs N ij between authors with i publications per author and authors with j publications per author is a function of i and j: N ij = f( i, j) using the normal count procedure for counting i or j. We have assumed that the distribution of co-author pairs’ frequencies can be considered to be reflection of a social Gestalt and therefore can be described by the corresponding mathematical function based on well-known general characteristics of structures in interpersonal relations in social networks. We have shown that this model of social Gestalts can better explain the distribution of co-author pairs than by a simple bivariate function in analogy to Lotka's Law. This model is based on both the Gestalt theory and the old Chinese Yin/Yang theory.