Theo Kretschmer

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

The original Lotkas Law refers to single scientist distribution, i.e. the frequency of authors Ai with i publications per author is a function of i: Ai=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 Nij between authors with i publications per author and authors with j publications per author is a function of i and j: Nij=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 Lotkas Law. This model is based on both the Gestalt theory and the old Chinese Yin/Yang theory.

Gender bias in journals of gender studies

The causes of gender bias favoring men in scientific and scholarly systems are complex and related to overall gender relationships in most of the countries of the world. An as yet unanswered question is whether in research publication gender bias is equally distributed over scientific disciplines and fields or if that bias reflects a closer relation to the subject matter. We expected less gender bias with respect to subject matter, and so analysed 14 journals of gender studies using several methods and indicators. The results confirm our expectation: the very high position of women in co-operation is striking; female scientists are relatively overrepresented as first authors in articles. Collaboration behaviour in gender studies differs from that of authors in PNAS. The pattern of gender studies reflects associations between authors of different productivity, or “masters” and “apprentices” but the PNAS pattern reflects associations between authors of roughly the same productivity, or “peers”. It would be interesting to extend the analysis of these three-dimensional collaboration patterns further, to see whether a similar characterization holds, what it might imply about the patterns of authorship in different areas, what those patterns might imply about the role of collaboration, and whether there are differences between females and males in collaboration patterns.

A New Centrality Measure for Social Network Analysis Applicable to Bibliometric and Webometric Data

A fairly large number of publications in sociology, in computer science or in information sciences, as well as in studies of collaboration in science deal with the studies of social networks with unweighted ties because measures involving unweighted ties are easier to calculate. A few studies on networks with weighted ties have been conducted. Such studies not only need more complex formulas but also a process of quantification specially when quantitative empirical data are not directly available. The later are, however, directly available under the condition of using bibliometric or webometric data. Consequently, new complex measures of the degree centrality are introduced including weighted ties possible for use of the analysis of co-authorship or citation networks. Both co-authorship relations and citations are well-quantified data (weighted ties).

Co-authorship pair distribution patterns by gender

This paper examines impact of gender both on publication productivity and on patterns of scientific collaborations in social sciences in Turkey. The research is based on bibliographic data on national level publications in Turkey. It consists of 7,835 papers written by 6,738 scientists. The findings suggest that (1) there are gender differences at publication productivity, participation, presence and contribution; that (2) there are significantly different tendencies at keeping established co-authorship ties for inter-gender and intra-gender pairs; that (3) there are significant regularities exhibited by coauthor pairs based on each partner author’s publication productivity and findings further show that (4) regularities are different for inter-gender and intra-gender co-authorships. This study contributes to literature by exemplifying an integrated approach to better examine role of gender in scientific collaborations. In addition to descriptive social network analysis methods, it exploits and adopts parametric models from the literature: (1) Social Gestalt theory, a model based on bi-variate distributions of co-author pairs’ frequencies; (2) Lotka’s power law distribution on publication productivity of single authors; (3) Power law distributions of co-author pairs’ frequencies.

Reflection of co-authorship networks in the Web: Web hyperlinks versus Web visibility rates

About ten years ago a new research field called “webometrics” emerged. Similarities between methods used in webometrics and scientometrics or informetrics are evident from the literature. Are there also similarities between scientometric and Web indicators of collaboration for possible use in technology policy making? Usually, the bibliometric method used to study collaboration is the investigation of co-authorships.In this paper, Web hyperlinks and Web visibility indicators are examined to establish their usefulness as indicators of collaboration and to explore whether similarities exist between Web-based structures and bibliographic structures.Three empirical studies of collaboration between institutions and individual scientists show that hyperlink structures at the Web don’t reflect collaboration structures collected by bibliographic data. However Web visibility indicators of collaboration are different from hyperlinks and can be successfully used as Web indicators of collaboration.

Studies in Co-authorship Pairs Distribution: Part-2: Co-author pairs’ frequencies distribution in journals of gender studies

Previous studies have presented well-ordered collaboration structures of co-author pairs. Kretschmer and Kretschmer have shown that, for high impact SCI journals, the distributions of co-author pairs’ frequencies can be considered to be a reflection of a social Gestalt. This study is an extension of that work to the social sciences, namely eleven journals in women’s and gender studies. After overlapping or mixing the eleven distributions of co-author pairs, the data reveal the same tendency to a social Gestalt. However the shapes of social Gestalts for gender studies differs markedly from the corresponding shapes of the high impact SCI Journals. Simulation shows that the change of the shape from the Gestalt of the mixed journals of gender studies towards the shape of the four mixed SCI journals could be continuous.

Application of a New Centrality Measure for Social Network Analysis to Bibliometric and Webometric Data

There is a rapid increase of network analysis in several scientific disciplines beginning some decades ago. In the literature there are few studies on networks with weighted ties since they not only need more complex formulas but need a process of quantification when quantitative empirical data are not directly available. However quantitative empirical data are directly available under the condition of using bibliometric or Webometric data. In conclusion a new complex measure of the degree centrality is introduced including weighted ties possible for use of the analysis of co-authorship or citation networks. Both co-authorship relations and citations are well quantified data (weighted ties). This new measure is applied to a bibliographic co-authorship network and its reflection on the Web as an example. The new measures of degree centrality show the whole network on the Web has a more centralized structure than the bibliographic network.

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.

Studies in Co-authorship Pairs Distribution: Part-1

There are different versions of counting co-author pairs. We refer to two of them in the present paper including two corresponding hypotheses. Whereas the first version leads to a power function distribution of the co-author pairs the other version shows a bivariate distribution of co-author pairs’ frequencies hence producing threedimensional graphs. The regularities for the second kind of distributions are very different from simple power law distributions. These new regularities may be described by a model for the intensity function of interpersonal attraction (Social Gestalt). Complementarities are a crucial determinant of this model. In conjunction with these complementarities, various shapes of the distribution of observed co-author pairs’ frequencies emerge. As the difference between the two shapes increases, the correlation between these two shapes decreases. After mixing these two shapes a new shape of social Gestalt emerges which can be successfully described with the help of the mathematical function for a social Gestalt. The change of any shape to any other shape of the social Gestalt can be shown by simulation (or morphing). For comparison of two or more shapes the overlay of these shapes into a single frame is possible: either overlay of standardized shapes or of the originals. The present paper is focused on a theoretical approach verified by empirical studies explained in two papers published in this issue (Guo et.al.[1] and Kundra et.al[2]).

Who is collaborating with whom? Part II. Application of the methods to male and to female networks

The theoretical approach of 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. The application of these new methods to male and female networks is shown in Part II. After regression analysis the visualized Social Gestalts are rather identically with the corresponding empirical distributions (R2>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.