Zipf–Mandelbrot–Pareto model for co-authorship popularity

Abstract

Each co-author (CA) of any scientist can be given a rank (r) of importance according to the number (J) of joint publications which the authors have together. In this paper, the Zipf-Mandelbrot-Pareto law, i.e. J ∝ 1/(ν + r) ζ is shown to reproduce the empirical relationship between J and r and shown to be preferable to a mere power law, J ∝ 1/r α . The CA core value, i.e. the core number of CAs, is unaffected, of course. The demonstration is made on data for two authors, with a high number of joint publications, recently considered by Bougrine (2014) and for 7 authors, distinguishing between their "journal" and "proceedings" publications as suggested by Miskiewicz (2013). The rank-size statistics is discussed and the α and ζ exponents are compared. The correlation coefficient is much improved (∼ 0.99, instead of 0.92). There are marked deviations of such a co-authorship popularity law depending on sub-fields. On one hand, this suggests an interpretation of the parameter ν. On the other hand, it suggests a novel model on the (likely time dependent) structural and publishing properties of research teams.Thus, one can propose a scenario for how a research team is formed and grows. This is based on a hierarchy utility concept, justifying the empirical Zipf-Mandelbrot-Pareto law, assuming a simple form for the CA publication/cost ratio, cr = c0 log2(ν + r). In conclusion, such a law and model can suggest practical applications on measures of research teams.In Appendices, the frequency-size cumulative distribution function is discussed for two sub-fields, with other technicalities * previously at GRAPES, ULG, Liège, Belgium;

Modeling the Epidemic Growth of Preprints on COVID-19 and SARS-CoV-2

“…We also analyze the distribution of the COVID-19 preprints among the many available servers. We find that the corresponding rank-frequency distribution follows a power law (at least for the first few largest servers), similar to the Zipf law found in many preferential attachment processes, such as the frequency of words in a text [23], the size distribution of cities [24], the wealth distribution of individuals [24], the number of scientific citations [25], the number of joint publications [26], and the distribution of nodes in social networks [27], among others. We thus argue that the distribution of manuscripts among repositories also seems to follow a similar preferential attachment dynamics, whereby servers that already have more preprints tend to get more submissions.…”

“…It should be emphasized that the problem studied here, namely the growth dynamics of COVID-19 preprints, is a direct manifestation of an underlying complex social process akin to other systems in Sociophysics [26,[36][37][38]. It may therefore be possible to develop a microscopic dynamical model, say, at the level of agents, as there is for other social dynamical systems, where the statistical and dynamical trends reported here could be studied in more detail.…”

“…for n ≥ 1 and ρ > 0. Zipf-like laws are particularly ubiquitous in linguistics and social processes, such as the frequency of words in a text [23], the size distribution of cities [24], the wealth distribution of individuals [24], the number of scientific citations [29], the distribution of degree of nodes in social networks [26,36,37], and the distributions of the tags in collaborative tagging networks [38], among others. The exponential function has also been applied to rank-size distributions, such as for urban and rural settlements [see e.g., [39] and references therein].…”

Modelling the epidemic growth of preprints on COVID-19 and SARS-CoV-2

“…We also analyze the distribution of the COVID-19 preprints among the many available servers. We find that the corresponding rank-frequency distribution follows a power law (at least for the first few largest servers), similar to the Zipf law found in many preferential attachment processes, such as the frequency of words in a text [23], the size distribution of cities [24], the wealth distribution of individuals [24], the number of scientific citations [25], the number of joint publications [26], and the distribution of nodes in social networks [27], among others. We thus argue that the distribution of manuscripts among repositories also seems to follow a similar preferential attachment dynamics, whereby servers that already have more preprints tend to get more submissions.…”

A study of self-organization of scientific communications: from statistical patterns to law

“…Zipf's pattern was repeatedly specified. In particular, in [7] the regularity was considered in the aspect of accounting for co-authorship.…”