An Assortativity Analysis of Co-Authorship Networks and Authors’ Swing among Various Types of Open Access of Sources of Publications on “Open Science” from 1999 to 2018

Typically, indexing services of scientific publications provide a variety of relational and attribute datasets and as such they are often subjected to a variety of social network analyses. Here, we are focusing on the time-dependent bipartite graph of authors and sources (journals etc.), where the former publish their contributions. Moreover, we are interested in the Open-Access (OA) type of sources (at the time of publication). A first step in the analysis of such a dataset often is to aggregate over time (typically over one or more years, during which the OA type of a sources might remains the same) deriving thus a number of weighted graphs of authors vs. sources for each time period. Subsequently, one may project such a bipartite graph over the mode of authors in order to obtain the so-called co-authorship graphs among individual authors. As for the OA type of publications, we are partitioning the set of authors according to whether publish in sources having a combined or mixed OA type, which includes as values/categories all possible combinations among the four main OA types: paywalled, bronze, gold and green. Apparently, this is a categorical attribute of authors in the co-authorship graph such that, to each author, there corresponds a unique mixed OA type, corresponding to sources of all publications in which this author has published. Furthermore, to measure assortativity (or mixing) of the co-authorship graph, one might use Mark Newman's attribute assortativity coefficient for the mixed OA type as a categorical attribute. Furthermore, for any two successive periods, each one including a number of years, one may count the authors' swing among all existing categories of the attribute of mixed OA type. Thus, one may find how many authors who have published in the mixed OA type i in the first period are publishing in the mixed OA type j in the next period. Knowledge of the swing of authors among mixed OA types shows which combinations of OA types tend to draw the interest of the majority of authors whose publications are included in the collected dataset. In our case of "Open Science" publications, we find that the mixed OA type attribute assortativity coefficient of authors in the co-authorship graph is moderately high during the period from 1999 to 2018, while it further drops during the subsequent period from 2012 to 2018, implying that the paywalled "domination" appears to weaken in more recent years and though a considerable number of authors still prefer to publish in paywalled sources, a good number of them funnels their publications towards mixed combinations of gold and green types of OA.

Transcript

1. An Assortativity Analysis of Co-Authorship Networks and Authors’ Swing among Various Types of Open Access of Sources of Publications on “Open Science” from 1999 to 2018 Moses A. Boudourides1 Visiting Professor of Mathematics, New York University Abu Dhabi Northwestern University School of Professional Studies 1 Moses.Boudourides@northwestern.edu with Giannis Tsakonas & Sergios Lenis 4th European Conference on Social Networks (EUSN 2019) Zurich, September 9-11, 2019 Presented on September 10, 2019
2. The Dataset
11. The Bipartite Graph of Authors-Publications for 155 Authors publishing before and after 2011
17. Mixed OA Types
19. Assortativity of a Partition Let P = {P1, P2, . . . , Pp} be a vertex partition of graph G. Identifying P to a p–assignment AP of enumerative attributes to the vertices of G , one can define (cf. Mark Newman, 2003), the (normalized) enumerative attribute assortativity (or discrete assortativity) coefficient of partition P as follows: rP = rP(AP) = tr MP − ||M2 P || 1 − ||M2 P || , where MP is the p × p (normalized) mixing matrix of partition P. Equivalently: rP = i,j∈V (Aij − ki kj 2m )δ(AP(i), AP(j)) 2m − i,j∈V (ki kj 2m )δ(AP(i), AP(j)) , where {Aij} is the adjacency matrix of graph G, m is the total number of edges of G, ki is the degree of vertex i and δ(x, y) is the Kronecker delta.
20. Mixing and OA Type Assosartivity Coefficient The OA-type assortativity coefficient of the co-authorship network in 1999-2011 is = 0.563
21. The OA-type assortativity coefficient of the co-authorship network in 2012-2018 is = 0.406
22. Authors’ Swings The OA-type assortativity coefficient of the graph of authors’ swings before and after 2011 is = 0.001 (non-assortative graph)