Scientific journal co-authorship network model

The traditional representation of a complex system (CS) in the form of a network or a graph makes it possible to identify many aspects of the system’s behavior, see [2-4]. The network is based on pairwise relationships between network objects. In this case, the nodes of the co-authorship network correspond to the authors, and the edge between the nodes is constructed if there is at least one publication in which both authors participated, see the fundamental works [5, 6]. Such a model is able to express many complex properties of CS, its advantage lies in its simplicity and the ability to use graph theory in the analysis. The model has been studied quite well in terms of the distribution of degrees of network nodes [5], ranking of authors [6], dynamics of evolution [7, 8], identification of communities [9], and prediction of new co-author relations [10, 11]. However, this CS modeling does not reveal all the information that can be extracted directly from the list of articles and their authors, for example, does not reflect the total number of articles prepared by co-authors. To overcome this shortcoming, several methods for constructing networks of co-authorship, extending the traditional approach, were considered, see [6, 12]. But fixing only binary relations between system objects excludes interaction involving groups of network objects. A possible solution to the problem is to generalize the pair interaction to the interaction of an arbitrary set of nodes. In this case, the networks are called hypcrnctworks. The main mathematical structures used as a CS model include bipartite graphs, hypergraphs, and simplicial complexes [13]. The concept of a hypcrgraph [20] was proposed in [21] as applied to the analysis of CSs and providing a computationally feasible tool that can be adapted to many analytical situations. In the study of co-authorship, as a rule, the nodes corresponding to the authors form a hyperedge in the case of a joint publication [22, 23]. This paper presents a co-authorship network model that takes into account group relationships that arise between co-authors. The network is modeled using a hypcrgraph whose vertices correspond to authors and whose edges correspond to scientific articles (SA). The data we analyze is extracted from the electronic archive (https://www.dia-endojournals.ru/jour/issue/archive) of the quarterly scientific and practical medical peer-reviewed journal Diabetes Mellitus (ISSN 2072-0378), published since 1998. The journal is indexed in the international abstract and full-text databases. The hypcrgraph Hca, built oil the basis of the selected archive data, has size m(Hca) = 991 and order n(Hca') = 1694. Since only those SAs that have two or more authors are considered, there are no loops in the constructed hypergraph. The hypergraph Hca is not connected, it consists of 97 components, of which 68 components have one edge, the maximum component includes about 64.75 % vertices (authors) and 67.4% edges (articles). The parameters of the hypcrgraph (and its components) are measured and its topological properties (simple, star, strong star, conformal, Holly) are revealed. The use of the hypcrgraph language allows to get an idea of the shape of cooperation in the system under consideration. Most of the authors of the co-authored journal articles are indirectly related to each other due to the presence of joint works. The vertex degree distributions (the maximal component) have a long tail, i.e. most authors have a small number of joint SAs. The same can be said about the distribution of edge degrees, indicating that most SAs have a small number of co-authors. All components, except for the maximal, have one or another considered property. Moreover, the properties of conformity and Helly are common to all components, regardless of size and order. The property of simplicity is more characteristic of components with a small number of edges, the same can be said about the probability of being a star. Two components have all the considered properties. It should be noted that based on the incidence matrix of a hypergraph, a traditional network of co-authorship can be built, in which two authors are connected if they have at least one joint work. The associated multigraph G(Hca') is one of the models of such a network in which the weight of an edge between two authors is equal to the number of joint works. This work continues the study and approbation of methods for analyzing networks of co-authorship, see [1].