Weighted multiplex network of scientific journal authors

The organizational structure and topology of complex systems (CS) represented as a set of interacting objects are traditionally studied based on their representation in the form of network structures. The standard approach consists of studying graphs whose vertices correspond to objects and edges correspond to one of the possible types of connections [1–3]. Such a model as applied to the system of scientific co-authorship was used in the fundamental works [4, 5]. This representation allows to study such properties of the system as evolution [6, 7], prediction of new co-authorship links [8, 9], identifying communities [10]. An important limitation of this approach is that it captures only binary interactions. A possible way to overcome this limitation is to generalize binary interaction to the interaction of an arbitrary set of actors, for example, by using the formalism of bipartite graphs, hypergraphs, and simplicial complexes. A modern methodology for modeling group relations in CS is described in [19–21]. It is based on the definition of multilayer networks and is suitable for representing most СS. Multilayer networks are defined by a set of nodes interacting with each other in several ways simultaneously. Each type of connection corresponds to a layer, a copy of any “physical” node can be present in several layers. The simplest classification of multilayer networks distinguishes two categories based on the absence or presence of inter-layer connectivity, which is a significant topological discriminator between two classes of models: non-interconnected networks of networks and interconnected ones. In the case where the connections cannot be explicitly determined based on the data, an important tool for studying the topology is the concept of an inter-layer edge (multilink) [22]. It defines the structure of connections between nodes in all layers. If relationships can be identified from the data and layers are explicitly connected to each other, tensor-like structures are needed [19]. One class of interconnected networks are multiplex networks, in which the nodes of each layer represent copies of the same object and only inter-layer connections among copies of the same physical node are allowed. The mathematical apparatus used to describe and analyze multiplex networks is proposed in [22, 27, 29]. This paper presents the results of the analysis of the weighted multiplex network 𝑀𝑐𝑐 constructed on the basis of real data extracted from the articles of the scientific journal “Sakharnyi Diabet”. The 𝑀𝑐𝑐 structure consists of two weighted layers, the nodes of which are the authors of the articles. The edges between the nodes of the first layer are established based on the binary co-authorship relation, and the edges of the second layer are based on the citation relation. The basic properties of nodes and links that determine the network structure are analyzed. The parameters of nodes of each layer that affect the topology of weighted networks, such as degree, weighted degree, and the inverse participation coefficient, are calculated. Their distributions and correlations including interlayer ones are presented. The high level of inter-layer correlation of node degrees indicates that nodes with a significant number of links in one layer are also highly connected in another. This is also true for the weighted degree. An important characteristic of multiplexity is the concept of the overlap between two layers reflecting the presence of links between the same nodes in both layers. The obtained values of the overlap coefficients indicate active interaction between the authors. The parameters of the multiplex nodes based on the concept of a multilink provide additional information about the relationship between nodes in different layers, in contrast to the sum of links in a single-layer aggregated network. Multidegree, multistrength, the inverse coefficient of multiparticipation, their distributions and correlations were calculated. The analysis of the results allows us to conclude that although it is impossible to conclude from the limited data that co-authors cite mainly co-authors, it is possible to conclude that mutual citations prevails between co-authors. The presented formalism allows us to significantly expand the understanding of author relationships in the scientific field under consideration.