Structural properties of the multiplex network of scientific journal authors

A multilayer network — of which multiplex network is particular case — is a network made up by multiple layers, each of which represents a certain binary relationship between network actors. An example of such a system is a social network in which actors are interconnected by several types of social relations. Bibliographic information on a set of publications of scientific journals can be a source for constructing and studying multilayer networks of various types. Examples include multiplex networks, where different layers reflect the collaboration of authors in different scientific sections of the same scientific field [1]; two-layer networks of authors who are co-authors in the first layer and cite each other in the second [2]; three-layer co-authorship/citation/keyword networks, where the third layer reflects the use of the same keywords by authors in their works [3]. This paper contains the results of the analysis of the parameters of the weighted multiplex network built on the basis of real data extracted from a long-term archive of articles of the scientific journal “Sakharnyi Diabet”. The network consists of two layers: scientific co-authorship and citation. The nodes of the network are the authors of the journal articles. The first layer is the co-authorship graph, the vertices correspond to the authors, the connection between two vertices is established if the corresponding authors have joint publications, the edge weight is equal to the number of publications. The second layer is the directed citation graph, the edge between the citing and cited is established if the reference list of the article in which the citing author participates contains a link to an article from the journal in which the cited author participates. The details of the construction and the parameters of the layers are given in the work [8]. For multilayer networks structural properties of single networks must be modified to take into account their multilayer nature and to distinguish links. In this paper we investigate the set of basic metrics that characterize the structural properties of multiplex network and are the extension of classical network metrics to the case of multiplexes [6, 7]. These include centrality measures which allow ranking nodes and node clustering which reflect the tendency of nodes to form triangles. A number of methods for modifying parameter are considered. One way is a transformation of a multilayer network into a single-layer network for which the corresponding parameters (for example, the degree 𝐾𝑖) are calculated. Aggregation of the parameter values calculated separately for each layer (︁ 𝐶𝑙𝑦 ℳ )︁ gives an idea of the features of the node’s connections in the layers. And consideration of several layers simultaneously, as for example when determining the clustering coefficient 𝐶𝑖,1, allows us to identify the interconnectedness of the structures in which the node is involved. The results of parameters calculating and analysis are presented. The article is a continuation of the work [8].