Comparison of scientific collaboration graphs: Math-Net.Ru as a case study

This paper presents a study of two scientific collaboration graphs, which were constructed using the data obtained from all-Russian mathematical portal Math-Net.Ru. One of the graphs is a citation-based scientific collaboration graph. It is a directed graph with no loops and multiple edges. The vertices represent the authors of papers, while edges represent one author has cited another. The second graph is a co-authorship graph, that is, an undirected graph in which the vertices are authors, while the edges represent the fact that two authors have written at least one paper together. The main characteristics of both graphs – degree and significance of vertices, diameter and average distance, connected components and clustering – are examined. In both graphs, we observe a similar connection structure – presence of a giant component and a large number of small components. Using the two graphs, a partition of the set of Math-Net.Ru authors is constructed. In the set, over 40 authors who have co-authored a paper with another author have not cited their coauthors in other papers. This means that there is no deliberate mutual citation in Math-Net.Ru journals.