A study of two graphs of scientific cooperation based on co-authorship and citation according to the all-Russian mathematical portal was conducted Math-Net.Ru. A citation-based scientific collaboration graph is a directed graph without loops and multiple edges, whose vertices are the authors of publications, and arcs connect them when there is at least one publication of the first author that cites the publication of the second author. A co-authorship graph is an undirected graph in which the vertices are the authors, and the edges record the co-authorship of two authors in at least one article. The customary study of the main characteristics of both graphs is carried out: diameter and average distance, connectivity components and clustering. In both graphs, we observe a similar connectivity structure – the presence of a giant component and a large number of small components. The similarity and difference of scientific cooperation through co-authorship and citation is noted.

According to the portal Math-Net.Ru a graph of journal citation is constructed. To increase the reliability of the model, the citation time interval was chosen from 2010 to 2021, when the distribution of citation articles stabilized at the level of 3500-4500 citations per year. The structure of link aging is studied and it is shown that their half-life is equal to 8 years. Therefore, the publication date of the cited articles was limited to 2002. For the constructed citation graph, the main properties, such as a small diameter and a high density, are obtained, indicating a high level of scientific communication in the Math-Net.Ru. The absence of the “Matthew effect” as a pronounced advantage in quoting established journals in relation to less well-known ones is shown. Adequacy of the journal citation graph Math-Net.Ru as a model of scientific communication confirmed by comparing the ranking of journals in the citation graph with their SCIENCE INDEX rating in eLIBRARY.RU. A direct moderate relationship between the two rankings is shown. A number of meaningful conclusions are drawn from the analysis of the citation graph.

Scientific co-authorship is a direct reflection of scientific collaboration. There is empirical evidence of the value of co-authorship, for example, articles with a large number of authors tend to be cited more often, which is important for calculating various indexes. Many foreign studies show an increase in co-authorship both in general and in various scientific disciplines, however, it is quite difficult to judge the situation with co-authorship of Russian scientists based on research according to Web of Science or Scopus for a number of reasons. According to the portal Math-Net.Ru some issues of co-authorship in the field of mathematical and computer sciences in Russia are investigated. In particular, it shows a small but steady increase in the average number of co-authors per publication and an increase in the number of articles co-authored over the years 2000-2020.