The authors propose a method for complex bibliometric analysis of scientific productivity of large-scale (federal or national) Russian universities. Special attention is paid to co-authorship. The technique is used to study the status and trends characterizing the publication activity of the Ural Federal University. The authors introduce such complementary notions as limitations on co-authorship (factors acting negatively on co-authorship) and requirements for co-authorship (factors acting positively on co-authorship), as well as the notion of level of co-authorship. The article also proposes certain modification of the concept of window of citation, in which, unlike the classical interpretation of this concept, the citation window is always equal to the publication window. All this made it possible to identify more clearly the influence of various factors on the processes of co-authorship.