This paper presents the results of a study of the graph of research collaboration. The graph is constructed using the database of the All-Russian mathematical portal Math-Net.Ru. It is a directed graph without loops and multiple edges. The most indicative characteristics of the graph, such as connectivity and modularity, are given. It is shown that the graph has a structure consisting of several nested contours. The innermost contour is the maximum component of strong connectivity, while the outermost one represents a small number of small components that are not connected either with each other or with other contours.