The web graph is the most popular model of real Web fragments used in Web science. The study of communities in the web graph contributes to a better understanding of the organization of the fragment of the Web and the processes occurring in it. It is proposed to allocate a communication graph in a web graph containing only those vertices (and arcs between them) that have counter arcs, and in it to investigate the problem of splitting into communities. By analogy with social studies, connections realized through edges in a communication graph are proposed to be called "strong" and all others "weak". Thematic communities with meaningful interpretations are built on strong connections. At the same time, weak links facilitate communication between sites that do not have common features in the field of activity, geography, subordination, etc., and basically preserve the coherence of the fragments of the Web even in the absence of strong links. Experiments conducted for a fragment of the scientific and educational