Calculation of Flows Intensities Transformations in Acyclic Directed Networks

The problem considered in this paper is discussing last year’s sufficiently intensively in different biological journals [1-3]. In Tsitsiashvili [4] a problem of a decomposition of balance equations for flows intensities in queuing networks is solving. Such problem is connecting with calculation of flows intensities of proteins networks. Main idea of this procedure is to find clusters with cyclically equivalent nodes and order them by their maximal distance from input clusters so that direct edges may be only from clusters with smaller to clusters with larger distances. Therefore, it is possible to divide all nodes into sets A0,A1,...,Ap so that every edge of the graph is only from node i ∈ At to node j ∈ Aq, t