The study of the duration of transient processes in growing random graphs with a non-linear preferential attachment rule

A study of the duration of transients processes in random graphs with preferred attachment was carried out, during which it was found out that for some random graphs transient processes can last very long. For some known growing graphs the absence of stationary distribution of the vertices attachment degree has been found out for the first time. This makes the calculation methods and the techniques for analyzing transient processes up-to-date, because real networks modelled by this graphs, do not have stationary characteristics either. Real networks having stationary characteristics, can for a long time, even if they are too large, stay in the transient mode which does not let estimate these networks by stationary solutions. While modeling these networks, the methods for analyzing the transient modes are also urgent as they provide for controlling the errors of stationary solutions application. The paper gives the example of the stationary solution error control for a random graph, widely used in modeling of growing networks.