On the Connectivity of Quasi-random Graphs

Graph theory is widely used to study the structural properties of complex discrete systems. Thus, to assess the ability of a system to maintain certain structural properties when the con-nections between its elements are broken, it is important to study different types of graph con-nectivity. Quasi-random graphs are a model of complex discrete systems with random disrup-tions of connections between system elements. The problem of estimating the probability of connectivity in quasi-random graphs is considered. The concepts of multiframe and polynomi-al of a connected graph are introduced. A new estimator of connectivity for quasi-random graphs based on a 3-edge connected graphs is presented.