Little tricks leading to a significant acceleration of the calculation of the reliability of a random graph

Methods for preparing conditions for the efficient use of graph structure decomposition are proposed, which makes it possible to speed up the calculation of its general terminal reliability, that is, the probability that all its vertices will be connected in the case of reliable vertices and unreliable edges that can fail independently with given probabilities. The main idea is to enumerate the states of edges in an arbitrary section and use known equations for decomposition in the cases of 1, 2 or 3 reliable edges. A technique for finding a cut that divides the graph approximately in half is proposed. Experiments show that the proposed approach is quite effective.