Lower Bound on the Reliability of a Network with a 2-Connected Structure

The connectedness probability of a random graph (whose edges fail independently with a given probability $q$) in the class of random graphs generated by 2-connected multigraphs with a given number of edges and fixed values $x_1$, $x_2$ of the first and second components of their acyclic spectra is estimated. It is proved that the connectedness probability of a certain estimating random graph described in the paper is a lower bound for the connectedness probability of any random graph from this class for any $q$. This effectively computable bound can be used to estimate the network reliability if the network structure is a 2-connected graph with a small number of edges.