Fast Rough Bounds for the Coefficients of the Network Reliability Polynomial

The problem of fast estimating of reliability polynomial' coefficients is considered in the paper in the case of all-terminal reliability (probability of a graph being connected). Obtaining lower and upper bounds for each coefficient of a reliability polynomial in one of its possible representation is based on counting all trivially known connected and disconnected realizations (states) of a random graph, based on easily derived information about graph's structure, such as existence of chains and their lengths.