Fast Rough Bounds for the Coefficients of the Network Reliability Polynomial

Abstract

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.