Reliability polynomials and link importance in networks

The reliability polynomial is a graph invariant which is of interest where graphs are used as models of systems such as communication networks, computer networks, and transportation networks. This paper examines the use of reliability polynomials to rank the edges in a graph in terms of overall importance to graph reliability. For a given edge e in the graph G, G-e and G*e denote the graph with the link deleted and contracted (respectively); p (0>