A Full Characterization of Irrelevant Components in Diameter Constrained Reliability

In classical network reliability analysis, the system under study is a net-work with perfect nodes but imperfect link, that fail stochastically and independently. There, the goal is to find the probability that the resulting random graph is connected, called reliability. Although the exact reliabil-ity computation belongs to the class of NP-Hard problems, the literature offers three exact methods for exact reliability computation, to know, Sum of Disjoint Products (SDPs), Inclusion-Exclusion and Factorization. Inspired in delay-sensitive applications in telecommunications, Héctor Cancela and Louis Petingi defined in 2001 the diameter-constrained relia-bility, where terminals are required to be connected by d hops or less, being d a positive integer, called diameter. Factorization theory in classical network reliability is a mature area. However, an extension to the diameter-constrained context requires at least the recognition of irrelevant links, and an extension of deletion-contractio