  In classical network reliability analysis, the system under study is a
network 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 \emph{reliability}. Although the exact
reliability computation belongs to the class of $\mathcal{NP}$-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, H\'ector
Cancela and Louis Petingi defined in 2001 the diameter-constrained reliability,
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-contraction
formula. In this paper, we fully characterize the determination of irrelevant
links. Diameter-constrained reliability invariants are presented, which,
together with the recognition of irrelevant links, represent the
building-blocks for a new factorization theory. The paper is closed with a
discussion of trends for future work.
