2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164088The two-terminal reliability, known as the pair connectedness or connectivity function in percolation theory, may actually be expressed as a product of transfer matrices in which the probability of operation of each link and site is exactly taken into account. When link and site probabilities are $p$ and $ρ$, it obeys an asymptotic power-law behavior, for which the scaling factor is the transfer matrix's eigenvalue of largest modulus. The location of the complex zeros of the two-terminal reliability polynomial exhibits structural transitions as $0 \leq ρ\leq 1$.a few critical polynomials are at the end of the .tex source fileDiscrete MathematicsNetworking and Internet Architecturetext