Corrigendum to “Degree-Based Approximations for Network Reliability Polynomials”. Comment on J. Complex Networks 2025, 13, cnaf001

arXiv:2510.06247v1 Announce Type: new
Abstract: Our original paper cite{VanMieghem2025} described the stochastic approximation $overline{rel}_G(p)=bigl[1-phi_D(1-p)bigr]^{N}$ in cite[eq. (2.2)]{VanMieghem2025} and the first-order approximation $(R_1)_G(p)=prod_{i=1}^{N}!bigl[1-(1-p)^{d_i}bigr]$ in cite[eq. (4.1)]{VanMieghem2025} as upper bounds for the all-terminal reliability polynomial (rel_G(p)). The present corrigendum clarifies that the unique upper bound is (Pr[hat D_{min}geq 1]), which is difficult to compute exactly, because we must account for correlated node-isolation events. Both the stochastic approximation $overline{rel}_G$ and the first-order approximation $(R_1)_G$ ignore those correlations, assume independence and, consequently, do not always upperbound (rel_G(p)) as stated previously. The complete graph (K_{3}) is a counterexample, where both approximations lie below the exact reliability polynomial $rel_{K_3}(p)$, illustrating that they are not upper bounds. Moreover, as claimed in cite{VanMieghem2025}, the first-order approximation $(R_1)_G$ is not always more accurate than the stochastic approximation $overline{rel}_G$. We show by an example that the relative accuracy of the stochastic approximation $overline{rel}_G$ and the first-order approximation $(R_1)_G$ varies with the graph $G$ and the link operational probability $p$. }{network robustness, node failure, probabilistic graph, reliability polynomial