The reliability network when edges deleted corresponds to binomial random graph model that is also called Bernoulli Model. The page 3 of Random Graphs book (2000) by Svante Janson, Tomasz Luczak and Andrzej Rucinski states that the reliability network where vertices deleted instead do not correspond to the Bernoulli Model.
What is the Random Graph model for Reliability Network where vertices deleted intstead of edges?