Abstract We study homological properties of random quadratic monomial ideals in a polynomial ring $R = {\mathbb {K}}[x_1, \dots x_n]$, utilizing methods from the Erd̋s–Rényi model graphs. Here, for graph $G \sim G(n, p),$ we consider coedge ideal $I_G$ generated by monomials corresponding to missing edges $G$ and Betti numbers $R/I_G$ as $n$ tends infinity. Our main results involve setting edge ...