In this paper, we present a formula for computing the Tutte polynomial of the signed graph formed from a labeled graph by edge replacements in terms of the chain polynomial of the labeled graph. Then we define a family of ring of tangles links and consider zeros of their Jones polynomials. By applying the formula obtained, Beraha-Kahane-Weisss theorem and Sokals lemma, we prove that zeros of Jones polynomials of (pretzel) links are dense in the whole complex plane
