The edit distance function of a hereditary property H is the asymptotically largest edit distance between a graph of density p ∈ [0, 1] and H . Denote by P n and C n the path graph of order n and the cycle graph of order n, respectively. Let C * 2n be the cycle graph C 2n with a diagonal, and C n be the graph with vertex set {v 0 , v 1 , . . . , v n−1 } andMarchant and Thomason determined the edit distance function of C * 6 . Peck studied the edit distance function of C n , while Berikkyzy et al. studied the edit distance of powers of cycles. In this paper, by using the methods of Peck and Martin, we determine the edit distance function of C * 8 , C n and P n , respectively.