Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity $s{approx}t$ if the corresponding graph algebra $underline{A(G)}$ satisfies $s{approx}t$. A graph G=(V,E) is called an $(xy)x{approx}x(yy)$ graph if the graph algebra $underline{A(G)}$ satisfies the equation $(xy)x{approx}x(yy)$. An identity $s{approx}t$ of terms s and t of any type ${ au}$ is called a hyperidentity of an algebra $underline{A}$ if whenever the operation symbols occurring in s and t are replaced by any term operations of $underline{A}$ of the appropriate arity, the resulting identities hold in $underline{A}$. In this paper we characterize $(xy)x{approx}x(yy)$ graph algebras, identities and hyperidentities in $(xy)x{approx}x(yy)$ graph algebras.