Summary: Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type \((2,0)\). A graph \(G\) satisfies an identity \(s \approx t\) if the corresponding graph algebra \(A(G)\) satisfies \(s \approx t\). \(G\) is called a \((xx)y \approx x(yx)\) graph if \(A(G)\) satisfies the equation \((xx)y \approx x(yx)\). An identity \(s \approx t\) of terms \(s\) and \(t\) of any type \(\tau\) 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 \((xx)y \approx x(yx)\) graph algebras, identities and hyperidentities in \((xx)y \approx x(yx)\) graph algebras.