A formula $\phi(x,y)$ has the order property if the are $(a_i)_{i<\omega}$ and $(b_j)_{j<\omega}$ such that $$ i< j \,\,\,\,\, \,\, \text{iff} \,\,\,\,\, \,\, \models \phi(a_i, b_j).$$ A theory $T$ is called stable if there is no formula with the order property.
Is the theory of graphs stable?
No, the theory of graphs is not stable.
Consider the graph with elements $\{a_i,b_i\mid i\in \omega\}$ and edge relation $R$, where $a_iRb_j$ if and only if $i<j$. This shows that the formula $xRy$ has the order property relative to the theory of graphs.