Isomorphism and Subgraphs · Easy problem

Let $G=C_4$ have vertices $1,2,3,4$ and edges $12,23,34,14$. Let $H$ have vertices $a,b,c,d$ and edges $ab,bc,cd$ only (missing $ad$). Consider the map $\varphi:1\mapsto a,\,2\mapsto b,\,3\mapsto c,\,4\mapsto d$. How many edges of $G$ map under $\varphi$ to a pair that is NOT an edge of $H$?