A graph reconstruction problem involving common neighbors

Given a simple graph $G = (V, E)$ on $v$ vertices and two distinct vertices $x, y \in V$, the co-degree $c_{x,y}$ associated to the pair $\{x, y\}$ is the number of their common neighbors in the graph $G$. The co-degree sequence of $G$, denoted by $γ(G)$, is the list of all the co-degrees associated