algorithms - Reconstructing a graph given access to its cut function

Given an unweighted graph $G = (V, E)$, let the cut function on this graph be defined to be:
$C:2^V rightarrow mathbb{Z}$ such that:
$$C(S) = |{(u,v) in E : u in S wedge v notin S}|$$
Suppose you have the ability to query $C$, but otherwise have no knowledge of the edge set $E$. Is it possible to reconstruct $G$ by making only polynomial (in $|V|$) many queries to the cut function?