Let \(P\) be a finite subset of \(\mathbb{R}^2\), Erdős asked how the number of distinct distances grows as the size of \(P\) grows. We examine a graphical variant of this problem asking how many distinct realizations the graph \(G\) can have with vertices in the set \(P\), as \(P\) grows. We present recent progress that establishes essentially sharp bounds for this question for almost all graphs on four vertices.