  For a finite point set $E\subset \mathbb{R}^d$ and a connected graph $G$ on
$k+1$ vertices, we define a $G$-framework to be a collection of $k + 1$ points
in E such that the distance between a pair of points is specified if the
corresponding vertices of $G$ are connected by an edge. We consider two
frameworks the same if the specified edge-distances are the same. We find tight
bounds on such distinct-distance drawings for rigid graphs in the plane,
deploying the celebrated result of Guth and Katz. We introduce a congruence
relation on the wider set of graphs, which behaves nicely in both the
real-discrete and continuous settings. We provide a sharp bound on the number
of such congruence classes. We then make a conjecture that the tight bound on
rigid graphs should apply to all graphs. This appears to be a hard problem even
in the case of the non-rigid 2-chain. However we provide evidence to support
the conjecture by demonstrating that if the Erd\H os pinned-distance conjecture
holds in dimension $d$ then the result for all graphs in dimension $d$ follows.
