A globally rigid framework 
in 
is a finite framework for
which all placements in the same Euclidean space
having the same corresponding edge lengths are congruent
to 
. Equivalently, the edge
lengths determine all pairwise distances between the
vertices (Gortler et al. 2010).
Congruence permits translations, rotations, and reflections. Global rigidity requires uniqueness among all equivalent placements, whereas local rigidity requires uniqueness only among sufficiently nearby placements. The ambient dimension is fixed in the definition. A graph is generically globally rigid when its generic frameworks are globally rigid.
