A generically rigid graph in 
is a finite graph whose every
generic framework in 
is locally rigid. Equivalently,
it suffices that some generic framework is locally
rigid (Asimow and Roth 1978). Generic means that all placement coordinates
are algebraically independent over the
rationals. Local rigidity
means that every sufficiently nearby placement preserving the edge
lengths is congruent to the original placement.
The dimension 
is part of the definition. Every generically
globally rigid graph is generically rigid in the same
dimension, but local rigidity alone does not require uniqueness among distant equivalent
placements.
