  We consider simple random walks on random graphs embedded in $\mathbb{R}^d$
and generated by point processes such as Delaunay triangulations, Gabriel
graphs and the creek-crossing graphs. Under suitable assumptions on the point
process, we show an annealed invariance principle for these random walks. These
results hold for a large variety of point processes including Poisson point
processes, Mat\'ern cluster and Mat\'ern hardcore processes which have
respectively clustering and repulsiveness properties. The proof relies on the
use the process of the environment seen from the particle. It allows to
reconstruct the original process as an additive functional of a Markovian
process under the annealed measure.
