  We study the energy function of the Kuramoto model in random geometric graphs
defined in the unit circle as the number of nodes diverges. We prove the
existence of at least one local minimum for each winding number $q \in
\mathbb{Z}$ with high probability. Hence providing a large family of graphs
that support patterns that are generic. These states are in correspondence with
the explicit twisted states found in WSG and other highly symmetric networks,
but in our situation there is no explicit formula due to the lack of symmetry.
The method of proof is simple and robust. It allows other types of graphs like
$k-$nn graphs or the boolean model and holds also for graphs defined in any
simple closed curve or even a small neighborhood of the curve and for weighted
graphs. It seems plausible that the method can be extended also to higher
dimensions, but a more careful analysis is required.
