  We introduce two common divisor graphs associated with a finite skew brace,
based on its $\lambda$- and $\theta$-orbits. We prove that the number of
connected components is at most two and the diameter of a connected component
is at most four. Furthermore, we investigate their relationship with
isoclinism. Similarly to its group theoretic inspiration, the skew braces with
a graph with two disconnected vertices are very restricted and are determined.
Finally, we classify all finite skew braces with a graph with one vertex, where
four infinite families arise.
