An effective method to compute closure ordering for nilpotent orbits of   $\theta$-representations
  We develop an algorithm for computing the closure of a given nilpotent $G_0$-orbit in $\g_1$, where $\g_1$ and $G_0$ are coming from a $\Z$ or a $\Z/m\Z$-grading $\g= \bigoplus \g_i$ of a simple complex Lie algebra $\g$. 
W.A. de Graaf, E.B. Vinberg, and O.S. Yakimova
math.AG math.RT