  Using simulations, we construct the effective dynamics in metabasin space for
a Lennard-Jones glass-former. Metabasins are identified via a scheme that
measures transition rates between inherent structures, and generates clusters
of inherent structures by drawing in branches that have the largest transition
rates. The effective dynamics is shown to be Markovian but differs
significantly from the simplest trap models. We specifically show that
retaining information about the connectivity in metabasin space is crucial for
reproducing the slow dynamics observed in this system.
