  We show that the geometry of minimum spanning trees (MST) on random graphs is
universal. Due to this geometric universality, we are able to characterise the
energy of MST using a scaling distribution ($P(\epsilon)$) found using uniform
disorder. We show that the MST energy for other disorder distributions is
simply related to $P(\epsilon)$. We discuss the relationship to invasion
percolation (IP), to the directed polymer in a random media (DPRM) and the
implications for the broader issue of universality in disordered systems.
