Let G = (V,E) be a unit-capacity graph with n vertices and m edges.
Let T denote all the spanning trees in G.
If we run Karger's algorithm, we will get a random spanning tree in T formed by the contracted edges, we denote this distribution of spanning trees by D1.
On the other hand, if we assign a random weight in (0,1) to each edge and compute a minimum spanning tree using Kruskal's algorithm, then another distribution D2 over T is obtained.
Show that the distributions D1 and D2 are identical.
I have no idea where to start. Any hint is helpful!