What is the time complexity of this implementation of Karger's Algorithm?

I was searching for implementation of Karger's Algorithms and found this:

 //Find, and Union are the use of Disjoint set union on the nodes.
 MinCut(edges, V, E):
     vertices=V
     While(vertices > 2):
         i=Random integer in the range [0,E-1]
         set_1=find(edges[i].u)
         set_2=find(edges[i].v)
         if(set_1 != set_2):
             vertices = vertices-1
             Union(u, v)
     ans=0
     For(i in the range 0 to E-1):
         set_1=find(edges[i].u)
         set_2=find(edges[i].v)
         if(set_1 != set_2):
             ans = ans + 1
     Return ans

Unlike other implementations I've seen online, this one doesn't involve adjacency matrices, self-loop removal etc.

While I understand how this works, I don't understand whether it'll be significantly slower than other implementations. We aren't removing any edges, so it seems there will be a lot of operations wasted on edges where set_1 == set_2.

The note at the end says that the time complexity for MinCut is ~O(E), but why does the while loop run for O(E) times? Can someone please elaborate on this?

Thanks