Data structure implementation of MST (Minimum spanning tree) through Fibonacci heaps

How can a fibonacci heap store the information needed by the algorithm? In order to achieve good efficiency, when would you run the Consolidate routine?

Algorithm :

MST(G) 2 T ← {} // set that will store the edges of the MST 3 for i ← 1..n 4 Vi ← {i} 5 Ei ← {(i, j) : j is a vertex and (i, j) is an edge of G} // set of all edges incident with vertex i 6 end for 7 while there is more than one set Vi 8 choose any Vi 9 extract minimum weight edge (u, v) from Ei 10 one of the endpoints u of this edge is in Vi ; let Vj be the set that contains the other endpoint v 11 if i 6= j then 12 T ← T ∪ {(u, v)} 13 combine Vi and Vj into Vi (destroying Vj ) 14 combine Ei and Ej into Ei (destroying Ej ) 15 end if 16 end while 17 return T 18 end MST 

Would you have to add any additional fields to nodes in the heaps or use any additional data structures?