The question might be for a minimum spanning tree,

if I understand correctly. That would

be a case for Kruskal's algorithm.

https://en.wikipedia.org/wiki/Kruskal%27s_algorithm

Regards,

Joachim

There are actually two well-known, simple and efficient algorithms to solve this optimization problem. These are the Kruskal's and Prim's algorithms.

Dear Gaurish, could you precise? Your question leads to disambiguation. Is your graph acyclic? I hope yes, since I understand your question as follows:

CONVERT = keep all vertices and edges, and choose a root. There are more possibilities, from which you want that (those) where the height of the tree is minimal.

(?)

Kruskal algorithm should do it.