FindSpanningTree

FindSpanningTree[g] finds a spanning tree of graph g that connects all vertices with minimum total edge weight.

Examples

Spanning tree of a complete graph:

FindSpanningTree[CompleteGraph[5]]

From a grid:

FindSpanningTree[GridGraph[{3, 3}]]
(* Tree with 9 vertices, 8 edges *)

Minimum spanning tree with weights:

g = Graph[{1 <-> 2, 2 <-> 3, 1 <-> 3}, 
  EdgeWeight -> {1, 2, 3}]
FindSpanningTree[g]

Please visit the official Wolfram Language Reference for more details.