minimum spanning tree
Given a graph with weighted edges, a minimum spanning tree is a spanning tree with minimum weight, where the weight of a spanning tree is the sum of the weights of its edges. There may be more than one minimum spanning tree for a graph, since it is the weight of the spanning tree that must be minimum.
For example, here is a graph of weighted edges and a minimum spanning tree for that graph. The edges of are drawn as solid lines, while edges in but not in are drawn as dotted lines.