What is minimum spanning tree

Given an unguided connected graph, an extension tree of this graph is a subgraph which is a tree that connects all vertices. A single graph may have different extension trees. We can mark a weight at each edge, which is a number that represents how unfavorable it is, and assign a weight to the extension tree calculated by the sum of the weights of the edges that compose it. A minimum spanning tree is then an extension tree with a weight less than or equal to each of the other possible spanning trees. Generalizing more, any non-directional graph (not necessarily connected) has a minimal forest of trees, which is a union of minimal extension trees of each of its related components.