最小生成树是一副连通加权无向图中一棵权值最小的生成树。

在一给定的无向图 G = (V, E) 中，(u, v) 代表连接顶点 u 与顶点 v 的边（即 ），而 w(u, v) 代表此边的权重，若存在 T 为 E 的子集（即 ）且为无循环图，使得

的 w(T) 最小，则此 T 为 G 的最小生成树。

最小生成树其实是最小权重生成树的简称。

一个连通图可能有多个生成树。当图中的边具有权值时，总会有一个生成树的边的权值之和小于或者等于其它生成树的边的权值之和。广义上而言，对于非连通无向图来说，它的每一连通分量同样有最小生成树。

A minimum spanning tree is a spanning tree of a connected, undirected graph. It connects all the vertices together with the minimal total weighting for its edges.

A single graph can have many different spanning trees. We can also assign a weight to each edge, which is a number representing how unfavorable it is, and use this to assign a weight to a spanning tree by computing the sum of the weights of the edges in that spanning tree. A minimum spanning tree (MST) or minimum weight spanning tree is then a spanning tree with weight less than or equal to the weight of every other spanning tree. More generally, any undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of minimum spanning trees for its connected components.