Abstract: Solving the problem of minimum spanning tree has been widely used to solve searching issues in reality. However, the node of a connected graph net is often changed, and, once it's changed, the traditional algorithm has to recalculate the minimum spanning tree. But, even the graph node changes, not all of minimum spanning tree will be changed, which results in unnecessary waste. This article is aimed at improving Kruskal algorithm and Prim algorithm, which can update the minimum spanning tree when the graph changes without recalculating.

Key words: Kruskal algorithm, Prim algorithm, minimum spanning tree, connected graph net