Shortest Path Problem in network can be acted as a model for many application problems

but the iteration process of the conventional solution algeorithm is complex.In this paper

the shortest path algorithm based on the matrix multiplication in a weighted-graph are described

and its time complexity is as same as Dijkstra algorithm.In a given network graph

this algorithm delete spare nodes or edges and reach the goal that reduced network graph and improved speed of solving problem under the condition of unchanged shortest parth.Finally

we give examples

e.g.Traveling Salesman Problem

shortest path problem

to illistrate its advanteges

possessing merits of simple operation and easy understanding

compared with dynamic programming technology.