For the weight matrix corresponding to a weighted graph,the two-dimensional initial weight path matrix and general weight path matrix were defined.And the multiplication operation of the general weight path matrices was derived,by which a method to detect negative cycle in negative weighted directed graph was obtained.If the graph with negative weight did not have negative cycle,this method could also be used to find all the minimum weights and all the shortest paths of all pairs clearly at the same time through the final general weight path matrix.This method was applied also to simple direct...
