Applying algorithm finding shortest path in the multiple- weighted graphs to find maximal flow in extended linear multicomodity multicost network

The shortest path finding algorithm is used in many problems on graphs and networks. This article will introduce the algorithm to find the shortest path between two vertices on the extended graph. Next, the algorithm finds the shortest path between the pairs of vertices on the extended graph with multiple weights is developed. Then, the shortest path finding algorithms is used to find the maximum flow on the multicommodity multicost extended network is developed in the article [12].