Graph is an excelent mathematical means used in many applications as communication, transportation, economy, informatics, ... In traditional graph the weights of vertexes and edges are independent, where the distance of a path is the sum of weights of the vertexes and the edges on that path. On the other side, in many practical applications, weights at vertexes are not equal for all paths going through these vertexex, but are depending on leaving and coming edges. Furthermore, capacities of vertexes and edges of a network are shared by many commodities with different costs. Hence, studying networks of mutiple weights is needed. In the presented paper, the algorithm finding shortest path in network with multiple weights is applied to implement the general algorithm finding the maximum concurent flow on the multicost multicommodity extended network.

Keywords : Network, Graph, Multicost Multicommodity Flow, Libear Optimization, Aproximation.