Extended network and algorithm finding maximal flows

Graph is a powerful mathematical tool applied in many fields as transportation, communication,informatics, economy, in ordinary graph the weights of edges and vertexes are considered independentlywhere the length of a path is the sum of weights of the edges and the vertexes on this path. However, inmany practical problems, weights at a vertex are not the same for all paths passing this vertex, but dependon coming and leaving edges. The paper develops a model of extended network that can be applied tomodelling many practical problems more exactly and effectively. The main contribution of this paper isalgorithm finding maximal flows on extended networks