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This thesis deals with the maximum flow problem in network. First part describes and explains basic terms of graph theory, which gives theoretical base for following text. Next part is dedicated to algorithms that may be used to solve a maximum flow problem. Each described algorithm contains a brief history, general notation and a practical example. The next very important part of the thesis is in specific computer science applications such as computer vision and web mining. As an essential part of the thesis is developed software in programming language Java, which allows user to compare the implemented algorithms and to solve large network flows problems.