The classical example used to introduce this problem in lectures is the one about the soviet rail network: https://jeffe.cs.illinois.edu/teaching/algorithms/boo

The classical example used to introduce this problem in lectures is the one about the soviet rail network: https://jeffe.cs.illinois.edu/teaching/algorithms/book/10-maxflow.pdf https://jeffe.cs.illinois.edu/teaching/algorithms/book/10-ma... Legend has it both Soviets and Americans studied it, both identifying the bottleneck for opposite reasons: Americans wanted to disrupt as much as possible by destroying as few rails as possible while Soviets wanted to extend the network's ability to transport goods with building the fewest connections... Both problems are equivalent, known as the max flow min cut theorem.