Determination of a state of flow through or a cut of a parameterized network

Provided are techniques for determining a state of flow through, or a cut of, a network in which some the capacities of at least some of the conduits are dependent upon a specified parameter. Initially, a derived network is obtained by replacing capacities in the original network that depend upon the parameter. A particular flow state then is identified for that derived network, and this flow state is used to determine either a state of flow through or a cut of the original network.