According to the maximum flow - minimum cut theorem, what is true about the values in a network?

The maximum flow - minimum cut theorem states that in any flow network, the maximum amount of flow that can be sent from a source to a sink is equal to the total capacity of the edges in the minimum cut separating the source and the sink. This fundamental result establishes a direct relationship between the maximum flow and the minimum cut in the network.

When calculating the maximum flow, one looks for the most efficient way to send the flow through the network without exceeding the capacity of any of the edges. Meanwhile, a minimum cut is defined as the smallest total weight (or capacity) of the edges that, if removed or "cut," would disconnect the flow from the source to the sink.

Since the theorem guarantees that the value of the maximum flow will exactly equal the value of the minimum cut, this means that both values are intrinsically related in such a way that knowing one allows you to deduce the other in a well-defined network context. Hence, the chosen answer accurately reflects this key aspect of the theorem where the maximum flow is equal to the capacity of the minimum cut.