What does the capacity of a cut in a flow network represent?

In the context of flow networks, the capacity of a cut represents the maximum amount of flow that can be blocked or prevented from traveling from the source to the sink. A cut divides the set of vertices into two disjoint subsets, effectively separating the source from the sink. The capacity of this cut is calculated by summing the capacities of the edges that cross from the source side to the sink side. This value indicates the greatest total flow that can be eliminated or "cut off" from reaching the sink.

Understanding this concept is crucial when analyzing flow networks, especially in relation to the max-flow min-cut theorem, which states that the maximum flow in a network is equal to the minimum capacity of a cut. By knowing this, one can determine the limits of flow within the network based on the constraints created by cuts.