In a flow network, what do weights or edges denote?

In a flow network, the weights on the edges specifically represent the capacities, which indicate the maximum amount of flow that each edge can support. This means that each edge has a limit on how much flow can pass through it, which is crucial for determining how the overall flow through the network can be managed.

When analyzing a flow network, understanding the capacities helps in optimizing the flow from a source vertex to a sink vertex while ensuring that the limits on each edge are not exceeded. This concept is essential in various applications, such as transportation systems, communication networks, and fluid dynamics, where managing the flow efficiently is critical.

The other options highlight different aspects that are not directly represented by the weights of the edges in a flow network. For example, while duration of tasks may be relevant in project management contexts (not typically in flow networks), or types of flow might refer to different categories of flow rather than the maximum flow capacity, the primary meaning of weights in this context always pertains to the edge capacities.