What do inflow and outflow signify at a vertex in a flow network?

In a flow network, the terms inflow and outflow are used to describe the movement of resources (such as water, traffic, or data) at a specific vertex or node.

Inflow refers to the total capacity entering that vertex, meaning the amount of resource being received from other vertices or edges connected to it. This measurement is crucial for determining how much of the resource is available at that point in the network.

On the other hand, outflow signifies the total capacity exiting the vertex. This is the volume of resources being sent out to connected vertices. Understanding outflow is important for assessing how much of the resource is being distributed further in the network.

This definition aligns perfectly with the correct answer because it clearly delineates the roles of inflow and outflow in a flow network, focusing on their respective capacities. The other choices are misleading in their descriptions and do not accurately reflect the fundamental principles concerning inflow and outflow in flow networks.