What is the difference between flow and capacity in a network?

Conditions

• Applies to edges in a flow network.
• Flow must be less than or equal to capacity ($f \le c$).

Reasoning, step by step

1. Define capacity as the maximum limit of an edge.
2. Define flow as the current amount passing through the edge.
3. Compare the two values to establish the constraint that flow cannot exceed capacity.

Example

In the video example, the edge from S to a has a capacity of 5 and a flow of 3. The speaker summarizes that capacity is the maximum volume the edge can hold, while flow is the amount it is currently carrying.

Common misconceptions

• Thinking flow and capacity are the same thing.
• Believing that flow can temporarily exceed capacity if the network is congested.
• Confusing the total flow of the network with the flow on a single edge.

Watch the explanation

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• What does the notation $c(u,v)$ mean in a flow network?
• What is a flow network in graph terms?