How do you read the numbers on the edges of a flow network diagram?

Conditions

• The diagram uses standard flow network notation.
• Two numbers are associated with each edge.

Reasoning, step by step

1. Locate an edge in the flow network diagram.
2. Identify the two numbers written on or near the edge.
3. Read the first number as the flow ($f$).
4. Read the second number as the capacity ($c$).
5. Verify that the first number is less than or equal to the second number.

Example

The video annotates the edge from S to a with '3, 5' and the edge from a to b with '4, 6'. The speaker explains that we typically write them as 'flow, capacity' or 'flow/capacity', so 3 is the flow and 5 is the capacity for the first edge.

Common misconceptions

• Reading the first number as capacity and the second as flow.
• Assuming the numbers represent the source and sink node IDs rather than edge attributes.
• Thinking the comma or slash separates two different edges rather than two attributes of the same edge.

Watch the explanation

Explore next

• What is the difference between flow and capacity in a network?
• What does the notation $c(u,v)$ mean in a flow network?
• Which nodes are the source and sink in the example flow network?