A Graph that represents Flow, we can use it to find the maximum flow.

Maximum Flow - Systematic Approach §

Flow Network Graph 2023-08-28 09.42.13.excalidraw

• Start from the top most path.
  • ABCEF
• Find the lowest capacity Edge, write down it’s value
  • e.g. A -> B = 4
• Take the value of the lowest capacity edge and take it from all edges on that path.
  • A -> B = 4
    • 4 - 4 = 0
  • B -> C = 6
    • 6 - 4 = 2
  • C -> E = 5
    • 5-4 = 1
  • E -> F = 15
    • 15-4 = 11

Examples of Systematic Approach

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Remaining Capacity §

• Take the remaining capacity of the pipes as found in the first part of the question.
• Then take that from the maximum flow of that pipe.

e.g. A-C has a remaining capacity of 120, but max of 400