4. The following matrix gives the capacities of the pipes in a system.
| To From | S | \(T\) | A | \(B\) | \(C\) | D |
| S | - | - | 16 | 26 | - | - |
| T | - | - | - | - | - | - |
| A | - | - | - | - | 13 | 5 |
| B | - | 16 | - | - | - | 11 |
| C | - | 11 | - | - | - | - |
| D | - | 11 | - | - | - | - |
- Represent this information as a digraph.
- Find the minimum cut, expressing it in the form \(\{ \} \mid \{ \}\), and state its value.
- Starting from having no flow in the system, use the labelling procedure to find a maximal flow through the system. You should list each flow-augmenting route you use, together with its flow.
- Explain how you know that this flow is maximal.