4 The table defines a network in which the numbers represent lengths.
| A | B | C | D | E | F | G |
| A | - | 5 | 2 | 3 | - | - | - |
| B | 5 | - | - | - | 1 | 1 | - |
| C | 2 | - | - | - | 4 | 1 | - |
| D | 3 | - | - | - | 4 | 2 | - |
| E | - | 1 | 4 | 4 | - | - | 1 |
| F | - | 1 | 1 | 2 | - | - | 5 |
| G | - | - | - | - | 1 | 5 | - |
- Draw the network.
- Use Dijkstra's algorithm to find the shortest paths from A to each of the other vertices. Give the paths and their lengths.
- Draw a new network containing all of the edges in your shortest paths, and find the total length of the edges in this network.
- Find a minimum connector for the original network, draw it, and give the total length of its edges.
- Explain why the method defined by parts (i), (ii) and (iii) does not always give a minimum connector.