The idea, step by step
State the relationship first
Choose what the vertices represent and exactly when an edge is drawn. In a direct-bus-service network, towns are vertices and a direct service creates an edge. Two nearby towns are not connected merely because they appear close together.
Write all vertices first, including isolated objects. Then translate each stated pair into an edge. Check the complete edge list after drawing; a neat picture with an invented connection is still an incorrect model.
Read an undirected table once
In a connection table, 1 means a direct link and 0 means none. An undirected table is symmetric because a link from P to Q also links Q to P. Use only one side of the diagonal when listing edges.
A zero diagonal means there are no self-links. Compare each row with the neighbours in your diagram to check for missed edges. The row total gives that vertex’s degree.
| From / to | A | B | C | D |
|---|---|---|---|---|
| A | 0 | 1 | 0 | 1 |
| B | 1 | 0 | 1 | 0 |
| C | 0 | 1 | 0 | 1 |
| D | 1 | 0 | 1 | 0 |
A common trap
Drawing a connection just because objects are nearby.
Instead: The stated edge rule, not page distance, determines the links.
See the thinking
From a travel description
Services are AB, BC, CD, DA; E has no service. Describe the network.
- Create vertices A–E.
- Draw exactly the four stated edges.
- E remains isolated.
From a table
List the edges in the supplied connection table.
| From / to | A | B | C | D |
|---|---|---|---|---|
| A | 0 | 1 | 0 | 1 |
| B | 1 | 0 | 1 | 0 |
| C | 0 | 1 | 0 | 1 |
| D | 1 | 0 | 1 | 0 |
- Row A gives AB and AD.
- Row B adds BC; BA repeats AB.
- Row C adds CD; the final row repeats known links.
Check your understanding
Computers A–D have only cables AB and BC. Must D appear?
Show answer
Yes, isolated.
D belongs to the stated set even without a cable.
Your turn
6 questions · 15 marks · Work at your own pace.
Read the questions online
- Draw vertices A–D with edges AB, AC and CD.3 marks
- Do services AB and BC alone justify a direct edge AC?2 marks
- A connection table has rows and columns in the order A, B, C. Its rows are (0,1,1), (1,0,0), (1,0,0). List each undirected edge once.2 marks
- An undirected table has AB=1 and BA=0. Explain the problem.3 marks
- Mia, Noah and Priya share chess; Priya and Leo share music. Draw an edge for each pair sharing a club.3 marks
- A model includes six towns, two without roads. A student draws four vertices. What is missing?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Draw vertices A–D with edges AB, AC and CD.3 marks
Place all four vertices.
Join AB, AC and CD only.
Any drawing with exactly those vertices and three edges. - Do services AB and BC alone justify a direct edge AC?2 marks
They describe a two-edge journey, not a direct service.
No. - A connection table has rows and columns in the order A, B, C. Its rows are (0,1,1), (1,0,0), (1,0,0). List each undirected edge once.2 marks
Read above the diagonal only.
AB and AC. - An undirected table has AB=1 and BA=0. Explain the problem.3 marks
A mutual link must appear in both positions.
Correct an entry or use a directed model.
It is not symmetric. - Mia, Noah and Priya share chess; Priya and Leo share music. Draw an edge for each pair sharing a club.3 marks
Chess makes three pairs.
Music adds PL.
MN, MP, NP and PL. - A model includes six towns, two without roads. A student draws four vertices. What is missing?2 marks
The vertex set must include every stated town.
Two isolated town vertices.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum
Vertices, edges and connections; drawing networks from situations; interpreting connectedness and routes; comparing representations; using networks to explain practical relationships.
Official curriculum source ↗