Understand the idea.
State the relationship first
Before drawing a network, state what each vertex represents and exactly what qualifies as an edge. For direct bus services, an edge means a stated direct service, rather than geographical closeness or an indirect journey.
Create every vertex first, including objects without connections. Add only the listed pairs, then compare the completed drawing with the original description so neither missing links nor invented ones survive.
Read an undirected table once
In a connection table, read the row and column labels together. A at row A, column B means edge AB. In an undirected network, the matching entry at row B, column A records the same edge.
List entries on only one side of the diagonal to count each edge once. A zero diagonal excludes self-links. For a simple undirected network, each row total is the degree of that row’s vertex.
| 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 |
See the method in action.
From a travel description
Services are AB, BC, CD, DA; E has no service. Describe the network.
Worked solution
- 1
Include all the stated locations.
E remains part of the model even though no service reaches it.
- 2
Translate only the listed services.
Each service supplies one undirected edge.
- 3
Describe the connected groups.
The four edges form a cycle on A, B, C and D; E has degree zero and remains isolated.
A cycle A–B–C–D–A and isolated E.
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 |
Worked solution
- 1
Read row A beyond its diagonal.
The entries under B and D are 1; the entry under C is 0.
- 2
Continue above the diagonal.
Row B adds BC and row C adds CD; entries below the diagonal would duplicate existing edges.
- 3
Check the completed edge list.
Each row contains two 1s, giving degree sum 8 and hence four undirected edges.
AB, AD, BC, CD.
Try it yourself.
Check your understanding
Computers A–D have only cables AB and BC. Must D appear?
Show answer & reasoning
Yes, isolated.
Yes. D is one of the four specified computers, so include it as an isolated vertex. Only A, B and C have incident cables in the given model.
Keep practising
6 worksheet questions · 15 marks
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 and . 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 and . 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 ↗