The idea, step by step
Choose data to match the question
The same towns can form networks of roads, direct buses or internet links. Choose the relationship that answers the question. An edge must have a consistent meaning across the network. State whether connections are two-way and include isolated sites.
If journey time or distance matters, attach relevant weights with units. A route total is the sum of its edge weights. Fewer edges do not necessarily mean a quicker or shorter route.
Say what the model cannot establish
Connectedness shows that a route exists under the model’s rules. It does not guarantee affordability, accessibility or reliability. Examine link failures when the real question concerns emergency access.
A useful recommendation explains which weakness a new connection fixes. State limitations such as congestion, closures, one-way roads or capacity. These are mathematical assumptions to evaluate, rather than reasons to abandon modelling.
A common trap
Assuming a connected network is automatically fast or reliable.
Instead: Connectivity guarantees only reachability. Test other properties with the needed data.
See the thinking
Join two groups
Edges are AB, BC, CA and DE. Add one edge so every vertex is reachable.
- The components are {A,B,C} and {D,E}.
- An edge must join different components.
Compare weighted routes
A–B–D takes 8 and 9 minutes. A–C–E–D takes 4,5,3 minutes. Which is quicker?
- The first total is 17.
- The second total is 12.
- 17−12=5.
Check your understanding
Why cannot an unweighted road network prove the quickest journey?
Show answer
It does not supply journey times.
Links differ in length or speed; connectedness alone has no timing information.
Your turn
6 questions · 14 marks · Work at your own pace.
Read the questions online
- Libraries are vertices and direct delivery services are edges. Interpret an isolated vertex.2 marks
- Components are {A,B,C} and {D,E,F}. Suggest a link connecting them.2 marks
- A route has lengths 3.2,1.5,2.8 km. Find its total.2 marks
- A chain AB,BC,CD gains edge AD. Explain a reliability benefit.3 marks
- Why can a three-link route be shorter than a two-link route?2 marks
- A road model assumes every road is two-way and open. Give two limitations for emergencies.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Libraries are vertices and direct delivery services are edges. Interpret an isolated vertex.2 marks
Apply the stated vertex/edge rule.
A library without a direct service in the model. - Components are {A,B,C} and {D,E,F}. Suggest a link connecting them.2 marks
Choose endpoints in different components.
For example CD. - A route has lengths 3.2,1.5,2.8 km. Find its total.2 marks
3.2+1.5+2.8=7.5.
7.5 km. - A chain AB,BC,CD gains edge AD. Explain a reliability benefit.3 marks
The cycle gives an alternative route around a failed edge.
All vertices remain connected after any one of the four edges fails. - Why can a three-link route be shorter than a two-link route?2 marks
Link count and total distance are different quantities.
Its edge weights can have a smaller total. - A road model assumes every road is two-way and open. Give two limitations for emergencies.3 marks
Explain how each omitted condition affects actual reachability.
One-way restrictions and road closures may invalidate routes.
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 ↗