Understand the idea.
Choose data to match the question
Choose a network whose edge meaning matches the question. The same towns can be linked by direct buses, roads or internet cables, producing different networks. Include every stated site and specify whether links are two-way.
When comparing journeys, attach weights with clear units, such as minutes. Add the weights along each route. A route with more edges can still take less time because the number of links and their total weight measure different things.
Say what the model cannot establish
Connectedness establishes reachability under the model’s rules. It does not supply information about speed, cost, accessibility or resilience unless the model includes suitable data for those questions.
Explain a recommendation by identifying the weakness it fixes. A new edge between separate components restores reachability; an alternative connection may help during a closure. Assess assumptions such as one-way travel, congestion and link capacity before applying the model.
See the method in action.
Join two groups
Edges are AB, BC, CA and DE. Add one edge so every vertex is reachable.
Worked solution
- 1
Find the existing components.
AB, BC and CA form one connected group; DE forms the other.
- 2
Join a vertex from each group.
C and D belong to different components, so the new edge connects the two groups.
- 3
Check that every vertex is reachable.
A and B already reach C, while E already reaches D. The new link therefore makes the whole network connected.
For example CD.
Compare weighted routes
A–B–D takes 8 and 9 minutes. A–C–E–D takes 4,5,3 minutes. Which is quicker?
Worked solution
- 1
Total the first route’s times.
A–B–D uses its two stated links in sequence.
- 2
Total the second route’s times.
A–C–E–D uses three links, whose times must all be included.
- 3
Compare the totals.
A–C–E–D has the smaller total, so it is quicker by 5 minutes despite using more links.
A–C–E–D is quicker by 5 minutes.
Try it yourself.
Check your understanding
Why cannot an unweighted road network prove the quickest journey?
Show answer & reasoning
It does not supply journey times.
An unweighted road network records links but supplies no journey times. Roads may have different lengths, speed limits or delays, so the fewest-link route need not be the quickest.
Keep practising
6 worksheet questions · 14 marks
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
.
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 ↗