Study guide: Model Graphs and Compare Routes
Compare two paper paths: A-B-D has costs 2+8 minutes; A-C-E-D has costs 3+2+2 minutes. State hop counts,time totals and one missing real-world factor.
Ideas to explain in your own words
- A graph represents vertices and edges. A neighbor list records which vertices are directly connected. An edge does not automatically indicate distance or direction unless the model defines those features. The supplied undirected graph is fictional and complete; interpret adjacency rather than a picture’s spacing.
- Breadth-first exploration of an unweighted graph discovers vertices by hop distance from a start. Marking a vertex when discovered prevents adding it repeatedly. A queue holds discovered work waiting to be expanded. The supplied model asks for layers, not weighted shortest distance.
- A weighted route has a total cost equal to the sum of its edge costs under this additive model. The fewest-edge route can have a larger cost than another route. State the metric, such as minutes or energy units, before comparing paths; different metrics can favor different choices.
- A graph simplifies a system. Its available edges, direction, costs and updates determine what answers it can support. A route may fail in practice if the model omits closures, accessibility requirements or variable conditions. Keep the computed result separate from a guarantee about the real world.
Useful vocabulary
- graph
- Vertices connected by edges.
- neighbor
- A vertex directly connected by an edge.
- weight
- A stated edge cost or quantity.
Watch your reasoning
- Nearby labels on a diagram do not create an edge.
- Fewest hops need not mean minimum travel time when edges have different costs.
- Count of edges is not the same as sum of weighted costs.
- A shortest modeled path is not automatically usable by every traveler.
A worked review example
The distinct undirected edges are J–K, J–L, K–M and L–N. Put every edge in both endpoint lists: J:[K,L], K:[J,M], L:[J,N], M:[K], N:[L]. K has direct neighbors J and M. N is not a direct neighbor of K: the route K→J→L→N uses intermediate vertices. Nearby labels create no extra edges. These lists represent exactly the supplied connections, not every possible real network. Model may include a closed connection. Which omitted detail matters? The supported answer is Edge availability update. Identify which missing model detail affects the requested decision. A shortest modeled path is not automatically usable by every traveler. A graph simplifies a system. The supplied facts, rather than an assumed real-world detail, determine this paper case. Compare the recorded action or value with the stated rule before choosing an answer.
Make a practice plan
- Make a four-row summary, one row for each lesson, with its computing idea and one worked decision.
- Explain one tempting mistake using the actual supplied example.
- Complete the new unit review before consulting its explanations.
- Try the transfer task on paper and compare your evidence against the model response.