A little room to wonder

Transport Networks & Routes

A transport network represents places as nodes and connections as links. Comparing routes means adding the right link values under stated rules, rather than trusting whichever line looks shortest on a sketch.

Can a route with three links have a smaller total than a route with only two?

An iron bridge provides a visible connection between two riverbanks.
A bridge can be one link in a wider transport network. Its photographed length is not used for any of the invented four-node distances.Daniel Schwen · Source · CC BY-SA 3.0

Represent connections before judging a route

In a network, nodes stand for selected places and links for connections between them. A number on a link might represent distance, time or another cost. Choose one meaning at a time. A diagram can show the correct connections without being drawn to geographic scale.

Direction also matters. An undirected link can be used both ways in the model; an arrow permits only its indicated direction. A missing link means the model supplies no direct connection. It does not mean the places are physically next to each other or that travel takes zero time.

Worked example: compare all simple routes

An invented network has these two-way distances: A–B four units, B–D three, A–C two, C–D eight and B–C one. There is no direct A–D link. Without revisiting nodes, possible A-to-D routes are A–B–D = seven, A–C–D = ten, A–B–C–D = thirteen, and A–C–B–D = six.

Six is the smallest total in this complete list of simple routes. It uses three links, so fewest links and shortest total are different goals. Because all link distances are positive, adding a loop that revisits a node cannot improve this distance total. That conclusion depends on the chosen positive distance model.

A route objective changes the answer

Distance is not travel time. To compare time, you need time values, including any waiting or transfer rules the model chooses to include. A single short link could be slow, and a longer link could be quicker. Reusing distance numbers as minutes silently changes the evidence.

Likewise, a shortest route may not answer a question about required stops or usable facilities. Write the objective first, then check every candidate against its constraints. The network can support a transparent comparison without deciding what a real traveller should do.

Record the assumptions with the result

A useful route explanation lists the links, their units, direction rules and calculation. Keeping the rejected alternatives makes a minimum claim easier to assess. Testing only two routes supports a comparison between those two, not a claim about every possible route.

The four-node example is fully fictional. You can change a link or make it one-way and work through the consequences on paper. No current timetable, personal journey, booking or travel through an unfamiliar place is needed.

Only if you feel like trying

Find the shortest paper route

  1. Draw the five supplied links with their distance values and mark them two-way. List the four simple A-to-D routes.
  2. Calculate every total and identify why fewest links does not select the shortest distance here.
  3. Change B–C to a one-way link from B to C. Recheck which routes remain possible and which is now shortest.

Optional fictional network calculation. This is not current transport information or real-trip planning.