How Robust Is a Transport Network?
Real transport networks build in backup lines and alternate routes on purpose, so a single closure does not cut off the whole system. Use a real train or metro network to work out how much of that redundancy is structurally necessary.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
A metro map looks redundant on purpose: most stations can be reached by more than one route, so a single line closure does not cut off half the city. Take a real train or metro network — the Paris Métro, the London Underground, or your own city's system — and represent it as a weighted graph. Strip it down to its minimum spanning tree, the cheapest set of connections that still reaches every station, and compare that bare-bones version with the real network. The difference is the redundancy engineers built in on purpose. Graph theory here is AI HL content (syllabus topics 3.14 to 3.16); if you are studying AI SL or an AA course, treat this as an extension beyond your normal syllabus.
Guiding Questions
- Choose a real metro or train network and represent it as a weighted graph, using journey time or distance as edge weights.
- Find the minimum spanning tree of your network using Kruskal's or Prim's algorithm. How many of the real lines does it keep, and how many does it cut?
- Remove one line from the real network. Which journeys become impossible, and which just get longer? Is the network still connected?
- How many lines would need to fail before your network splits into two disconnected pieces? Is that number the same everywhere on the network, or are some stations more exposed than others?