How many flights does it take to get anywhere?

AI HLAI SL Ambitious Also in: Geometry & Voronoi

Research question

In the network of [a set of airports], what is the maximum number of flights needed to travel between any two (the diameter), and which airports would most reduce it if given one new route?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Airline networks have hubs, which keep journeys short. Building a network from OpenFlights data and asking where a new route would help most is a real network-design problem.

The mathematics you'll need

Directed graphs and adjacency matrices
Powers of the adjacency matrix to count routes
Shortest paths and diameter
Effect of adding an edge

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Routes and airports from OpenFlights; restrict to a region or airline to keep it manageable.

OpenFlights data — Airports (with latitude/longitude) and airline routes as CSV.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Choose and justify the subnetwork.
Build the adjacency matrix.
Use matrix powers to find shortest path lengths.
Find the diameter and critical pairs.
Test new routes and reflect on the data's age (a snapshot).

Pitfalls that cost marks

Using the whole world network (too large).
Ignoring that the data is an old snapshot.
Directed vs undirected routes unclear.

Showing personal engagement

Include your home airport.
Plan a real trip using your model.
Compare hub-and-spoke and point-to-point airlines.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Weight edges by distance and compare the shortest-by-flights and shortest-by-distance routes.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).