Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

Which Underground station is the most central?

AI HLAI SL Solid Also in: Statistics

Research question

Using a graph of the London Underground (or another metro), which stations have the highest degree and closeness centrality, and how well do these measures predict station passenger numbers?

Make it yours, then agree it with your teacher.

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Why it makes a good exploration

Transport networks are graphs with real weights. Computing centrality and comparing it with TfL's passenger counts tests whether network position explains how busy a station is.

The mathematics you'll need

Graphs, degree and shortest paths
Closeness centrality (explain)
Correlation between centrality and passenger counts
Spearman's rank

Where the data comes from

Build the graph from the official map (one or two lines, or zone 1); station entry/exit counts from TfL open data.

Transport for London open data — Timetables, station entry/exit counts, cycle-hire journeys and air quality for London.

Real data for this idea

Primary source: Transport for London open data: Station crowding and entry/exit counts. Use the yearly entries and exits per station as weights for your network. Licence: Check TfL's open data terms; attribution is required.

Links checked October 2026; we link to the data and never copy it. More free data sets.

A possible outline

Define the graph (stations as vertices, links as edges).
Compute degree and closeness.
Rank stations.
Correlate with passenger counts.
Reflect on interchanges, tourism and rail connections.

Pitfalls that cost marks

A network too large to handle — restrict it sensibly.
Unweighted edges without justification.
Ignoring mainline rail interchanges.

Showing personal engagement

Use a metro you know.
Predict the most central station first.
Propose a new link and measure its effect.

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

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Not a natural fit	The core technique sits in the AI course or at HL; an AA SL student could use it only as clearly explained new mathematics.
AA HL	Not a natural fit	The mathematics is mainly from the AI course; at AA HL the exploration would need an AA-level approach (calculus, proof or probability theory) to reach the top of Criterion E.
AI SL	Good fit	Graphs, degree and shortest paths; Closeness centrality (explain)
AI HL	Good fit	Graphs, degree and shortest paths; Closeness centrality (explain)

Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: a network too large to handle — restrict it sensibly; and unweighted edges without justification. Say how each one affects your answer.

Use of mathematics (E)

SL: graphs, degree and shortest paths; closeness centrality (explain); correlation between centrality and passenger counts; spearman's rank, each explained in your own words and carried out correctly.

How networks & graphs explorations reach the top bands in general: Networks, graphs & algorithms IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Weight edges by travel time and recompute centrality.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL networks & graphs exploration adds.

See a complete IA, marked

What is the quickest way to deliver a leaflet to every house on my estate? (AI HL) is a complete networks & graphs exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AI HL and AI SL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Graphs, degree and shortest paths, closeness centrality (explain), correlation between centrality and passenger counts and spearman's rank.

Where can I get data for this IA?

Build the graph from the official map (one or two lines, or zone 1); station entry/exit counts from TfL open data. Checked sources and tools: Transport for London open data.

Turn this idea into your IA

The planner opens with “Which Underground station is the most central?” filled in: the question, the maths and the data sources.

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