IA idea · Networks, graphs & algorithms
Which Underground station is the most central?
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?
Adapt it: change the place, the data or the comparison until the question is yours.
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
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
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.
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
- 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.
Taking it further
Weight edges by travel time and recompute centrality.