How does Google rank pages? PageRank on a small website

AI HLAA HL Ambitious Also in: Probability, Pure maths

Research question

What are the PageRank scores of the pages in [a small website such as my school's], found as the steady state of a Markov chain, and how sensitive are they to the damping factor?

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

Why it makes a good exploration

PageRank turned the web into a Markov chain. Mapping the links of a real small website and computing its ranking with matrices is advanced, authentic AI HL mathematics.

The mathematics you'll need

Adjacency and transition matrices
Steady-state vectors and eigenvectors with eigenvalue 1
The damping factor and why it is needed
Matrix powers with technology

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

Map the links between 8–15 pages of a small website by hand.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

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

Explain the random-surfer model.
Build the transition matrix.
Find the steady state (powers and eigenvectors).
Vary the damping factor.
Reflect on dead ends, link farms and what “importance” means.

Pitfalls that cost marks

Columns not summing to 1.
Dead-end pages not handled.
Presenting numbers without interpretation.

Showing personal engagement

Use your school's or club's website.
Suggest a link change to raise an important page and test it.
Compare the ranking with page visit counts if available.

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

Taking it further

Prove that the damped matrix has a unique steady state (outline the idea) or compare with simple link counting.

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).