IA idea · Networks, graphs & algorithms
How connected is my year group? Analysing a friendship network
Research question
In an anonymised friendship network of my year group, what is the average shortest path between two students, and is the “friendship paradox” (your friends have more friends than you) true?
Adapt it: change the place, the data or the comparison until the question is yours.
Why it makes a good exploration
Network scientists study “small worlds” and the friendship paradox. With careful ethics, a year-group network gives unusual primary data and some surprising mathematics.
The mathematics you'll need
- Graphs, degree and degree distribution
- Adjacency matrices and powers to count paths
- Shortest path lengths
- Mean degree vs mean degree of friends
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
With teacher approval and consent, collect anonymised “who do you talk to regularly” data; never publish names.
- 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
- Plan the survey ethically and anonymously.
- Build the adjacency matrix.
- Compute degrees and path lengths.
- Test the friendship paradox.
- Reflect on survey honesty and one-way friendships.
Pitfalls that cost marks
- Any identifiable data in the IA.
- Directed vs undirected friendships not defined.
- Too small a network to say anything.
Showing personal engagement
- Explain why the paradox happens in your own words.
- Compare with an online network you use (conceptually).
- Discuss what the network means for spreading news or illness.
See Criterion C: personal engagement for what examiners look for.
Taking it further
Compare your network's clustering with a random network of the same size.