IA ideas library
Graph theory and network IA ideas (AI HL and beyond)
Graph theory turns routes, timetables and connections into mathematics. AI HL includes adjacency matrices, minimum spanning trees, the Chinese postman problem and travelling-salesman bounds; Markov chains and transition matrices sit next to them.
These ideas use networks you can draw yourself — your school, your bus routes, your delivery round — so the IA is personal by construction.
Networks, graphs & algorithms ideas (9)
- What is the shortest route to walk every corridor in my school?AI HLSolid
- What is the cheapest way to connect villages with fibre broadband?AI HLAI SLSolid
- Planning the shortest delivery round: bounds for the travelling salesman problemAI HLSolid
- How does Google rank pages? PageRank on a small websiteAI HLAA HLAmbitious
- How connected is my year group? Analysing a friendship networkAI HLAI SLSolid
- Which Underground station is the most central?AI HLAI SLSolid
- Will one phone brand take over? Brand loyalty as a Markov chainAI HLSolid
- How many flights does it take to get anywhere?AI HLAI SLAmbitious
- What is the fewest number of exam sessions my school needs?AI HLAA HLAI SLSolid
Also relevant (10)
- How fast does news spread through a year group?AI SLAI HLAA SLAA HLSolid
- Voronoi diagrams in a grid city: Euclidean or taxicab distance?AI SLAI HLAA HLAmbitious
- Which airport is really closest? Voronoi diagrams on a curved EarthAI SLAI HLAmbitious
- Should bigger hospitals get bigger regions? Weighted Voronoi diagramsAI HLAI SLAmbitious
- Why do flight paths curve on the map?AA SLAA HLAI SLAI HLAmbitious
- How does RSA encryption work, and how long would it take to break a small key?AA HLAA SLAmbitious
- How long does a game of Snakes and Ladders last?AI HLAA HLAmbitious
- Which Monopoly squares are landed on most often?AI HLAA HLAmbitious
- What are the chances of rolling a Yahtzee in one turn?AA SLAA HLAI SLAI HLSolid
- What are the odds in a Risk battle?AA SLAA HLAI SLAI HLSolid
Frequently asked questions
Is graph theory only for AI HL students?
It is only examined in AI HL, but anyone can use it if they explain it clearly. A small, carefully explained network is better than a huge one you cannot justify.
What software helps with graph theory?
A spreadsheet for matrices, GeoGebra for drawing, or a few lines of Python. Show one iteration of an algorithm by hand, then use technology for the rest.
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Other topics: Modelling · Calculus · Differential equations · Statistics · Probability · Geometry & Voronoi · Finance · Sport · Environment · Health & biology · Pure maths · Art & music · Games & puzzles