ideaLive
Search Algorithms
A landing page for BFS, DFS, Dijkstra, A*, Bellman-Ford and Floyd-Warshall.
Beauty in maths topic
Graphs and Networks
Graphs and networks describe relationships: routes, dependencies, colours, flows, spread and structure.
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live pages
6
prototype tools
5
planned ideas
What this area includes
Search algorithms: BFS, DFS, Dijkstra, A*, Bellman-Ford and Floyd-Warshall
Colouring, planarity and map problems
Random graphs and networks that change suddenly
Connections to epidemics, diffusion and Markov chains
Questions to explore
What changes when we focus on connections instead of coordinates?
Which properties are local and which are global?
How can a network suddenly become connected?
Working pages and tools
These are the pages currently available to open from this topic.
ToolPrototype
Graph Theory Visualiser
Build graphs and compare BFS and DFS traversal step by step.
ToolPrototype
Dijkstra Visualiser
Explore weighted shortest paths, tentative distances and settled nodes.
ToolPrototype
A* Search Visualiser
Explore goal-directed shortest path search using g, h and f scores.
ToolPrototype
Graph Colouring Visualiser
Use greedy colouring and compare vertex-order strategies.
ToolPrototype
Random Graph Lab
Explore G(n, p), connected components and random network behaviour.
ideaLive
Integer Orchard
A thought experiment connecting rational slopes, irrational directions and exact lattice hits.
ToolPrototype
Planarity and Map Colouring
Explore planar graphs, Euler's formula, crossings and why maps become graph-colouring problems.
Planned directions
These ideas are not built yet, but they show where this topic could grow next.
ideaPlanned
Non-Euclidean Music
Planned exploration of musical patterns generated by curved, warped or graph-like spaces.
ideaPlanned
Musical Graphs
Planned exploration of chord progressions, voice leading and melodic movement as networks.
ideaPlanned
Network Epidemics
Planned bridge between graph networks, probability and differential-equation models of spread.
ideaPlanned
Diffusion on Graphs
Planned exploration of heat, pollution or information flowing across connected networks.
ideaPlanned
Markov Chain Explorer
Planned lab linking probability, matrices and long-run behaviour in systems that move between states.
Connected topics
themeLive
Beauty in Maths
A portal for connected mathematical explorations: pattern, surprise, structure, nature and emergence.
themeLive
Maths in Music
Rhythm, tuning, symmetry, timing, pattern and musical structure through mathematics.
themeLive
Cryptography and Secret Messages
Codes, ciphers, primes, modular arithmetic, public keys and secure communication.
themeLive
Topology and Surfaces
Shape, connectedness, holes, surfaces, knots and geometry that survives stretching.
themeLive
Operations Research
Optimisation, scheduling, routing, allocation and making good decisions under constraints.
How to use this section
This is one of the strongest bridges between mathematics and computer science.