The mathematics of things and the connections between them. It's behind your map app, your social feed and the internet itself. Eleven units, lots of pictures, and no prior knowledge needed beyond basic arithmetic.
Start with Unit 1Every concept starts in plain words, with no symbols until you need them.
A diagram for every new idea. Some respond when you hover over or tap them.
Worked examples from real life: friendships, roads, timetables, tournaments.
Short questions throughout, with answers hidden until you're ready.
Eleven units, all available now. Work through them in order: each one builds on the vocabulary of the units before it.
Vertices, edges and degree; the handshake lemma; directed and weighted graphs; common graph families; how to store a graph.
Walks, paths and cycles; connected pieces; distance; the single vertex or edge whose loss splits a network.
Graphs with no cycles; why a tree with n vertices has n − 1 edges; spanning trees; cheapest networks with Kruskal's and Prim's methods.
Breadth-first and depth-first search; finding your way out of a maze; putting tasks in a valid order.
Dijkstra's algorithm, step by step; negative weights with Bellman–Ford; all distances at once with Floyd–Warshall.
The seven bridges of Königsberg; when you can trace a graph without lifting your pen; routes for postmen and travelling salespeople.
Bipartite graphs; pairing people with jobs; Hall's marriage theorem; stable matchings.
How much can a pipe network carry? Maximum flow, minimum cut, and the surprising fact that they are equal.
Scheduling exams without clashes; the chromatic number; greedy colouring; the four colour theorem.
Graphs you can draw with no crossings; Euler's formula V − E + F = 2; the three utilities puzzle.
Ramsey theory, random graphs, what matrices reveal about graphs, and how real-world networks are shaped.