Graph Theory: The Math of What's Connected to What

A graph is just a map of relationships: who is friends with whom, which files import which other files, how data flows through a network. This guide teaches you to think in connections, find the shortest path, and see the graph theory running your package manager, your social feed, and the internet itself.

1. Nodes, Edges, and the Graphs You Already Use A graph is nothing more than a collection of things and the connections between them. The things are nodes, the connections are edges, and the pattern shows up in social networks, dependency trees, and the internet itself. This phase teaches you to see and draw graphs.
2. Finding the Shortest Path and Detecting Cycles Once you can draw a graph, the natural questions are: what is the shortest route from A to B, and does this graph loop back on itself? This phase covers BFS, DFS, Dijkstra's algorithm, and the cycle detection that saves package managers from infinite loops.
3. Graphs That Run the World Graphs are not a niche math topic. They are the structure behind Google search, social networks, package managers, and the internet itself. This phase connects the nodes and edges you have learned to the systems you use every day.