What is Graph Theory?

Graph Theory · Axiom Academy

Discover how mathematics reveals the hidden structure of connections all around us. Below is a simple graph. Click on the circles (vertices) and the lines (edges) connecting them to explore! Graph theory ignores physical details and focuses purely on structure. Click on each network type to see how different real-world systems can all be represented as graphs! People are vertices, friendships are edges Stations are vertices, routes are edges Pages are vertices, links are edges Atoms are vertices, bonds are edges Click anywhere in the canvas below to add vertices. Click on two vertices to connect them with an edge. Explore how relationships build! What Problems Can Graph Theory Solve? Graph theory isn't just about drawing dots and lines. It's a powerful tool for solving real-world problems! Finding the shortest path between two locations, whether you're delivering packages or routing data packets across the internet. Scheduling exams without conflicts, assigning radio frequencies, or coloring maps so no adjacent regions share the same color. Building efficient networks like power grids or computer networks by finding spanning trees that connect all vertices with minimal total edge weight. Understanding how robust a network is, identifying critical connections, and analyzing social influence patterns. Graphs are just vertices and edges. This simplicity makes them incredibly powerful for representing any kind of relationship or connection.

This is the written version of the interactive lesson above. See the full Graph Theory course.