Graphs Are Everywhere

Graph Theory · Axiom Academy

Discover how the same mathematical structure connects social networks, cities, computers, and even molecules. Let's start with something familiar. Click on people in this friendship network to explore their connections! ✈ Step 2: Transportation Networks Now let's look at cities connected by flights. Click on cities to see their direct flight connections! Step 3: Explore Different Domains Graphs appear in many fields. Select different domains to see how the same structure appears everywhere! Step 4: Same Structure, Different Context Let's see how different real-world systems can have identical graph structures. A graph is a mathematical structure consisting of nodes (vertices) connected by edges . It's one of the most versatile tools in mathematics. The same graph structure appears in countless domains: social networks, transportation, the internet, biology, chemistry, computer science, and many more. Understanding graphs gives you a universal language for reasoning about connections. By stripping away context-specific details and focusing on the pure structure of connections, graph theory provides tools that work everywhere. An algorithm to find the shortest path works for road networks, social connections, and computer networks alike! In this course, you'll learn to think in graphs, understand their properties, and use powerful algorithms to solve real-world problems across any domain where connections matter.

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