# Learn Graph Theory

> A free, interactive algorithm visualizer for learning graph theory and operations research. The platform offers 30+ step-by-step algorithm visualizations (BFS, DFS, Dijkstra, MST, TSP, network flow, and more), structured lessons, practice problems, and in-depth articles. Aimed at computer science students, coding-interview candidates, and educators. All content is free and available in English, French, Spanish, German, and Chinese.

## Algorithm Visualizations
Interactive, step-by-step visualizations with real-time execution. Each page explains the algorithm, its complexity, and use cases.

- [Breadth-First Search (BFS)](https://learngraphtheory.org/algorithm/bfs)
- [Depth-First Search (DFS)](https://learngraphtheory.org/algorithm/dfs)
- [Dijkstra's Shortest Path](https://learngraphtheory.org/algorithm/dijkstra)
- [Bellman-Ford](https://learngraphtheory.org/algorithm/bellman-ford)
- [Floyd-Warshall](https://learngraphtheory.org/algorithm/floyd-warshall)
- [Prim's Minimum Spanning Tree](https://learngraphtheory.org/algorithm/prim)
- [Kruskal's Minimum Spanning Tree](https://learngraphtheory.org/algorithm/kruskal)
- [Boruvka's Algorithm](https://learngraphtheory.org/algorithm/boruvka)
- [Tarjan's Strongly Connected Components](https://learngraphtheory.org/algorithm/tarjan-scc)
- [Kosaraju's Strongly Connected Components](https://learngraphtheory.org/algorithm/kosaraju-scc)
- [Topological Sort](https://learngraphtheory.org/algorithm/topological-sort)
- [Articulation Points](https://learngraphtheory.org/algorithm/articulation-points)
- [Bridges](https://learngraphtheory.org/algorithm/bridges)
- [Traveling Salesperson Problem (TSP)](https://learngraphtheory.org/algorithm/tsp)
- [Hamiltonian Path](https://learngraphtheory.org/algorithm/hamiltonian-path)
- [Eulerian Path](https://learngraphtheory.org/algorithm/eulerian-path)
- [Graph Coloring](https://learngraphtheory.org/algorithm/graph-coloring)
- [Maximal Clique](https://learngraphtheory.org/algorithm/maximal-clique)
- [Bipartite Check](https://learngraphtheory.org/algorithm/bipartite-check)
- [Cycle Detection](https://learngraphtheory.org/algorithm/cycle-detection)
- [Maximum Flow](https://learngraphtheory.org/algorithm/max-flow)
- [Minimum Cut](https://learngraphtheory.org/algorithm/min-cut)
- [Chordality](https://learngraphtheory.org/algorithm/chordality)
- [Facility Location](https://learngraphtheory.org/algorithm/facility-location)
- [K-Means Clustering](https://learngraphtheory.org/algorithm/k-means-clustering)
- [Multi-Vehicle Routing](https://learngraphtheory.org/algorithm/multi-vehicle-routing)
- [Capacitated Vehicle Routing](https://learngraphtheory.org/algorithm/capacitated-vehicle-routing)

## Lessons
Guided lessons that build graph theory understanding from fundamentals to advanced topics.

- [Introduction to Graphs](https://learngraphtheory.org/lesson/introduction-to-graphs)
- [Fundamental Structures](https://learngraphtheory.org/lesson/fundamental-structures)
- [Trees and Applications](https://learngraphtheory.org/lesson/trees-applications)
- [Graph Traversal](https://learngraphtheory.org/lesson/graph-traversal)
- [Shortest Path Algorithms](https://learngraphtheory.org/lesson/shortest-path-algorithms)
- [Minimum Spanning Trees](https://learngraphtheory.org/lesson/minimum-spanning-trees)
- [Graph Connectivity](https://learngraphtheory.org/lesson/graph-connectivity)
- [Network Flow](https://learngraphtheory.org/lesson/network-flow)

## Articles
In-depth explanatory articles covering algorithms, theory, and applications.

- [BFS vs DFS: Key Differences](https://learngraphtheory.org/articles/bfs-vs-dfs.html)
- [Shortest Path Algorithms](https://learngraphtheory.org/articles/shortest-path-algorithms.html)
- [Minimum Spanning Trees (MST)](https://learngraphtheory.org/articles/minimum-spanning-trees.html)
- [Traveling Salesperson Problem (TSP)](https://learngraphtheory.org/articles/traveling-salesperson-problem.html)
- [Vehicle Routing Problem (VRP)](https://learngraphtheory.org/articles/vehicle-routing-problem.html)
- [Max-Flow Min-Cut Theorem & Network Flow](https://learngraphtheory.org/articles/network-flow-max-flow-min-cut.html)
- [Graph Coloring Problem](https://learngraphtheory.org/articles/graph-coloring-problem.html)
- [A* Search Algorithm: Step-by-Step Guide + Visualizer](https://learngraphtheory.org/articles/a-star-search-algorithm.html)
- [Graph Algorithms Time Complexity](https://learngraphtheory.org/articles/graph-algorithms-complexity.html)
- [History of Graph Theory](https://learngraphtheory.org/articles/history-of-graph-theory.html)
- [Applications of Graph Theory](https://learngraphtheory.org/articles/applications-of-graph-theory.html)
- [Graph Theory in Software Engineering](https://learngraphtheory.org/articles/software-engineering-concepts.html)
- [Graph Algorithms for Coding Interviews](https://learngraphtheory.org/articles/coding-interviews.html)
- [Graph Theory Interview Questions](https://learngraphtheory.org/articles/interview-questions.html)

## Key Pages

- [Home](https://learngraphtheory.org/)
- [All Algorithms](https://learngraphtheory.org/algorithms)
- [All Lessons](https://learngraphtheory.org/lessons)
- [Practice Problems](https://learngraphtheory.org/practice)
- [Blog & Articles Index](https://learngraphtheory.org/articles/)
- [FAQ](https://learngraphtheory.org/faq.html)

## Optional

- [Developers](https://learngraphtheory.org/developers)
- [Sitemap](https://learngraphtheory.org/sitemap.xml)