Explore the basics of graph theory, learn to represent graphs in C++, and master essential algorithms like DFS and Dijkstra to solve complex optimization problems, including matching and network flow.

Graph algorithms are the core of many real-world applications of computer science,  such as automotive navigation or routing in computer networks. They’re also a common subject in coding interviews at top-tier tech companies.
 
In this course, we’ll learn about the basic concepts of graph theory and how to represent graphs as data structures in code. We’ll study essential graph algorithms such as depth-first search or Dijkstra's algorithm to traverse graphs and find shortest paths. Finally, we’ll learn to solve more complex optimization problems on graphs, such as matching and network flow problems.

Learn Graph Algorithms in C++

# Adjacency

For an edge $e = (u, v)$ that connects node $u$ to node $v$, we say that $v$ is **adjacent** to $u$, or that $v$ is a **neighbor** of $u$. The edge $e$ is called **incident** to both $u$ and $v$. 

The number of neighbors of a node $v$ is called the **degree** of $v$, written deg($v$). 

In the following example graph, $c$ is a neighbor of $b$, as there is an edge $(b, c)$. But $b$ is not a neighbor of $c$, as there is no edge $(c, b)$. The degree of node $a$ is deg$(a) = 2$, as it has two neighbors.

Learn about the fundamental concepts of graph theory, such as adjacency and paths.

Introduction

Graph Representations

Graph Traversal

Shortest Paths

Spanning Trees

Flow Problems

Conclusion

Appendix

Graph Terminology I

Adjacency