Graph theory is a branch of mathematics that deals with the study of graphs. A graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects are called nodes or vertices and the relations are called edges.

Basic Concepts

  • Vertices: These are the individual points or nodes in a graph.
  • Edges: These are the connections between the vertices.
  • Degree of a vertex: The number of edges connected to a vertex.
  • Path: A sequence of vertices connected by edges.
  • Cycle: A path that starts and ends at the same vertex.

Types of Graphs

  • Undirected Graph: Edges have no direction.
  • Directed Graph: Edges have a direction.

Applications

Graph theory has applications in various fields such as computer science, operations research, and social sciences.

Example

Here is a simple example of a graph:

A -- B -- C
|       |
D -- E -- F

This is a directed graph where each node is labeled with a letter.

Learn More

To learn more about graph theory, you can visit our Graph Theory Tutorial.

Graph Theory

If you're interested in the history of graph theory, you can read about it in our History of Graph Theory section.