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Graph theory is a branch of mathematics that deals with the study of graphs. A graph is a mathematical representation of a set of objects, called vertices or nodes, connected by links, called edges. Graphs are a fundamental tool for modeling and solving problems in various fields, including computer science, operations research, social sciences, biology, and many others.
 
In a graph, vertices represent entities, and edges represent relationships between these entities. Graph theory focuses on understanding the properties and relationships between these entities and how they are connected.

Here are some key concepts in graph theory:

Vertex (Node): A fundamental element of a graph, representing an entity or an object.

Edge (Link): A connection between two vertices, representing a relationship between the corresponding entities.

Degree of a Vertex: The number of edges incident to a vertex. In a directed graph, there is an in-degree and an out-degree for each vertex.

Directed Graph (Digraph): A graph in which edges have a direction, indicating the flow or direction of a relationship between vertices.

Undirected Graph: A graph in which edges have no direction, and relationships between vertices are symmetric.

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