What is Graph Theory?

Graph theory is a concept of mathematics that deals with the study of graphs and their properties. A graph is a group of vertices (also called nodes) and edges connecting them. The vertices represent objects or entities, and the edges represent the relationships between them.

Graph theory is used to model and analyze various problems, including those in computer science, engineering, and the social sciences. Some of the key concepts in graph theory include:

A graph has two parts or components: 

• A node or a vertex can be used to define a graph, which is a type of data structure.
• A link between two nodes u, v that may be uniquely identified as an edge E or ordered pair is called a node (u,v).

Degree: The number of edges that are adjacent to a vertex determines its degree.

Path: A path defines a sequence of edges that connect a series of vertices.

Cycle: A cycle is a path that starts and ends at the same vertex.

Connectedness: A graph is connected if there is a path between two vertices.

Components: A graph can be divided into connected components, that are maximal connected subgraphs.

Trees: A tree is a form of a connected acyclic graph, meaning it has no cycles.

Graph theory has an extensive range of applications, including in computer science, where it is used to model networks and design algorithms for solving problems on graphs. It is also used in the social sciences to model social networks and to study the spread of diseases. In engineering, it is used to design communication networks and to model transportation systems.