Mathematics | Graph Theory Basics

Graph theory is a basic branch of discrete mathematics that mainly focuses on the relationship between objects. These objects are called vertices and these vertices are joined by edges. Graphs are common in computer science, network analysis, and many other everyday uses because they provide a good representation of connection, relationship, and process. Here we shall discuss graph theory, different types of graphs, terms used in the subject, and how to solve sample problems.

Graph Theory Basics

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 of the graph correspond to vertices and the relations between them correspond to edges. A graph is depicted diagrammatically as a set of dots depicting vertices connected by lines or curves depicting edges.
Formally,

“A graph $G=(V,E)$consists of $V$, a non-empty set of vertices (or nodes), and $E$, a set of edges. Each edge has either one or two vertices associated with it, called its endpoints.”