# Graph

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**What is a graph?**

A graph is a pictorial representation of data and values which are represented in an organized manner.

In terms of data structures, a graph is an abstract data type which implements graph theory concepts such as the implementation of **directed and undirected graphs**.

**Graph** is a very important concept in data structures. It can be defined as:

- A graph is a non-linear data structure.
- It is a flow structure consisting of nodes and edges.
- It consists of a finite number of vertices and edges which are connected using links.
- A graph is a pair of the set
**(V, E)**, where**V**is the set of vertices or nodes and**E**is the set of edges, interconnected by lines or edges. - The edges contain weights or cost if the graph is a weighted graph.

This figure illustrates a graph which consists of a finite number of vertices called **nodes** and finite set of ordered pair **(u,v)** called **vertices**.

The** (u,v)** in vertices represent that an edge exists from edge **u** to edge **v**.

The graph is represented in the form of Adjacency Matrix, Adjacency List, Incidence Matrix and Incidence List.

**The basic operations to be performed are adding vertices, edges and displaying the graph by its vertices.**

The Adjacency Matrix represents the graph in a 2D matrix. The Adjacency List is the representation of the graph in the form of Linked Lists. Also, using these values we can represent it in the form of programs.