**What Is Graph in Data Structure PDF?**

A graph is a fundamental data structure in computer science and is widely used to represent relationships between objects. In this article, we will explore what a graph is and how it is represented in data structure PDFs.

## The Basics of Graphs

A graph consists of a set of vertices (also known as nodes) connected by edges. These vertices can represent any entity, such as cities, people, web pages, or even molecules.

The edges represent the connections or relationships between these entities.

Graphs are used to model various real-world scenarios. For example, in social networks, vertices can represent individuals, and edges can represent friendships or connections between them.

Similarly, in transportation networks, vertices can represent locations, and edges can represent roads or routes between them.

## Types of Graphs

Graphs can be classified into different types based on their properties and the nature of the relationships they represent. Some common types of graphs include:

**Undirected Graph:**In an undirected graph, the edges have no direction associated with them. This means that if there is an edge connecting vertex A to vertex B, there is also an edge connecting vertex B to vertex A.**Directed Graph:**In a directed graph (also known as a digraph), the edges have a specific direction associated with them.This means that if there is an edge connecting vertex A to vertex B, there might not necessarily be an edge connecting vertex B to vertex A.

**Weighted Graph:**In a weighted graph, each edge has a weight or cost associated with it. These weights can represent various factors, such as the distance between two locations or the cost of traveling between them.

## Representing Graphs in Data Structure PDFs

When representing graphs in data structure PDFs, different methods can be used based on the requirements and the operations that need to be performed on the graph. Some commonly used representations include:

### Adjacency Matrix:

In an adjacency matrix representation, a matrix of size N x N is used, where N is the number of vertices in the graph. Each cell of the matrix represents an edge between two vertices.

If there is an edge between vertex i and vertex j, then cell (i, j) will contain a non-zero value. Otherwise, it will contain zero.

### Adjacency List:

In an adjacency list representation, each vertex in the graph has a list associated with it. This list contains all the vertices that are directly connected to the given vertex by an edge.

This representation is memory-efficient compared to the adjacency matrix representation for sparse graphs (graphs with fewer edges).

These are just two examples of how graphs can be represented in data structure PDFs. There are other representations as well, such as incidence matrix and edge list, which have their own advantages and use cases.

## Conclusion

In summary, a graph is a powerful data structure that allows us to represent relationships between entities. Whether it’s analyzing social networks or optimizing transportation routes, graphs play a crucial role in various applications.

Understanding different types of graphs and their representations in data structure PDFs is essential for effective problem-solving and algorithm design.