**What Is Graph With Example in Data Structure?**

In data structure, a graph is a non-linear data structure that consists of nodes (also known as vertices) and edges. It is a powerful tool used to represent relationships between different entities.

A graph can be used to model various real-world scenarios such as social networks, transportation networks, computer networks, and more.

## Graph Components

A graph consists of two main components:

**Nodes (Vertices):**These are the fundamental units of a graph. Each node represents an entity or an object.For example, in a social network graph, each node can represent a person.

**Edges:**These are the connections or relationships between nodes. They represent the link or interaction between the entities represented by the nodes. For example, in a social network graph, each edge can represent a friendship between two people.

## Types of Graphs

There are several types of graphs based on their characteristics and properties. Some common types include:

**Undirected Graph:**In this type of graph, the edges have no direction. The relationship between nodes is symmetric. For example, if there is an edge connecting node A to node B, it implies that there is also an edge connecting node B to node A.**Directed Graph (Digraph):**In this type of graph, the edges have a specific direction. The relationship between nodes is asymmetric.For example, if there is an edge connecting node A to node B, it does not imply that there is also an edge connecting node B to node A.

**Weighted Graph:**In this type of graph, each edge is assigned a weight or cost. These weights can represent various properties such as distance, time, or cost. Weighted graphs are commonly used in route planning algorithms or optimization problems.**Cyclic Graph:**A cyclic graph is a graph that contains at least one cycle (a path that starts and ends at the same node). In other words, it is possible to traverse the graph and return to the same node without revisiting any other node.**Acyclic Graph:**An acyclic graph is a graph that does not contain any cycles. It is not possible to traverse the entire graph and return to the same node without revisiting any other node.

## Graph Example

To better understand graphs, let’s consider an example of a social network.

Suppose we have a social network with five individuals: Alice, Bob, Claire, David, and Emma. We can represent this social network using a graph.

Here is how the graph representation would look like:

Alice ----- Bob | | Claire ----- David ----- Emma

In this example, each person is represented by a node (vertex), and the friendships between them are represented by edges. For instance, there is an edge between Alice and Bob because they are friends. Similarly, there are edges between Claire and David, David and Emma.

This graphical representation helps us visualize the relationships between individuals in the social network.

### Conclusion

In summary, a graph is a versatile data structure used to represent relationships between entities. It consists of nodes (vertices) and edges, and it can be used to model various scenarios.

Understanding graphs is essential for solving complex problems and designing efficient algorithms.