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Last Updated: Sep 23, 2023

# Applications of Graph Data Structure Ayush Mishra
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## Introduction

"Graphs have a wide range of applications in fields of study like computer science, mathematics, and engineering and are an effective tool for representing and analyzing complex relationships between data.”

In this blog, we will discuss the application of graph data structures and examine how they can be used to solve real-world problems.

## Graph Data Structure

Graphs, as non-linear data structures, consist of a limited set of nodes or vertices interconnected by edges. They offer practical solutions by mirroring various real-world scenarios, such as telephone networks, circuit networks, and social networks. For instance, in a telephone network, nodes symbolize individual users, while edges depict the connections forged through phone lines. Thus, graphs in data structures serve as powerful tools for modeling and addressing complex problems in a network-like fashion.

The application of graph data structure is used in computer science, mathematics, and physics and has many practical applications in fields such as computer networks, Artificial Intelligence, and logistics.

## Features and Properties of Graphs

A graph is a type of mathematical representation of a set of objects called vertices or nodes, and the connections are called edges. Some common features and properties of graphs include:

1. Degree: The degree of a vertex is the number of edges incident to it.

2. Path: A path in a graph is a sequence of edges that connects two vertices.

3. Connected: A graph is said to be a connected graph if a path exists between every pair of vertices.

4. Complete: A graph is said to be a complete graph if there is an edge between every pair of vertices.

5. Directed/Undirected: A graph is said to be directed if edges have a direction and undirected if edges do not.

6. Weighted/Unweighted: A graph is said to be weighted if edges have a value or weight associated with them and unweighted if they do not.

7. Cyclic/Acyclic: A graph is cyclic if a path begins and ends at the same vertex and acyclic if there is no such path.

8. Subgraph: A subgraph of a graph is a graph that is a subset of the vertices and edges of the original graph.

9. Adjacency Matrix: A matrix representation of a graph where rows and columns represent vertices, and the entries indicate the presence or weight of edges between them.

10. Incidence Matrix: A matrix representation of a graph where rows represent vertices, columns represent edges, and the entries indicate the presence of a vertex in an edge.

## Real-Life Applications of Graph Data Structure

Real-life application of graph data structure in various fields are:

1. Computer Science: Graphs are used to model many problems and solutions in computer science, such as representing networks, web pages, and social media connections. Graph algorithms are used in pathfinding, data compression, and scheduling.

2. Social Networks: Graphs represent and analyze social networks, such as the connections between individuals and groups.

3. Transportation: Graphs can be used to model transportation systems, such as roads and flights, and to find the shortest or quickest routes between locations.

4. Computer Vision: Graphs represent and analyze images and videos, such as tracking objects and detecting edges.

5. Natural Language Processing: Graphs can represent and analyze text, such as in syntactic and semantic dependency graphs.

6. Telecommunication: Graphs are used to model telecommunication networks, such as telephone and computer networks, and to analyze traffic and routing.

7. Circuit Design: Graphs are used in the design of electronic circuits, such as logic circuits and circuit diagrams.

8. Bioinformatics: Graphs model and analyze biological data, such as protein-protein interaction and genetic networks.

9. Operations research: Graphs are used to model and analyze complex systems in operations research, such as transportation systems, logistics networks, and supply chain management.

10. Artificial Intelligence: Graphs are used to model and analyze data in many AI applications, such as machine learning, Artificial Intelligence, and natural language processing.

## Real-life Example of Graph Data Structure

Some real-life examples of the application of graph data structure are:-

1. Social Network:  In a social network, individuals (represented as nodes) are connected through relationships (represented as edges). The nodes in this graph represent the individuals, and the edges represent their relationships, such as friendships or connections. The graph can analyze data such as the number of connections an individual has, the most popular individuals in the network, and the formation of communities within the network.

2. Transportation Network: A transportation network is another real-life example of a graph data structure. This could include a map of roads and highways, with intersections represented as nodes and the roads connecting them represented as edges.

The graph can be used to find the shortest route between two locations, the number of routes between two places, and the overall connectivity of the transportation network.

Additionally, it can be used for traffic management, route optimization, and fleet management. In short, the transportation network is an excellent example of a graph data structure that can be used to model real-world problems with nodes and edges.
Check out this problemNo of Spanning Trees in a Graph

### Which data structure is used in a graph?

The adjacency matrix, adjacency list, and adjacency set are three data structures that can represent a graph. An adjacency matrix can be considered a table with rows and columns, an adjacency list can be viewed as a node object, and an adjacency set is made up of adjacent vertices set.

### What is DFS?

An algorithm for navigating or searching through tree or graph data structures is called depth-first search (DFS). The algorithm begins at the root node (choosing an arbitrary node) and proceeds to explore each branch as far as it can go before turning around.

### What is BFS?

A tree or graph data structure is searched for a node that matches a set of criteria using the breadth-first search algorithm, or BFS. Before moving on to nodes at the following depth level, it starts at the tree's root or graph and investigates every node at the current depth level.

### Name the types of graph data structure.

Twelve types of graph data structures are directed graphs, undirected graphs, trivial graphs, regular graphs, complete graphs, cyclic graphs, acyclic graphs, finite graphs, infinite graphs, bipartite graphs, simple graphs, and connected graphs.

### How are graphs represented in data structure?

Graphs in data structures can be represented in two main ways: adjacency matrices and adjacency lists. An adjacency matrix uses a 2D array where each cell represents a connection. An adjacency list represents edges as a list for each node's connections.

## Conclusion

This blog discussed the application of graph data structure. A graph data structure is a powerful tool for representing and analyzing relationships between entities. It can be used in various applications, from social networks to navigation systems.