Application of Graph Theory in Real Life:

Application of graph theory in real life – Graph theory is an area of mathematics that studies the structure of networks and relationships among objects. In recent years, its applications have extended far beyond mathematics, and it is now applied in many practical, real-world scenarios. Applications of Graph theory are useful in real life as well. Perhaps we are unaware that we are employing graph theory in our daily lives. In fact, graph theory is used in so many of our daily routine activities. Graphs are the basis of many things, ideas, concepts, operations, and processes in everyday life.

We know that everything in our world is interconnected; for example, cities are connected by road, rail, and air networks; hyperlinks connect webpages on the internet; an electric circuit or a computer chip’s various components are connected, and so on. Graph theory can assist engineers, scientists, and other professionals who want to analyze, comprehend, and optimize these networks.

Graph Theory is used in almost every area of interest and for many reasons in day-to-day life. Graphs are used in a variety of fields, including medicine, criminology, and even as a simple teenager problem of spreading rumors. In the real world, graph theory is used in the internet field, Google maps/ Yahoo maps, social media, web Page searching, City Planning, Traffic Control, Transportation & Navigation, Travelling Salesman Problems, GSM mobile phone networks, Map coloring, timetable scheduling etc. Graph theory can also be used to determine how viruses spread across borders or cities. Graph theory is used in biology and medicine to distinguish drug targets, decide the job of proteins or determine the qualities of vague capacity.

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So, let’s take a closer look at interesting applications of graph theory used in day-to-day life.

1. Applications of graph theory in the field of the Internet –

The Internet is the world’s most extensive and largest network ever devised by humankind. The Internet is thought to be a giant, virtual graph.

♦ Graph theory applications in Web Page search:

Websites and pages are linked in a graph, in web search engines such as Google, Yahoo, and Bing, which helps to rank websites and makes it possible for Google to display the best result at the top.

In web search engines such as Google, Yahoo, Bing, and others, it searches for web pages, where web pages are linked to each other on the Internet via hyperlinks. In the graph, every vertex represents a separate webpage, and every edge represents a link (or hyperlink) between two pages. It is important to note that links only go one way, so this graph is directed and extremely large.

The algorithms ‘PageRank‘ and ‘Googlebot‘ are used to help the connectivity process. The graph connects web pages and sites, which helps to rank pages and enables google to display the best page.

Some websites receive a large number of incoming links, whereas many smaller websites receive very few. This is the fundamental concept that Google employs when sorting search results. Websites with more incoming links are considered to be of higher quality and appear near the top of search results. Hence, a simple idea from graph theory, the PageRank Algorithm, helped Google outperform other search engines.

♦ Applications of graph theory in Social Media in connecting friends:

Consider one of the most common examples of graphs in everyday life: social media. In social media, the concept of graph theory is widely used. Graph theory applications are used connecting friends on social media. Users in social networking sites such as Facebook, Whatsapp, Messenger, Twitter, Google+, Linkedin, etc. are linked through a large graph. Here, people or users are represented by the vertices, and any connection between the users, such as followers, friendships, likes, or subscriptions, are represented by the edges.

Graph theory is used in connecting with people through a viral video. Each user is a vertex in this case, and when users connect, they form an edge. When a video reaches a certain number of connections/views, it is said to be viral. Strong and weak ties on social media are represented by graph theory.

♦ Applications of graph theory in using GPS (Google maps/ Yahoo maps):

Graph Theory is applied to use GPS to find a route based on user preferences (quickest route/shortest route) or to find the cheapest fare between two locations (destinations). In this case, the locations are represented by vertices, and their connections are represented by edges that contain information such as distance or fare. Based on the user settings, the software evaluates the critical path (optimal route).

♦ Uses of graph theory to map out the relationships between various entities:

One of the most important uses of graph theory is in mapping out the connections between different entities. For example, graph theory can be used to map out social networks, such as Facebook or Twitter, and analyze how people are connected to each other. Graph theory can also be used to map out networks of computers and analyze how they are connected to each other.

Read Also: Application of Graph Theory in Various Fields

2. Application of graph theory in Traffic Management –

Transport networks and traffic management are extremely important to the communication networks developing air and road transport systems. Graphs are also useful in transportation, navigation (route planning) and traffic control. Graphs can represent all flight, train, and subway networks, which can be used to develop efficient schedules.

Graph Theory is used to create an Intelligent Transportation System (ITS). In the future, the intelligent transportation system will use location data collected from smartphones and self-driving cars to alleviate traffic congestion and accidents more efficiently by routing cars.

With the help of this system, we could save millions of hours lost on the road each year, reduce environmental pollution, and enable emergency services to travel more quickly.

♦ Application of graph theory in Flight Networks:

Airlines use graph theory to connect innumerable cities in the most efficient way possible.

• The goal of a safe and orderly flow of traffic is achieved using Graph Theory.
• Air traffic controllers use Graph Theory to organize the air spaces and avoid crashes.
• Graph Theory is used to alleviate traffic congestion.

♦ Application of graph theory in Road Networks:

Graph Theory is used to create a perfect road transportation system as well as an intelligent transportation system. All roads and highways also form a large network that navigation services (like Google Maps) use to find the shortest route between two places.

• To travel faster, Graph Theory is used.
• Graph Theory is used to alleviate traffic congestion.
• Graph Theory is used to prevent vehicle accidents.

3. Application of graph theory in Traffic Lights –

Graph Theory is used in the operation of traffic lights, specifically the turning of Green/Red and the timing between them.

Here, we use the Vertex Coloring Technique to resolve time and space conflicts by identifying the chromatic number for the number of cycles required.

4. Application of graph theory in solving Crimes –

In the real world, it is the most important application of graph theory.

Graph theory, as you may be aware, is all about linking and the analysis of linking. It can assist you in tracing the one who spread the false rumour to a mastermind of a serious crime. Graph methods can be used in criminal investigation systems. In this case, it is supposed that the investigation’s people (occurrences) are represented by vertices of a graph, and edges represent possible connections.

5. Application of graph theory to clear Road Blockage –

When a city’s roads are blocked due to ice, the city plans to salt the roads. But advance planning is required to put salt on the roads.

In this situation, we use Euler paths or circuits to traverse the streets in the most efficient manner.

6. Application of graph theory to Develop Routes –

With the help of graph theory, a school administration plans to develop bus routes to pick up students and deliver them to school. Each stop is represented by a vertex, and the route is represented by an edge. In this case, we use a Hamiltonian path to represent the efficiency of including every vertex in the route.

With the help of graph theory, when visiting a water park, theme park, or zoo, you can plan an efficient route to visit a specific attraction or all of the attractions. Every vertex in the graph is represented by a Hamiltonian path or circuit.

7. Application of graph theory in GSM Mobile Phone Networks and Map Coloring –

All mobiles connect to the GSM network by scanning for nearby cells. For any GSM mobile phone network, the Vertex Colouring Algorithm can be used to allocate at most four distinct frequencies.

Only four frequency ranges are sufficient to operate GSM. Because according to the Vertex Colouring Algorithm, the map of cellular regions can be properly colored by using only four different colours.

8. Graph coloring – Applications of graph theory in solving Sudoku’s puzzles –

Graph coloring is a powerful tool for solving complex problems. It can be applied to solve real-world problems in many fields and even solve puzzles like Sudoku.

The application of graph theory in solving Sudoku puzzles is a real-life example. Individual cells on a Sudoku grid are colored using graph coloring. Each cell must be assigned a color, and no two cells of the same color can be adjacent. To do this, assign a color to each vertex and check to ensure that no two adjacent cells have the same color.

Graph coloring can also solve more complex puzzles such as 3-dimensional puzzles, image segmentation, scheduling problems, and circuit design. For example, efficient circuits with less crosstalk and fewer transistors can be designed using graph coloring.

In addition, graph coloring can solve the Traveling Salesman Problem. It is an important problem in computer science, in which a salesman must visit a set of cities while minimizing the total cost of travel. Graph coloring can be used to determine the shortest route between cities by assigning colors to the edges of the graph.

9. Some of the modern applications of graph theory in today’s world –

Many cutting-edge applications of graph theory are covered in Modern Applications of Graph Theory, including traffic networks, navigable networks and optimum routing for emergency response, placement of electric vehicle charging stations, and graph-theoretic techniques in molecular epidemiology.

The other application of graph theory in real life are as follows:

10. Graph theory is used to design computer Chips to connect millions of transistors that consist in Integrated circuits.

11. Graph theory is also used in Computer Network Security.

12. Graph theory concepts are used in computer hardware to model the physical layer’s limitations.

13. The main application area of graph theory in data mining is graph mining. The relational aspect of data is represented by graph mining.

14. We use Graph coloring techniques of Graph Theory in scheduling, such as Job scheduling, Aircraft scheduling etc.

15. Graph theory is also used extensively in the field of computer science, particularly for problems dealing with optimization.

16. Graph theory can be used to create algorithms for finding the shortest path between two points, or for finding the most efficient solution to a problem.

17. Graph theory is also used in artificial intelligence, where it is used to create algorithms for problem-solving.

Read Also: Application of Graph Theory in Various Fields

Read this article in ‘Hindi’: Application of graph theory in real life in hindi

There can be many other applications of graph theory that we might have forgotten in this article. If you want to tell us more about this topic, ‘Please Comment’.

(Source – Various books from the college library)

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