graph theory essay

Graph Theory, Computational Intelligence and Thought

Essays Dedicated to Martin Charles Golumbic on the Occasion of His 60th Birthday

• © 2009
• Marina Lipshteyn 0 ,
• Vadim E. Levit 1 ,
• Ross M. McConnell 2

The Caesarea Rothschild Institute, Mount Carmel, University of Haifa, Haifa, Israel

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Department of Computer Science and Mathematics, Ariel University Center of Samaria, Ariel, Israel

Department of computer science, colorado state university, fort collins, usa.

Part of the book series: Lecture Notes in Computer Science (LNCS, volume 5420)

Part of the book sub series: Theoretical Computer Science and General Issues (LNTCS)

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Table of contents (21 chapters)

Front matter, landmarks in algorithmic graph theory: a personal retrospective.

• Martin Charles Golumbic

A Higher-Order Graph Calculus for Autonomic Computing

• Oana Andrei, Hélène Kirchner

Algorithms on Subtree Filament Graphs

• Fanica Gavril

A Note on the Recognition of Nested Graphs

• Mark Korenblit, Vadim E. Levit

Asynchronous Congestion Games

• Michal Penn, Maria Polukarov, Moshe Tennenholtz

Combinatorial Problems for Horn Clauses

• Marina Langlois, Dhruv Mubayi, Robert H. Sloan, György Turán

Covering a Tree by a Forest

• Fanica Gavril, Alon Itai

Dominating Induced Matchings

• Domingos M. Cardoso, Vadim V. Lozin

HyperConsistency Width for Constraint Satisfaction: Algorithms and Complexity Results

• Georg Gottlob, Gianluigi Greco, Bruno Marnette

Local Search Heuristics for the Multidimensional Assignment Problem

• G. Gutin, D. Karapetyan

On Distance-3 Matchings and Induced Matchings

• Andreas Brandstädt, Raffaele Mosca

On Duality between Local Maximum Stable Sets of a Graph and Its Line-Graph

• Vadim E. Levit, Eugen Mandrescu

On Path Partitions and Colourings in Digraphs

• Irith Ben-Arroyo Hartman

On Related Edges in Well-Covered Graphs without Cycles of Length 4 and 6

• Vadim E. Levit, David Tankus

On the Cubicity of AT-Free Graphs and Circular-Arc Graphs

• L. Sunil Chandran, Mathew C. Francis, Naveen Sivadasan

O ( m log n ) Split Decomposition of Strongly Connected Graphs

• Benson L. Joeris, Scott Lundberg, Ross M. McConnell

Path-Bicolorable Graphs

• Andreas Brandstädt, Martin C. Golumbic, Van Bang Le, Marina Lipshteyn

Path Partitions, Cycle Covers and Integer Decomposition

• András Sebő

Properly Coloured Cycles and Paths: Results and Open Problems

• Gregory Gutin, Eun Jung Kim
• Computational Intelligence
• Graph theory
• artificial intelligence
• bicolorable graph
• bipartite graphs
• chordal graphs
• cocomparability graphs
• connected graphs
• constraints
• edge dominating set
• optimization
• algorithm analysis and problem complexity
• data structures

About this book

Editors and affiliations.

Marina Lipshteyn

Vadim E. Levit

Ross M. McConnell

Bibliographic Information

Book Title : Graph Theory, Computational Intelligence and Thought

Book Subtitle : Essays Dedicated to Martin Charles Golumbic on the Occasion of His 60th Birthday

Editors : Marina Lipshteyn, Vadim E. Levit, Ross M. McConnell

Series Title : Lecture Notes in Computer Science

DOI : https://doi.org/10.1007/978-3-642-02029-2

Publisher : Springer Berlin, Heidelberg

eBook Packages : Computer Science , Computer Science (R0)

Copyright Information : Springer-Verlag Berlin Heidelberg 2009

Softcover ISBN : 978-3-642-02028-5 Published: 20 July 2009

eBook ISBN : 978-3-642-02029-2 Published: 27 July 2009

Series ISSN : 0302-9743

Series E-ISSN : 1611-3349

Edition Number : 1

Number of Pages : XIV, 227

Topics : Artificial Intelligence , Algorithm Analysis and Problem Complexity , Mathematical Logic and Formal Languages , Discrete Mathematics in Computer Science , Data Structures , Computer Graphics

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Computer Science > Discrete Mathematics

Title: graph theory.

Abstract: This is a replacement paper. There are 6 chapters. The first two chapters are introductory. The third chapter is on extremal graph theory. The fourth chapter is about algebra in graph theory. The fifth chapter is focused on algorithms. The third section of the fifth chapter deals with computable time. The sixth chapter has sections on probability and enumeration.

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• Mathematics
• Number System and Arithmetic
• Trigonometry
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Applications of Graph Theory

• Applications of Set Theory
• Real-Life Applications of Graphs
• Applications of Graph Data Structure
• Real Life Applications of Bar Graph
• Real-Life Applications of Number Theory
• Real-life applications of network theory
• Real-Life Applications of Topology
• Real-Life Applications of Fractals
• Graph of Polynomial Functions
• Application of Derivatives
• Applications of Venn Diagrams in Real Life
• Applications of Dijkstra's shortest path algorithm
• Real-Life Applications of Discrete Mathematics
• Applications of Linear Algebra
• Applications of Computer Graphics
• Applications of Data Science
• Applications of tree data structure
• Applications of Priority Queue
• Applications of Queue Data Structure

Applications of Graph Theory: In mathematics and computer science, a graph is a mathematical structure that consists of two main components: vertices (or nodes) and edges. The study of these graphs in various contexts is called graph theory.

There are various applications of graph theory in real life such as in computer graphics and networks, biology, and many other fields as well. In this article, we will discuss real-life applications of graph theory in various fields like Computer Science, Biology, Sociology, and others in detail.

Table of Content

What is Graph Theory?

Applications of graph theory in computer networks, applications of graph theory in social network analysis, applications of graph theory in transportation networks, applications of graph theory in biological networks.

Graph theory is a branch of mathematics that deals with the study of graphs, which are mathematical structures used to represent pairwise relationships between objects. A graph consists of two main components: vertices (also called nodes) and edges.

• Each vertex typically represents an object or entity within a particular context.
• Edges indicate relationships or interactions between the corresponding vertices.

Graph theory finds applications in diverse fields such as computer science, biology, sociology, and transportation, among others. Its versatility lies in its ability to model and analyze complex relationships and systems using graph-based representations.

Let’s explore some key applications in each of these fields :

Computer Science

• Networks and Routing Algorithms: Graph theory is fundamental in designing computer networks and developing efficient routing algorithms for data transmission.
• Database Management: Graph databases use graph structures to represent and query relationships between data entities, offering advantages in data modelling and querying.
• Algorithm Design: Many algorithms in computer science, such as graph traversal algorithms (e.g., breadth-first search, depth-first search), rely on graph theory concepts.
• Biological Networks: Graph theory helps model and analyze biological networks like gene regulatory networks, protein-protein interaction networks, and metabolic pathways, aiding in understanding complex biological processes.
• Phylogenetics: Evolutionary relationships between species are often represented as phylogenetic trees, which can be analyzed using graph theory techniques.
• Social Network Analysis: Graph theory is central to social network analysis, which studies the structure and dynamics of social networks to understand social interactions, information flow, and community formation.
• Opinion Dynamics: Models based on graph theory are used to study how opinions, behaviors, and ideas spread through social networks.

Transportation

• Route Planning: Graph theory is indispensable in transportation networks for route planning, traffic optimization, and resource allocation, ensuring efficient movement of people and goods.
• Logistics: Graph-based models help optimize supply chain management, inventory routing, and delivery scheduling in transportation and logistics operations.

5. Other Fields

• Chemistry: Chemical compounds and reactions can be represented and analyzed as molecular graphs, aiding in drug discovery and materials science.
• Finance: Graph theory is applied in financial networks, portfolio optimization, and risk management to analyze interconnectedness and systemic risks in financial systems.

In computer networks, graph theory plays a crucial role in designing network topologies, developing routing algorithms, and optimizing data transmission. It helps in determining efficient paths for data packets to travel from source to destination, thereby improving network efficiency and reliability. Here’s how it works:

• Designing Network Topologies: Imagine a network as a web of connections between computers, servers, and devices. Graph theory helps design this web, deciding how to connect everything for the best performance and reliability. Whether it’s a simple star, a complex mesh, or something in between, graph theory guides the layout.
• Developing Routing Algorithms: Once the network is set up, graph theory jumps in again to figure out the best paths for data to travel. Each device in the network is like a point on a map, and the connections between them form the roads. Graph theory helps develop algorithms that navigate these “roads” efficiently, ensuring data gets where it needs to go quickly and reliably.
• Optimizing Data Transmission: In a busy network, data packets are constantly zipping around, trying to reach their destinations. Graph theory helps optimize this process by finding the fastest routes and avoiding traffic jams. By analyzing the connections between devices and the current traffic conditions, graph theory ensures smooth and speedy data transmission.

So, the next time you send an email, stream a video, or download a file, remember that behind the scenes, graph theory is hard at work, ensuring that data finds its way from point A to point B as quickly and efficiently as possible.

Read in Detail: Applications of Graph Data Structure

Social network analysis involves studying the structure and dynamics of social networks, such as friendships, interactions, and information flow among individuals or entities.

Graph theory provides tools and techniques to analyze network properties, identify influential nodes or communities, and understand social phenomena.

Here’s how SNA and graph theory work together:

• Understanding Relationships: Graph theory allows us to represent social networks as graphs, where each person is a node (point) and their relationships are edges (lines connecting them). This makes it easier to visualize and analyze who is connected to whom.
• Identifying Key Players: By applying graph theory algorithms, we can identify influential individuals or groups within a social network. These could be people who connect different groups together or those with a lot of connections, often called “hubs” or “influencers.”
• Predicting Behavior: By analyzing the structure of a social network using graph theory, we can make predictions about how information will flow or how behaviors might spread through the network. This is useful for understanding trends, predicting outcomes, or designing interventions.

Overall, social network analysis powered by graph theory helps us understand the complex dynamics of human interactions, from friendships and collaborations to information sharing and influence. It has applications in various fields, including sociology, psychology, marketing, and even cybersecurity.

Graph theory is essential in modeling transportation networks, including road networks, railway systems, and flight routes. It enables efficient route planning, traffic optimization, and resource allocation by analyzing the connectivity and distances between locations within the network.

• Modeling Networks: Graph theory allows us to represent transportation networks as graphs, with intersections as nodes and roads or tracks as edges. This makes it easier to understand how different places are connected and how we can move between them.
• Route Planning: Ever wondered how apps like Google Maps find the fastest route from one place to another? They use graph theory! By analyzing the connections between nodes and the distances along edges, algorithms can determine the shortest or fastest paths between locations.
• Traffic Optimization: Graph theory helps us understand traffic patterns and optimize traffic flow. By studying the graph, we can identify congested areas, plan alternative routes, or adjust traffic signals to keep things moving smoothly.
• Resource Allocation: Whether it’s deciding where to build new roads, adding more trains to a route, or scheduling flights, graph theory helps optimize resource allocation. By analyzing the network’s structure and demands, we can make better decisions about where to invest resources for maximum efficiency.

In essence, graph theory is like a mapmaker’s best friend when it comes to transportation networks. It helps us navigate the complexities of roads, rails, and runways to keep people and goods moving efficiently from place to place.

In biology and bioinformatics, graph theory is used to model and analyze biological networks such as gene regulatory networks, protein-protein interaction networks, and metabolic pathways. It aids in understanding biological processes, predicting gene functions, and identifying potential drug targets.

Here’s how it plays a crucial role in understanding biological systems:

• Modeling Biological Networks: Graph theory provides a framework for representing complex biological interactions as networks. For example, genes, proteins, or metabolites can be depicted as nodes, while interactions or relationships between them are represented as edges.
• Protein-Protein Interaction Networks (PPI): Proteins rarely work alone; they often interact with other proteins to carry out cellular functions. Graph theory helps in studying PPI networks to identify protein complexes, pathways, and functional modules. This information is crucial for understanding diseases and developing targeted therapies.
• Predicting Gene Functions: Graph-based computational methods can predict the functions of unknown genes by analyzing their interactions within biological networks. This helps prioritize experimental validation efforts and accelerate gene function discovery.
• Identifying Drug Targets: Graph theory is employed to identify potential drug targets by analyzing network properties and identifying nodes that, when targeted, could disrupt disease-associated pathways or protein interactions. This approach aids in drug discovery and development.

Summary – Applications of Graph Theory

Graph theory is like the ultimate puzzle solver in mathematics and computer science, helping us understand complex connections in everything from internet networks to how living cells function. It breaks down big, complicated systems into nodes (think of these as dots) and edges (the lines connecting the dots), making it easier to see how things interact.

Whether it’s figuring out the quickest route for your road trip, analyzing friendships on social media, improving how data travels across the internet, or even studying ecosystems, graph theory is behind the scenes, mapping out the best paths and solutions. It’s a tool that crosses into many fields—biology, sociology, transportation, and beyond—showing us the power of connections in solving real-world problems and unlocking the mysteries of nature and technology.

Applications of Graph Theory – FAQs

How is graphs used in everyday life.

Graphs are used in everyday life for various purposes like tracking personal finances, analyzing trends in sales data, visualizing progress in fitness goals, and understanding traffic patterns on maps.

What is the application of theory of graphs?

Graph theory applications include network analysis (e.g., social networks), logistics optimization (e.g., shortest path algorithms), computer science (e.g., algorithms), and biology (e.g., modeling metabolic pathways).

What are the applications of trees in graph theory in real life?

Tree structures in graph theory find applications in computer science (e.g., binary search trees for efficient data storage), transportation networks (e.g., hierarchical road systems), and organizational hierarchies (e.g., company management structures).

How is graph theory used in computer networks?

Graph theory is essential in designing network topologies, developing routing algorithms, and optimizing data transmission in computer networks. It helps determine efficient paths for data packets to travel from source to destination, improving network efficiency and reliability.

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Graph theory and its uses with 5 examples of real life problems

In the early 18-th century, there was a recreational mathematical puzzle called the Königsberg bridge problem. The solution of this problem, though simple, opened the world to a new field in mathematics called graph theory. In today’s world, graph theory has expanded beyond mathematics into our everyday life without us even noticing.

In this blog, I will start by discussing the original problem and its clever solution. Then, I will lay down what graph theory is and its main components. Finally, I will conclude with  5 applications of graph theory that are used today in the world of data science.

The origin of graph theory

Königsberg (now Kaliningrad, Russia) was a city from the old Kingdom of Prussia spanning along both sides of the Pregel river. The city had two islands that were connected to the mainland through bridges. The smaller island was connected with two bridges to either side of the river, while the bigger island was connected with only one. Additionally, there was one bridge connecting both islands. You can see the layout of the bridges in the image below.

Now, imagine that you are a tourist and want to cross all 7 bridges because they are the main attraction of the city. However, you are a bit lazy and do not want to walk too much. So, you do not want to cross the same bridge more than one time. Is there a path through the city that does this? Just as a simple rule, you can only cross the river through bridges, so no swimming. How would you solve this problem?

Superficially, the problem sounds simple to solve. Just try some paths and you will arrive at the solution. However, no  matter how many paths you try, you will not find a solution. Leonhard Euler, a famous  mathematician, realized this, and explained why it was impossible to make this path through the city.

Firstly, he realized that it does not matter how you travel inside the city. The only important part to consider for the problem was the connections between the different landmasses. He drew dots to represent the landmasses and lines connecting these dots to represent the bridges (as seen in the picture below). The location of the dots and the shape of the lines are not relevant for the problem, only their relation. In the end, he had an abstraction of the problem with only dots and lines, which  is now called a graph.

Second, he thought that in order to walk through a landmass you need to enter through a bridge and exit from a different bridge. This means that the dot representing that landmass needs two lines connecting it to represent the enter and exit line. More generally, the dot can have any even number of lines as connections. This does not necessarily apply for two dots, which are the first and last landmass in the path. Those dots can have an odd number of lines connecting them since you could only exit the first dot and only enter the last dot. From counting the lines connecting each dot of the Königsberg bridge problem, one can see that all of the landmasses have an odd number of connections. This proves that it is impossible to make a path that crosses through all bridges.

Euler changed the way of solving problems. He recognized that the problem was not about measuring and calculating the solution, but about finding the geometry and relations behind it. By abstracting the problem, he started the field of graph theory and his solution became the first theorem of this field. Since then, graph theory has developed not only from a mathematical perspective, but into many other fields such as physics, biology, linguistics, social sciences, computer sciences and more.

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What is graph theory?

Graph theory is the study of relationships between objects. These objects can be represented as dots (like the landmasses above) and their relationships as lines (like the bridges). The dots are called vertices or nodes, and the lines are called edges or links. The connection of all the vertices and edges together is called a graph and can be represented as an image, like the ones below:

One of the most important properties of graphs is that they are just abstractions of the real world. This allows the representation of graphs in many different ways, all of which are correct. For example, all the graphs above are visually very different from each other; however, they all represent the same relations, thus all are the same graph. You can check it by counting the number of edges that each vertex has.

Graphs can be divided into many different categories based on their properties. The most common categories are directed and undirected graphs. Directed graphs have edges with specific orientations, normally shown as an arrow. For example, in a graph representing a cake recipe, each vertex is a different step in the recipe and the edges represent the relation between these steps. You can put the cake in the oven only after mixing the ingredients; therefore, there is a directed edge from the mixing to the baking step. Undirected graphs have symmetric edges, just like the ones shown earlier. Another example is the graph of a social network, where vertices represent people and edges connect people that have a relationship. These relationships go both ways.

Another important feature is that the vertices or the edges can have weights or labels. Let's assume that you are building a graph from a series of warehouses and stores in a city to optimize the supply of the stores. You can have two types of vertices, warehouses and stores, and the edges that connect them can be weighted by either the physical distance between the two locations or by the cost to move the product from one location to another. Weights and labels are very important when using graph theory in real life applications, since it is a way to add complexity to the simple graph model.

Read more: Anomaly detection using network science

For now, I have described what a graph is and its properties, but not how to use graph theory to solve problems. Interestingly, once abstracted to a graph, the problem falls into a few fundamental categories, such as path finding, graph coloring, flow calculation and more. In the next section, I will address some of these categories, some real-life problems that fall into them and how to abstract the problems into graphs.

What are real life applications of graph theory?

In this section I present 5 different problems of graph theory with real life examples. The calculation of their solution can be done with a variety of algorithms that I encourage the reader to look up since they sometimes become highly complex for this introductory blog. Moreover, the solutions of such problems may not be unique nor exact. Graph theory algorithms depend on the size and complexity of the graph; this means that some solutions may just be a very good approximation to the exact solution. Even more, some problems have not even been solved, thus approximations are the best outcome.

Airline Scheduling (Flow problems)

One of the most popular applications of graph theory falls within the category of flow problems, which encompass real life scenarios like the scheduling of airlines. Airlines have flights all around the world and each flight requires an operating crew. Personnel might be based on a particular city, so not every flight has access to all personnel. In order to schedule the flight crews, graph theory is used.

For this problem, flights are taken as the input to create a directed graph. All serviced cities are the vertices and there will be a directed edge that connects the departure to the arrival city of the flight. The resulting graph can be seen as a network flow. The edges have weights, or flow capacities, equivalent to the number of crew members the flight requires. To complete the flow network a source and a sink vertex have to be added. The source is connected to the base city of the airline that provides the personnel and the sink vertex is connected to all destination cities.

Using graph theory, the airline can then calculate the minimum flow that covers all vertices, thus the minimum number of crew members that need to operate all flights. Additionally, by giving weights to the cities corresponding to its importance, the airline can calculate a schedule for a reduced number of crew members that do not necessarily visit all the cities.

This flow problem can also be applied to many other instances. For example, when having to supply stores from warehouses with a finite number of trucks, or when scheduling public transport in specific routes considering the expected amount of people that will be using it.

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Directions in a map (Shortest path)

Nowadays, we use our smart phones all the time to help us in our everyday lives. For me, it helps me by giving me directions to cycle from my location to a restaurant or a bar. But how are these directions calculated? Graph theory is the answer for this challenge, which falls in the category of defining the shortest path.

The first step is to transform a map into a graph. For these all-street intersections are considered as vertices and the streets that connect intersections as edges. The edges can have weights that represent either the physical distance between vertices, or the time that takes to travel between them. This graph can be directed showing also the one-way streets in the city.

Now, to give the direction between two points in the map, an algorithm only needs to calculate the path with the lowest sum of edge weights between the two corresponding vertices. This can be trivial for small graphs; however, for graphs created from big cities, this is a hard problem. Fortunately, there are many different algorithms that may not give the perfect solution, but will give a very good approximation, such as the Dijkstra's algorithm or the A* search algorithm .

Finding the shortest or fastest route between two points in the map is definitely one of the most used applications of graph theory. However, there are other applications of the shortest path problem. For example, in social networks, it can be used to study the “six degrees of separation” between people, or in telecommunication networks to obtain the minimum delay time in the network.

Solving Sudoku’s puzzles (Graph coloring)

Sudoku is a popular puzzle with a 9x9 grid that needs to be filled with numbers from 1 to 9. A few numbers are given as a clue and the remaining numbers needed to be filled follow a simple rule: they cannot be repeated in the same row, column or region. This puzzle, despite using numbers, is not a mathematical puzzle, but a combinational puzzle that can be solved with the help of graph coloring.

One can convert the puzzle to a graph. Here, each position on the grid is represented by a vertex. The vertices are connected if they share the same row, column or region. This graph is an undirected graph, since the relationship between vertices goes both ways. An important feature of the graph is the assignment of a label to each vertex. The label corresponds to the number used in that position. In graph theory, the labels of vertices are called colors.

To solve the puzzle, one needs to assign a color to all vertices. The main rule of Sudoku is that each row, column or region cannot have two of the same numbers, thus two vertices that are connected cannot have the same color. This problem is called graph coloring, and, as with other graph theory problems, there are many different algorithms that can be used to solve this problem ( Greedy coloring or DSatur algorithm , for example), but their performance depends highly on the graph itself.

The coloring problem is used normally for very fundamental problems. However, there are more real-life problems that can be translated to a coloring problem, such as scheduling tasks. For example, scheduling exams in rooms. Each exam is a vertex and there is an edge connecting them if it takes place at the same time. The graph created is called an interval graph, and by solving the minimum coloring problem of the graph, you obtain the minimum number of rooms needed for all the exams. This can be generalized with tasks that use the same resources, such as compilers of programming languages or bandwidth allocation to radio stations.

Search Engine Algorithms (PageRank algorithm)

Search engines such as Google let us navigate through the World Wide Web without a problem. Once a query is made to search a specific set of words, the engine looks for websites that match the query. After finding millions of matches, how does the engine rank them to show the most popular ones first?

The search engine solves this through graph theory by first creating a web graph, a graph where the vertices are the websites, and the directed edges follow hyperlinks within those websites. The result is a directed graph that shows all relations between websites. Additionally, one can add weights to the vertices to give priority to more important or influential websites.

To classify the most popular websites, different algorithms can be used. One of the first ones used by Google is called PageRank . Here, the engine assigns probabilities to click a hyperlink and iteratively adds them up to form a probability distribution. This distribution represents the likelihood of a person randomly arriving at a particular website. Then, the engine orders the list of websites according to this distribution and shows the highest ones.

This algorithm had many faults. One can exploit it by having for example blog websites with many links to a particular website to increase the click probability, or by buying hyperlinks in websites with higher weights. Nowadays, there are more complicated algorithms that also consider sponsored advertisement, but the main core is still graph theory and the relations between websites.

Social Media Marketing (Community detection)

In January 2022, Facebook had 2.9 billion active users. As a social media platform, most of the revenue comes from advertising. Having so many users, advertisers will find it very expensive to place their advertising campaigns within the reach of everyone. However, one can also just target the people that may be interested in your product. How can you define such a target audience?

Using graph theory, you can create a social network graph by assigning a vertex to each person. You connect vertices with edges if the persons have a relationship, such as friends in Facebook. This leads to an undirected graph. This massive graph would appear at the beginning very chaotic; however, one can always find patterns in it.

A way to find the ideal target audience is to decompose the graph into smaller sub-graphs. There are different algorithms that can do this, such as hierarchical clustering algorithms or minimum cut methods like the Karger's algorithm . The result is the division of the graph into clusters of people that are highly connected to each other, but less connected to other groups of people. These groups are called communities and they share common interests, like specific artists, brands or even political parties. Identifying these communities is advantageous for advertising since they are more likely to buy common products, follow similar artists or vote for similar parties.

The detection of communities can be also used for other purposes than advertisement. After identifying the communities, one can compare connections between groups or even within groups. If a group or a vertex within the group does not behave as their peers, it can be a sign of intrusion. This can be used as a security control. For example, if the vertices are computers or programs in a network, strange behavior could be caused by attacks on it. Identifying strange connections can improve the security of the network.

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In this blog, we went over how graph theory came to live from a simple mathematical puzzle. You now know the main characteristics of the field and the main problems that can be solved using graph theory. However, as an introduction to the field, the main goal of this blog is to encourage the reader to think about problems the way graph theory does: abstract the problem and remove all non-important parts behind. This will make the search for a solution much easier.

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Graph Theory Application in Computer Science Essay

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In the field of mathematics and other exact sciences, there is a range of theories that are aimed at explaining and studying theoretical concepts that can be implemented into practice. The graph theory can be regarded as one of the brightest examples of such concepts. Even though there are numerous problems that have not been solved yet, and certain hypotheses within the frame of the theory are not confirmed, such structures as graphs are widely used in different fields. Speaking about the field of computer networking, graphs can be used to describe and study data transfer systems; in addition, they remain an important tool helping to manage social networks and generate recommendations for users.

As it follows from its name, the discussed theory is aimed at studying graphs that present structures that consist of numerous knots that form unities with the help of verges. Importantly, the structure of a graph can be different due to the number of ends and knots that may vary. On that premise, it is widely accepted that there are about ten types of graphs, having different numbers of vertices. Speaking about the classification of graphs and the way to apply them, it needs to be noted that different graphs present structures helping to represent data related to various fields of knowledge. For instance, graphs can be used in linguistics, biology, and chemistry as they help to solve numerous problems related to studying structures of chemical substances, food chains. Apart from that, the use of graphs helps to define and describe processes taking place when new lexical units become popular and languages change. As it follows from these examples, it is obvious that the graph theory can be applied almost in every field of science because scientific knowledge always requires systematization.

When it comes to the field of computer science and networking, it is necessary to state that possible applications of graphs of different types are numerous. Speaking about the latter, it is important to pay attention to the task related to representation of data describing systems for data transfer. Thus, specialists in networking use graphs to outline systems of computer networks, study their properties, and implement changes. In fact, graphs used for that purpose help to create a kind of mathematical model that indicates the interconnection between the parts of system. When it comes to the most common examples, illustrating this way to use graphs, it is necessary to remember the Internet. The structure of the Internet can be presented with the help of graphs, and this way to use the discussed theory definitely helps to identify possible weaknesses of systems based on the type and properties of completed graphs (Xu, Wang, & Gu, 2014). This way to apply concepts from the graph theory is extremely significant to the field as it can be used to plan new networks and improve the older ones.

Apart from planning and studying networks, specialists in networking can use graph theory in order to provide services in social networks. The so-called social graph is a type of graph that includes a range of user profiles and represents links between them. Apart from that, social graphs can also be implicit. Such graphs also include information on interactions with other users but the types of links are less defined. The use of graphs presenting social links between users of popular social networks can be regarded as a way to fulfil numerous tasks. For instance, the data retrieved with the help of such graphs can be used in order to create proper recommendations for users. The latter may include messages and lists that indicate “people you may know” based on the information related to users’ friends and their activity in social networks (Jiang et al., 2013).

Apart from that, graphs can be used to generate recommendations related to media content based on activity showing preferences or users and their personal information. At the same time, it is important to note that graphs containing information on the activity of users can help to retrieve information that users may want to hide (such as the presence of fake accounts used for different purposes). In fact, if these accounts are used to operate on the fringes of the law, graphs can be successfully used to study the most recent activity of the user and identify his or her real personal details (Jin, Chen, Wang, Hui, & Vasilakos, 2013). Therefore, there is a number of ways to use graphs in social networks and they can sometimes prevent illegal activity in social networks. Even though some users do not want their personal details and data on social interactions to be processed and studied, there is no doubt that graphs in social networks help to simplify many processes and provide people with relevant information.

Having analyzed these ways to apply graphs in networking, it is possible to state that graph theory has advanced the knowledge in this field. In general, it is clear that graphs help to visualize any information to make it easier to understand. Importantly, graphs can be listed among the most common tools that are used for the purposes of network analysis by modern specialists. As is clear from the discussed examples, representing data with the help of graphs, it is possible to keep track of users’ interactions and fulfil a range of tasks helping to manage social networks.

Also, the use of graphs remains an important tool as it can help to control computer devices that form a network and create plans that can be easily understood. Analyzing the role of graph theory in the development of networking, it is possible to state that a range of conclusions made by researchers developing the theory can be applied to problems of computer networking related to connectivity. In other words, a graph often acts as a good tool allowing to track changes in computer networks. Taking into consideration all the ways to use graph theory in computer science and networking in particular, it needs to be stated that their role in advancing knowledge in the field and enhancing effectiveness of networks cannot be overestimated.

In the end, it is clear that graph theory can be applied by specialists in computer science and networking in numerous ways. Personally, I will apply the theory in order to use various computer network construction schemes and check if they are appropriate for a particular situation. At the same time, the theory can be used when there is a need to solve theoretic problems – representing the data with the help of graphs, I will make it more illustrative. Therefore, graph theory can be applied to solve both theoretical and practical problems.

Jiang, J., Wilson, C., Wang, X., Sha, W., Huang, P., Dai, Y., & Zhao, B. Y. (2013). Understanding latent interactions in online social networks. ACM Transactions on the Web (TWEB) , 7 (4), 18.

Jin, L., Chen, Y., Wang, T., Hui, P., & Vasilakos, A. V. (2013). Understanding user behavior in online social networks: A survey. IEEE Communications Magazine , 51 (9), 144-150.

Xu, K., Wang, F., & Gu, L. (2014). Behavior analysis of internet traffic via bipartite graphs and one-mode projections. IEEE/ACM Transactions on Networking (TON) , 22 (3), 931-942.

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Bibliography

IvyPanda . "Graph Theory Application in Computer Science." September 24, 2020. https://ivypanda.com/essays/graph-theory-application-in-computer-science/.