Applications of Graphs in Computer Science

Graphs are everywhere in computer science. From social networks to algorithms, graphs can provide a conceptual and computational framework for solving problems that might otherwise be difficult or impossible.

What is a Graph?

A graph is a collection of vertices and edges forming a structure used to model pairwise relations between objects. The vertices are generally drawn as circles or ovals, while the edges connect with each other. Graphs are typically used to model relationships between entities or objects by clicking pairs of these entities with edges in computer science.

When designing a graph algorithm, it helps to understand some basic properties and terminology first. Here are some common words you will come across when working with graphs:

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

Adjacency: Two vertices are adjacent if there is an edge between them.

Incidence: A vertex has incidence to the edges incident to it.

Types of Graph

• Undirected Graph: V and E represent vertices and edges, respectively. The edges (or arcs) have directions, but the vertices do not have any direction.
• Directed Graph: In this type of graph the edges have a direction or a sense of flow.
• Weighted Graph: An edge can be assigned a weight or cost to traverse that edge. This weight represents a measure of the border’s value, which is essential in algorithms where the price of a vertex is proportional to the distance to its neighbours. For example, if you want to find out how many hops away any two vertices are from each other in a graph, you can use the adjacency matrix.

Graph Applications

The mathematical field plays an essential role in different domains. Graphs are considered an outstanding modelling tool used to model several stages of relationships between all physical conditions. Several real-world problems can be represented with graphs. Here are some important graph applications:

• Social Networks: Graphs are special network conditions, with only one type of edge between vertices.
• Web Graphs: The web is an extensive collection of references to hyperlinks. In other words, the web is another excellent set of graph data.
• Biological Networks: Space (or biological networks) is one of the significant sources of real-world graphs. Examples are brain networks, protein communication networks, and diet networks.
• Information Graphs: Geographical information is structured according to a graph, and information A is linked to information B, when A stands for B in a certain way.
• Product Recommendations: A platform like Amazon recommends buying similar products while making a purchase. These recommended products are based on what other users have already purchased. For example, if you buy a book about Python, Amazon recommends purchasing a book about Scrum. At the heart of these systems are large graphs of bipartite.
• Neural Networks: Neural networks are formed by large graphs that connect neurons with artificial synapses. There are many different types of emotional networks, and the main difference between these types is the formation of graphs.
• Map Networks: Apps such as Maze, Google Maps, Apple Maps, and Uber are installed on all smartphones. Navigation problems are modelled like graph problems. Think of examples like travelling merchant problems, shortcut problems, Hammington routes, etc.
• Blockchains: The vertices are blocks, each holding multiple transactions, and the edges connect the following blocks. The largest branch from the first block is the current standard for historical transactions.
• Bitcoin Creation Graphs: Blockchain is an exciting graph often analysed in the world of cryptocurrency. Another insightful graph emerges when using Bitcoin wallets as vertices and transactions between wallets as edges. The resulting graph shows the flow of money between Bitcoin wallets. This graph is essential for learning about global cash flow patterns.

Conclusion

Graphs are considered the best tool for modelling relationships between physical situations. Many real-world problems can be represented using graphs. Different concepts involved in graph theory and its application in computer science demonstrate the application of graph theory.