Autor: Codenga 22.03.2024

Data is a crucial element of the modern world. Equally important is the ability to explore relationships between data. In practice, graphs are often used to study these relationships. In this article, we will present you with the most important types of graphs, their applications, and the most popular graph algorithms.

What is a Graph?

A graph is an abstract data structure that consists of vertices (sometimes also called nodes) and edges (connecting these vertices). Vertices represent objects, and edges represent relationships between them. Graphs are used to model various things, such as social networks, computer networks, road maps, etc. Here is an example of a simple graph:

This graph contains the following elements:

• Vertices: A, B, C
• Edges: (A, B), (A, C), (B, C)

So, it has three vertices and three edges. This is an example of an undirected graph.

Types of Graphs

Directed and Undirected Graphs

In a directed graph, edges have a specified direction, while in an undirected graph, edges do not have a specified direction. Here is an example of a directed graph:

Weighted and Unweighted Graphs

In weighted graphs, each edge has an assigned weight or cost, whereas in unweighted graphs, edges do not have such information. Below is an example of a weighted graph:

Edges have the following weights:

• (A, B) with weight 2
• (A, C) with weight 1
• (B, C) with weight 3

Connected and Disconnected Graphs

A connected graph is one in which there is a path between every pair of vertices. A disconnected graph is one that consists of at least two separate components.

Graph Algorithms

Graph algorithms are a set of procedures and rules used for the analysis and processing of graphs. Here are a few basic graph algorithms.

Breadth-First Search (BFS)

This algorithm is used to traverse or search through a graph breadth-first, starting from a given vertex, and then moving to all its neighbors before moving on to the neighbors of those neighbors.

Depth-First Search (DFS)

Unlike BFS, DFS explores deeper into the graph before selecting new vertices to visit.

Dijkstra's Algorithm

It is used to find the shortest path between two vertices in a weighted graph.

Kruskal's Algorithm and Prim's Algorithm

Both of these algorithms are used to find the minimum spanning tree in a weighted graph.

Main Applications of Graphs

Graphs have many applications in various fields. They are used to model relationships between individuals in social networks. Search engines use them to assess connections between web pages and assign them weights accordingly. Graphs are used in logistics and transportation to optimize routes. There are also special databases that store information in the form of graphs - this makes it easy to explore relationships between data. As you can see, graphs play an important role in many areas of life in today's world.