#### Overview of this book

Building your own applications is exciting but challenging, especially when tackling complex problems tied to advanced data structures and algorithms. This endeavor demands profound knowledge of the programming language as well as data structures and algorithms – precisely what this book offers to C# developers. Starting with an introduction to algorithms, this book gradually immerses you in the world of arrays, lists, stacks, queues, dictionaries, and sets. Real-world examples, enriched with code snippets and illustrations, provide a practical understanding of these concepts. You’ll also learn how to sort arrays using various algorithms, setting a solid foundation for your programming expertise. As you progress through the book, you’ll venture into more complex data structures – trees and graphs – and discover algorithms for tasks such as determining the shortest path in a graph before advancing to see various algorithms in action, such as solving Sudoku. By the end of the book, you’ll have learned how to use the C# language to build algorithmic components that are not only easy to understand and debug but also seamlessly applicable in various applications, spanning web and mobile platforms.
Chapter 1: Data Types
Free Chapter
Chapter 2: Introduction to Algorithms
Chapter 3: Arrays and Sorting
Chapter 4: Variants of Lists
Chapter 5: Stacks and Queues
Chapter 6: Dictionaries and Sets
Chapter 7: Variants of Trees
Chapter 8: Exploring Graphs
Chapter 9: See in Action
Chapter 10: Conclusion
Index
Other Books You May Enjoy

# The concept of graphs

Let’s start with the question what is a graph? Broadly speaking, a graph is a data structure that consists of nodes (also called vertices) and edges. Each edge connects two nodes. A graph data structure does not require any specific rules regarding connections between nodes, as shown in the following diagram:

Figure 8.1 – Illustration of a graph

This concept seems very simple, doesn’t it? Let’s try to analyze the preceding graph to eliminate any doubts. It contains 9 nodes with numbers between 1 and 9 as values. Such nodes are connected by 11 edges, such as between nodes 2 and 4. Moreover, a graph can contain cycles – for example, with nodes indicated by 2, 3, and 4 – as well as separate groups of nodes, which are not connected.

However, what about the topic of parent and child nodes, which you know from learning about trees? As there are no specific rules about connections in a graph,...