Overview of this book

Choosing the right data structure is pivotal to optimizing the performance and scalability of applications. This new edition of Hands-On Data Structures and Algorithms with Python will expand your understanding of key structures, including stacks, queues, and lists, and also show you how to apply priority queues and heaps in applications. You’ll learn how to analyze and compare Python algorithms, and understand which algorithms should be used for a problem based on running time and computational complexity. You will also become confident organizing your code in a manageable, consistent, and scalable way, which will boost your productivity as a Python developer. By the end of this Python book, you’ll be able to manipulate the most important data structures and algorithms to more efficiently store, organize, and access data in your applications.
Preface
Free Chapter
Python Data Types and Structures
Introduction to Algorithm Design
Algorithm Design Techniques and Strategies
Stacks and Queues
Trees
Heaps and Priority Queues
Hash Tables
Graphs and Algorithms
Searching
Sorting
Selection Algorithms
String Matching Algorithms
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Index

Graphs

A graph is a set of a finite number of vertices (also known as nodes) and edges, in which the edges are the links between vertices, and each edge in a graph joins two distinct nodes. Moreover, a graph is a formal mathematical representation of a network, i.e. a graph G is an ordered pair of a set V of vertices and a set E of edges, given as `G = (V, E)` in formal mathematical notation.

An example of a graph is shown in Figure 9.1:

Figure 9.1: An example of a graph

The graph `G = (V, E)` in Figure 9.1 can be described as below:

• `V = {A, B, C, D, E}`
• `E = {{A, B}, {A, C}, {B, C}, {B, D}, {C, D}, {D, D}, {B, E}, {D, E}}`
• `G = (V, E)`

Let’s discuss some of the important definitions of a graph:

• Node or vertex: A point or node in a graph is called a vertex. In the preceding diagram, the vertices or nodes are A, B, C, D, and E and are denoted by a dot.
• Edge: This is a connection between two vertices. The line connecting...