About the Book

Using graph theory, you can apply the tools of science and mathematics to study relationships between things. In Exploring Graph Theory With Julia, hobby coders and armchair mathematicians are given the opportunity to understand and explore graph theory without the proofs and formality found in other books.

No mathematics beyond high school algebra is assumed. Code samples and explanations are targeted to anyone who has completed a beginner course in a procedural programming language, such as Julia, Python, or R.

The book is divided into two parts. The first part describes the fundamental concepts of graph theory while guiding the reader through building a simple Julia graph library. This library is used throughout the book to explore concepts with concrete examples. The second part discusses how graph theory arises in different contexts, including recreation, industry, and science.

Table of Contents

NOTE: This is a preliminary outline of the book and may change in the future.

Part 1

• Chapter 1: What Is a Graph?
• Chapter 2: Telling Graphs Apart
• Chapter 3: Drawing Graphs

Part 2

• Chapter 4: Graphs and Maps
• Chapter 5: Graphs and Industry
• Chapter 6: Graphs and Games
• Chapter 7: Graphs and Music
• Chapter 8: Graphs and the Universe
• Chapter 9: Graphs and Knowledge

Appendices

• Appendix A: Getting Started with Julia
• Appendix B: Library Reference
• Appendix C: More on Graph Visualization

Release Schedule

The book will be released in four stages. Price increases will accompany the first three stages, so purchasing early, unfinished drafts of the book will be less expensive. Early supporters will receive regular updates at no extra cost. I have not settled on a price for the book yet. Please let me know what you'd like to pay by filling out the form at the top of this page.

Here is the rough plan for when each chapter in the book will be available:

• Chapters 1–3: September 2023
• Chapters 4–6: November 2023
• Chapters 7–9: January 2024
• Full release: March 2024

Frequently Asked Questions

Who is this book for?

The primary audience I’m writing for is hobby coders with an interest in math and science, but students in an undergraduate graph theory course will also benefit from the book. Exploring Graph Theory With Julia can supplement formal text books to expose students to practical applications of graph theory and provide them with tools to explore theory with a computer.

How long will the book be?

I’ll try and keep it under 300 pages, not including front matter, the glossary, or the index. Wish me luck.

Will a print version be available?

Yes, a print version will be available soon after the LeanPub version is published. I am currently working out publishing and distribution. I am also considering offering a spiral-bound version, but I have not worked out the logistics yet. Please let me know if you are interested in a spiral-bound version of the book.

Will the book contain exercises?

Yes. Some exercises are presented in line with the text as callouts. These exercises are intended to be easy and allow readers to take a break from the book and think about a new concept. Each chapter will contain a set of coding exercises that reinforce and extend the topics discussed in the chapter. Solutions to these coding exercises will be provided in a GitHub repository.

Why Julia?

Julia is easy to install on almost every operating system, especially using the juliaup tool. Julia's syntax is easy to grasp for folks already familiar with a language like Python or R. But most importantly, for loops in Julia are fast. Using Julia, you can write beginner-friendly code without sacrificing so much performance that using the code on a decently sized data set is impossible.

Another strength of Julia for hobby coders is that all of the standard library and nearly all of the third-party ecosystem is written in Julia. This does not automatically make everything easy to read, but at least you aren't required to learn another programming language just to try and understand how some parts of the language work.

Why not use Graphs.jl?

All of the code in this book is written from scratch. There are pedagogical advantages that make this choice attractive. Readers will implement fundamental algorithms themselves rather than call a function from a library they've never seen. I have always found writing things myself to be helpful for internalizing a new concept.

But there is another reason I have chosen to avoid using a package like Graphs.jl. When I imagine who will read my book, I think of a tinkerer — someone whose first instinct when confronted with the unknown is to poke, prod, take things apart, and rebuild them. Building a library from scratch and using it to explore things yourself seems highly aligned with that audience.

Additionally, many of the packages in the Julia ecosystem are targeted towards researchers and professionals. Personally, I find the way variables, functions, and types are named in most Julia packages to be unhelpful for the audience of this book. Writing everything from scratch allows me to use names I feel are more appropriate.

All that said, the graph library that readers build in this book is unsuitable for real-world applications. It is specifically designed for education. Readers interested in falling deeper down the graph theory rabbit hole are encouraged to check out the JuliaGraphs project.

About the Author

David Amos

I have a B.Sc. in mathematics, with a minor in computer science, from the University of Houston – Downtown. I spent three years pursuing a Ph.D. in mathematics at Texas A&M University before leaving academia for industry in 2015. Since then, I have worked as a system designer and programmer for distributed audio/visual systems, an analyst for a large event venue, and a technical writer.

I currently work on the User Education team at RelationalAI, teaching users about knowledge graphs and graph analytics.