# The Top 13 Resources for Understanding Graph Theory & Algorithms

Recently we announced the availability of some super efficient graph algorithms for Neo4j. In case you missed the announcement, we now have an easy-to-use library of graph algorithms that are tuned to make full use of compute resources.

As part of assisting with this ongoing project, I needed to come up to speed as well as compile a list of graph algorithm and graph theory resources. Although this seemed like a short task, my list grew and continues to grow.

So with that in mind, I wanted to share our list of graph theory and algorithms books, resources, and videos. Our team has reviewed many of these but many are still on our to-do list.

I’ve noted the Top 13 based on reviews or personal recommendations but included other resources that might warrant a look. You’ll also notice this is broken into two sections: Basics for those getting up to speed on graph technology concepts and Getting Serious for those ready to dive in deep.

I hope you have as much fun with these as I have. Please let me know if there are other notable resources I’ve missed or if my rating of the Top 13 is off.

### The Basics

These graph theory resources are for those just getting started with graph concepts and business users that need the fundamentals. (Sometimes just certain chapters are even enough.)

• Introduction to Graph Theory – Trudeau
• Go from zero understanding to a solid grasp of the basics in just a few weeks.
• Well written with context for non-mathematicians willing to do basic calculations for proofs.
• I covered this in two weeks and have no advanced degree in mathematics.
• First Course in Graph Theory – Chartrand and Zhang
• Extremely well-recommended. Longer history of graph theory with stress on significance.
• I was really smitten with this one! It’s a mix of history, context and explanation.
• Don’t be intimidated by the length or put off by the mix. You don’t have to read every chapter and it really has something for everyone.
• Graph Theory and Complex Networks: An Introduction – van Steen
• Reported to be a great introduction with careful attention paid to make the mathematics less intimidating.
• YouTube: Graph Theory + Series
• Lots of content from graph theory to algorithms.
• YouTube: Graph Algorithm Series
• Good series that is snappy and easy to understand.
• Free LEDA Chapter (5) on Graph Algorithms
• Not as reader-friendly as the other items here, but it has sample code you can play with.

### Getting Serious

These graph algorithm and theory resources are for those with more mathematics background or ready to spend more time going deep.

• The Timeless Way of Building – Christopher Alexander
• This covers classic design concepts for those building anything.
• I included upon Michael Hunger’s declaration it was the best for learning good design approaches.
• Network Science – Barabási
• A good, multidisciplinary approach to networks and complex systems.
• Many agree it’s extremely readable for a graduate level text with fantastic color graphics.
• I added this to my queue after seeing the tie to complexity studies and after four chapters I can confirm this is a real gem.
• The Algorithm Design Manual – Skiena
• Less academic with good examples that relate to practical problems.
• There are four chapters focused on graph algorithms as well as sprinkles throughout.
• Not for the total beginner, but it’s reasonable for most and especially for those building solutions.
• Although I have no coding background, I’m really enjoying this and find the explanations very understandable. I like the “war stories” sections in each chapter of how things can go wrong.
• Algorithms – Sedgewick and Wayne
• A good survey of data structure and algorithms used today with one chapter focused on graph algorithms.
• I have not not read this but was impressed with all the online supporting material and related MOOC.
• Introduction to Graph Theory – Douglas West
• Introduction chapters are reported to be very good but you’ll need some mathematics background.
• Reviews indicated that the variety of proofs were very helpful.
• Ongoing updates are online.
• Graph Theory and Its Applications – Gross and Yellon
• Highly regarded as a great introduction with some complaints that it jumps around a bit and not as mathematically deep as it could be.
• I really appreciated the long appendix of use cases and algorithms.
• Modern Graph Theory – Bollobas
• You’re going to need a knife and fork for this! But it seems like one of the few highly recommend texts dealing with more recent graph developments.
• Highly rated for its comprehensive coverage of “every major theorem” and as an indispensable reference for research.
• This is a mathematics course text with some noting a lack of application and context.

### Honorable Mentions

I had to cut the list off somewhere, but I also wanted to you see the other possible resources and provide feedback if you have experience with any of them.

• Graph Animations with Combinatorica
• Easy-to-understand visuals, although the companion text didn’t have great feedback.
• Nice to have a quick link for those that think in pictures.
• Pearls in Graph Theory – Hartsfield
• Recommended as an undergraduate-level introduction without a lot of technical detail.
• This almost made my Top 13 list just because it was so often cited with great fondness. It seems to cover similar topics to the Trudeau work.
• Introduction to Graph Theory – Wilson
• Topics are similar to the Trudeau book with some interesting examples and visuals. However, it lacks context and some of the logical explanations of Trudeau.
• It may be a nice supplement, but I wouldn’t recommend it completely on it’s own.
• Graph Introduction – Brody
• Classic course text with expanded and updated version of Brody’s previous work.
• Reportedly very mathematically focused.
• Graph Theory – Diestel
• Online introduction for those with a really solid mathematics base.
• Algorithms in C++ Part 5: Graph Algorithms – Sedgewick
• Another Sedgewick with an entire part (series of books) on graphs. It seems to cover some of the same material as the previously listed Sedgewick but in much more detail.
• A Walk through Combinatorics: An Introduction to Enumeration and Graph Theory – Bona
• Interesting to look at graph from the combinatorial perspective.
• The second half of the book is on graph theory and reminds me of the Trudeau book but with more technical explanations (e.g., you get into the matrix calculations).
• Although interesting, it’s probably best suited for those that really want to dive into the math theory.
• Network Flows – Ahuja, Magnanti and Orlin
• Praised for its introduction and integrated network theory, algorithms and applications.
• Some loved the detailed explanation of why certain algorithms work for network optimization and others felt it was too difficult to understand.
• I’ve only skimmed this but it’s impressively comprehensive regarding network flows. I would recommend the previously mentioned Network Science for more general network understanding.
• Analyzing Social Media Networks with NodeXL: Insights from a Connected World – Hansen, Shneiderman and Smith
• Networks: An Introduction – Newman
• Reported to be a great introduction to network theory for anyone with some college level calculus and matrix algebra.
• Explanations are reported to be clear and thorough.
• The Fascinating World of Graph Theory – Benjamin
• Reported to be an entertaining perusal of graph problems but others comment that it’s neither contextual enough for beginners nor detailed enough for those with more background.
• MITOpenCourseware

### More on YouTube

I’m certain I missed a lot of good videos; there are just too many to review!

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