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 resources on graph theory and algorithms. 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
- Seems like a good introduction of social network analysis (SNA) but I haven’t read or skimmed it.
- 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
- Graph Theory ++ math for computer science, lectures 6-10
- Algorithms for specific algorithms of interest

### More on YouTube

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

- Very basic concepts clearly explained
- Good introduction to terminology
- Similar to some of the others but I like the comparison at the beginning
- Nice intro with the matrix math relation introduced
- Simple description of breadth- vs depth-first search
- Introduction to more specific graph algorithm topics
- Introduction to graph concepts with some code samples
- If you have fun with the above, here’s another with Euler circuits and Paths

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