# Testing graph property on enumerated graphs

I wanted to verify some graph properties on all possible graph enumerations (or graphs satisfying certain properties). There is a list of all the graphs upto 10 vertices here, but that is not sufficient for my use.

1. Which would be the most user friendly and RAM efficient program/library to work with graphs, if I already have the graph with me.

2. What would be an easy and efficient way to generate graphs satisfying certian conditions. I tried to search about Nauty over net but it is difficult to find a tutorial.

• Try harder with nauty. – Yuval Filmus Jun 27 '18 at 20:10
• This depends a lot on the conditions. Nauty and its utility programs are nice and flexible, but they obviously aren't suitable for everything. If you care about planar graphs, you can look at plantri (but again, its interface is very "nauty-like", or very much similar to your standard Unix program). – Juho Jun 27 '18 at 20:17
• Essentially, you might just have to take Yuval's suggestion and try a little harder. After all, remember that this kind of software is usually intended for professional researchers and documentation can be scarce. – Juho Jun 27 '18 at 20:19

If you need to generate graphs, you can look at nauty: this is useful if you want to check whether a claim holds for all $n$-vertex graphs up to some small $n$. If you fancy planar graphs, you can have a look at plantri. I would not be surprised if you don't find tutorials, since this type of software is usually intended for professional researchers (but generally speaking, you should have little trouble in compiling and running if you are familiar with the typical Unix-like software).