Dear Szabolcs Horvát,
First of all, thank you for your reply and help! I really appreciate it. Based on the examples you presented above this tool is just perfect for me, but unfortunately I could not manage to make it work.
I downloaded the recommended Nauty and Traces, but I use Windows 10 instead of Mac, so at first I used Cygwin to compile and install these tools, however it did not work on my computer. Then I tried to use another computer with Linux to compile and install, and then just copied the files back to the original computer, but I am not convinced that this method solved the entire problem. And I also find out in your documentation that in your examples we assume that the gtools programs are in a directory that is on the operating systems PATH environment variable. Unfortunatelly I could not figure out how exactly these environments work in Mathematica, but maybe this cause the problem. I do not know, but I get the following warning messages after using the first example you wrote:
-Counts: The argument IGImport[IGDiameter[!geng -d3 -D3 -c 12],IGDiameter[Nauty]] is not a list.
-KeySort: The argument Counts[IGImport[IGDiameter[!geng -d3 -D3 -c 12],IGDiameter[Nauty]]] is not a valid Association or a list of rules.
I also tried the following:
Import["!geng -d3 -D3 12", "Graph6"]
But I got another error, which says 'Import: Cannot import data as Graph6 format.'
Do you have any ideas what could cause the problem? I think I need exactly this tool, so I would be really happy if I could make it work. Thank you for your help!
Also, I do not really know the rules and features of this forum, but I suppose only English is allowed. However if there is a private message option, then maybe it would be easier to discuss the problem there, because based on your name we both speak Hungarian... :)
Thank you for everything!