I created a paclet for graphs. It contains functions for generating graphs available on MathWorld and GraphData but not with dedicated functions. For example, one of my favorite graphs is the firecracker graph, but this is not available for any input.
I have also added some other functions including girth and rank polynomial.
There's also a function to insert a vertex into an edge and a function to test if a degree sequence is graphical.
I'm working on a function for coboundary polynomial.
