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I want to generate graphs with n vertices and e edges, and I also want the ability to count the number of non-isomorphic graphs with n and e. I was delighted to find these functions already implemented in Combinatorica as ListGraphs and NumberOfGraphs. Is there a modern equivalent that uses GraphData?

It's unfortunate that, although Combinatorica has been phased out as obsolete, some of its functionality hasn't yet been implemented in mainstream Mathematica. I tried using Combinatorica directly, but I always run into compatibility issues. As an alternative, then, is there a way to just make the old functionality work in modern Mathematica?

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