https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_...
If you want to start from a real-world dataset, take a look at Stanford's SNAP large network dataset collection.
https://snap.stanford.edu/data/
GP: Sounds like a great project. What's the application?
[0] https://en.wikipedia.org/wiki/Watts%E2%80%93Strogatz_model
https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_...
If you want to start from a real-world dataset, take a look at Stanford's SNAP large network dataset collection.
https://snap.stanford.edu/data/