For a research project I am working on, I need to generate random graphs which favour forming cliques without the largest cliques containing the same nodes. For instance, the Barabási–Albert model can generate graphs containing large cliques, but those cliques have mainly the same nodes because of preferential attachment.

Although I prefer using existing packages like Networkx or IGraph, I am okay with implementing research papers that have formalised generating such networks. The only criterium is that the generation of those graphs should not take more than 15 seconds for a graph with, for instance, 10.000 nodes and an average degree of 100.

I am also not sure if I should ask this question on here or on