Here, we are talking about degree assortativity (https://en.wikipedia.org/wiki/Assortativity). We know that the expected assortativity of graphs generated by Erdos-Renyi or Chung-Lu asymptotically approaches zero, and the Block Two-Level Erdos-Renyi (BTER) model generates graphs with highly positive assortativity. Are there existing random graph models that allow controlling assortativity in both directions?
References:
- Noldus, Rogier, and Piet Van Mieghem. "Assortativity in complex networks." Journal of Complex Networks 3.4 (2015): 507-542.
- Seshadhri, Comandur, Tamara G. Kolda, and Ali Pinar. "Community structure and scale-free collections of Erdős-Rényi graphs." Physical Review E 85.5 (2012): 056109.
2023-11-10
In Newman's original paper on assortativity, a sampling-based edge-rewiring mechanism is proposed for controlling assortativity. Also, Newman and Park proposed a model with controllable assortativity, but limited to non-negative assortativity.
Reference:
- Newman, Mark EJ. "Assortative mixing in networks." Physical review letters 89.20 (2002): 208701.
- Newman, Mark EJ, and Juyong Park. "Why social networks are different from other types of networks." Physical review E 68.3 (2003): 036122.