why using p_prime = 1 - np.sqrt(1 - p) in SBM_multiclass?

[FeiGSSS]

hi,
Thanks for your contribution! I'm wondering why you have to using p_prime = 1 - np.sqrt(1 - p) for SBM_multiclass? Is there any mathematical consideration?

[zhengdao-chen]

Thanks for the question. The reason is that to generate an undirected graph with a symmetric adjacency matrix, our method is to first sample an asymmetric matrix W and then compute the symmetrized matrix W = np.maximum(W, W.transpose()). Because of this, in order to make sure the symmetric W created at the end have the desired connectivities p and q, we need to sample the asymmetric W with p_prime and q_prime.