Contiguity and non-reconstruction results for planted partition models: the dense case

Understand

We consider the two block stochastic block model on $n$ nodes with asymptotically equal cluster sizes.

• The connection probabilities within and between cluster are denoted by $p_n:=\frac{a_n}{n}$ and $q_n:=\frac{b_n}{n}$ respectively.
• Mossel et al.(2012) considered the case when $a_n=a$ and $b_n=b$ are fixed.
• They proved the probability models of the stochastic block model and that of Erd{\&#34;o}s-R{\'e}nyi graph with same average degree are mutually contiguous whenever $(a-b)^2<2(a+b)$ and are asymptotically singular whenever $(a-b)^2>2(a+b)$.