Crossing the KS threshold in the stochastic block model with information theory

Abstract

Decelle et al. conjectured that community detection in the symmetric stochastic block model has a computational threshold given by the so-called Kesten-Stigum (KS) threshold, and that information-theoretic methods can cross this threshold for a large enough number of communities (4 or 5 depending on the regime of the parameters). This paper shows that at k = 5, it is possible to cross the KS threshold in the disassortative regime with a non-efficient algorithm that samples a clustering having typical cluster volumes. Further, the gap between the KS and information-theoretic threshold is shown to be large in some cases. In the case where edges are drawn only across clusters with an average degree of b, and denoting by k the number of communities, the KS threshold reads b ≳ k2 whereas our information-theoretic bound reads b ≳ k ln(k).