title: Detectability thresholds of general modular graphs.
abstract: We investigate the detectability thresholds of various modular structures in the stochastic block model. Our analysis reveals how the detectability threshold is related to the details of the modular pattern, including the hierarchy of the clusters. We show that certain planted structures are impossible to infer regardless of their fuzziness.
authors.affiliation: Department of Mathematical and Computing Science, Tokyo Institute of Technology, 4259-G5-22, Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8502, Japan.
authors.forename: Tatsuro
authors.initials: T
authors.lastname: Kawamoto
authors.affiliation: Department of Mathematical and Computing Science, Tokyo Institute of Technology, 4259-G5-22, Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8502, Japan.
authors.forename: Yoshiyuki
authors.initials: Y
authors.lastname: Kabashima