Minority communities in stochastic block models enter three phases of detectability—detectable, distinguishable, and resolvable—separated by the Kesten-Stigum threshold and two additional thresholds from the eigenvalue structure of the signal matrix.
ρ qs pin −λ− − ρ qs δ+λ ρ qs δ−λ ρ qs pout(qs −1) − − ρ qs δ+λ 1−ρ qb δ−λ 1−ρ qb poutqb # = ρ qs δ−λ qs−1 · 1−ρ qb δ−λ qb ·
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Detectability of minority communities in networks
Minority communities in stochastic block models enter three phases of detectability—detectable, distinguishable, and resolvable—separated by the Kesten-Stigum threshold and two additional thresholds from the eigenvalue structure of the signal matrix.