Detectability thresholds of general modular graphs

TL;DR

This paper analyzes the limits of detecting modular structures in stochastic block models, showing how detectability depends on the pattern's details and hierarchy, with some structures inherently undetectable.

Contribution

It provides a detailed analysis of detectability thresholds in modular graphs, highlighting the influence of cluster hierarchy and revealing impossible-to-infer structures.

Findings

Detectability thresholds depend on modular pattern details.

Hierarchical structures affect detectability.

Some planted structures are inherently undetectable.

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.