Category: Network Sci.

Summary: Measuring the finite-size spectral detection threshold for multi-community stochastic block models near the Kesten-Stigum bound.

Community detection in stochastic block models has a sharp information-theoretic boundary, but finite systems do not sit exactly on the asymptotic limit. This experiment asks how the spectral detection threshold scales with system size for multi-community block models near the Kesten-Stigum transition.

The script generates block-structured random graphs, performs GPU-accelerated eigendecompositions, and measures when spectral signatures become strong enough to recover community structure. By pushing to larger graph sizes, it aims to map a systematic finite-size crossover rather than rely on a handful of small examples.

That matters because practical graph inference is always finite, and threshold rounding can determine whether spectral methods succeed in realistic regimes. The value of the experiment is the size-resolved threshold map, not just confirmation of the asymptotic bound.

Method: GPU dense eigendecomposition of stochastic block model adjacency operators across sizes and signal levels near the Kesten-Stigum boundary.

What is measured: Spectral detection threshold, finite-size scaling behavior, recovery quality, eigenvalue separation, and system-size dependence.