Category: Network Sci.

Summary: Estimating when antagonistic shell-degree imbalance disrupts community-aligned spectral detection and relocalizes the leading eigenvector onto a nuisance shell mode.

Signed stochastic block models can support clear community recovery near detectability boundaries, but degree imbalance in a peripheral shell may generate a competing spectral signal. This experiment asks for the finite-size threshold where that shell imbalance becomes strong enough to pull the leading eigenvector away from the true community structure.

The GPU workflow studies signed SBM ensembles near the detectability edge and varies shell-focused antagonistic imbalance while tracking eigenvector alignment and localization. The goal is to locate the point where recovery collapses because the nuisance shell-degree mode overtakes the community mode.

That matters because detectability can fail for structural reasons that look like noise only at coarse resolution. The threshold map isolates one concrete mechanism by which peripheral imbalance can defeat spectral community recovery.

Method: GPU iterative-deepening spectral analysis of signed stochastic block models with controlled shell-degree imbalance near the detectability boundary.

What is measured: Critical imbalance threshold, community-mode alignment, shell-mode localization, spectral recovery collapse, and bracket width.