Category: Network Sci.

Summary: Testing when a shell of frustrated signed edges in a signed block model overtakes the planted community signal in the leading spectral mode.

Signed stochastic block models are meant to reveal community structure, but additional pockets of antagonistic or frustrated edges can compete with that signal. This experiment asks when a planted shell of such frustration becomes strong enough to pull the leading eigenvector away from the underlying two-community organization.

The script generates dense signed block-model matrices with a localized shell perturbation and uses GPU eigensolves to follow the top spectral mode while system size grows. Iterative deepening narrows the threshold where the dominant mode stops representing the global community split and becomes concentrated on the frustrated shell.

That matters because practical spectral methods can fail for structural reasons that look like noise at first glance. The experiment isolates one concrete failure mode: a localized signed anomaly that hijacks the top signal before the planted partition itself disappears.

Method: GPU dense symmetric eigensolves with iterative deepening and bisection on shell-confined signed frustration in stochastic block model ensembles.

What is measured: Critical frustration threshold, overlap of the leading mode with the planted community signal, shell localization, and bracket width.