Category: Network Sci.

Summary: Testing whether concentrating cross-community bridges onto high-degree nodes localizes the informative eigenvector and weakens community recovery near the detectability boundary.

Spectral community detection works by extracting eigenvectors that align with block structure, but those vectors can become misleading when hubs dominate them. This experiment asks how community recovery changes when cross-community bridge edges in a degree-corrected stochastic block model are concentrated onto the highest-degree nodes instead of being placed neutrally or anti-aligned with degree.

The simulation maps localization and label recovery near the spectral detectability boundary using batched GPU ensembles. By sweeping the bridge-placement rule and community signal strength together, it focuses on the regime where informative eigenvectors are barely strong enough to guide recovery.

That setting is important because practical networks often combine community structure with degree heterogeneity. The experiment isolates whether bridge-hub concentration creates a distinct localization penalty that is strongest precisely where detection is already fragile.

Method: Batched GPU spectral analysis of degree-corrected stochastic block models, comparing modularity-eigenvector localization and recovery across bridge-placement rules.

What is measured: Eigenvector localization, community label recovery, detectability-boundary behavior, and bridge-placement crossover effects.