Category: Network Sci.

Summary: Finding when shell-focused antagonism and degree imbalance jointly erase spectral community-detection signal in a signed block model.

Signed stochastic block models describe networks with both friendly and antagonistic ties, where community detection can fail for more than one reason. This experiment asks when two such effects combine destructively: antagonistic edges concentrated in shell-like parts of the network, and a competing signal caused by degree imbalance.

The script builds dense symmetric signed modularity operators, then bisects the shell-imbalance parameter while increasing system size through iterative deepening. The threshold is the point where the top eigenvector no longer carries reliable community information because the competing heterogeneity mode takes over.

That makes the problem more realistic than a clean block model with only one source of structure. It probes how spectral detection breaks down when informative community organization and misleading degree structure are both present.

Method: Dense symmetric eigensolve with iterative deepening and bisection on shell-focused antagonistic imbalance in a signed SBM.

What is measured: Critical shell-imbalance threshold, loss of top-eigenvector community signal, leading-mode behavior, and bracket width.