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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19828536 |
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Table of Contents:
- <p class="MsoNormal">We introduce the B-test (ℬ), a new hypothesis test for real-world networks grounded in the Boundary Algebra (BA) framework. Building on the third paper of this series, which established that networks under BA constraints produce asymmetric normal degree distributions with skewness γ = cos(2π/k) determined by spectral class k ∈ {0, 2, 3, 4}, the B-test evaluates whether the observed skewness differences between network clusters are consistent with their theoretical spectral assignments. The test statistic is ℬ = Σ_{i<j} |γ*_i − γ*_j| · Z²_{ij}, where Z_{ij} is the standardized skewness difference and the weights |γ*_i − γ*_j| are fixed by the spectral classes. Under H₀, ℬ follows a weighted chi-squared distribution with analytically determined parameters (Satterthwaite approximation), requiring no bootstrap or permutation procedure. Simulation results demonstrate Type I error control at 0.035 and power exceeding 0.88 for deviations of Δγ ≥ 1.0, with power approaching 1.0 for larger deviations. The B-test provides the first ontologically grounded hypothesis testing framework for network science.</p>