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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19828536 |
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| author | Roif, Avishai |
| author_facet | Roif, Avishai |
| 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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19828536 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The B-Test: A Spectral Consistency Test for Real-World Networks Under Boundary Algebra Roif, Avishai B-test Hypothesis Testing Boundary Algebra Spectral Consistency Network Clusters Satterthwaite Approximation Subsampling Estimator Skewness Difference Ontological Distance Network Science Methodology Weighted Chi-Squared Distribution Spectral Weights <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> |
| title | The B-Test: A Spectral Consistency Test for Real-World Networks Under Boundary Algebra |
| topic | B-test Hypothesis Testing Boundary Algebra Spectral Consistency Network Clusters Satterthwaite Approximation Subsampling Estimator Skewness Difference Ontological Distance Network Science Methodology Weighted Chi-Squared Distribution Spectral Weights |
| url | https://doi.org/10.5281/zenodo.19828536 |