Statistical power, accuracy, reproducibility and robustness of a graph clusterability test
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract Not all graphs are clusterable. Not all graphs have a clustered structure and can be meaningfully summarized through vertex clustering. Clusterable graphs are characterized by pockets of densely connected vertices that are only sparsely connected to the remaining graph. In this article, we re-introduce a very simple and intuitive, yet highly informative, statistical hypothesis test for graph clusterability that is based on vertex and neighborhood samples. The goal of this test is to determine if a graph meets the necessary structural conditions to be summarized meaningfully through vertex clusters. Our test is based on the hypothesis that a clusterable graph will display, on average, a local neighborhood induced subgraph density that is greater than the graph’s overall density. The test is also applied to graph comparisons, to test whether one graph has a stronger clustered structure than another. Significance is assessed using the t -statistic. Since it is based on sampling, we provide a focused examination of our test’s sensitivity to sample size. The main contribution of this article is a detailed examination of our test’s accuracy, sensitivity to sample size, conclusion reproducibility and robustness. Our empirical results remain consistent with our earlier conclusions and demonstrate the almost perfect accuracy of our test, even with very small samples of the graph. They also reveal that our test remains robust even under severe departures from the null hypothesis.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it