Relationships between Node Degrees and Hyperedge Sizes in Empirical Hypergraphs
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Bibliographic record
Abstract
We investigate networks represented as hypergraphs and propose a a novel measure that captures the relationship between their node degrees and hyperedge sizes. We test the presence of such an association in 36 empirical hypergraphs from diverse domains, with a focus on social networks. Using nested model comparisons, we classify each such relationship as linear, monotonic, non-monotonic, or absent. Results reveal that true absence of this relationship is rare, while nearly half exhibit non-monotonic patterns. We evaluate three correlation measures of this association and find that Pearson correlation best aligns with relationship direction. We also consider three ways to capture this relationship (called: bipartite, node-centric or edge-centric) and show that the bipartite one yields most consistent results. We discuss the implications of existence of relationship between node degrees and hyperedge sizes for dynamic processes on social systems.
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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