A Binary Search Algorithm for Correlation Study of Decay Centrality vs. Degree Centrality and Closeness Centrality
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Bibliographic record
Abstract
Results of correlation study (using Pearson's correlation coefficient, PCC) between decay centrality (DEC) vs. degree centrality (DEG) and closeness centrality (CLC) for a suite of 48 real-world networks indicate an interesting trend: PCC(DEC, DEG) decreases with increase in the decay parameter δ (0 < δ < 1) and PCC(DEC, CLC) decreases with decrease in δ. We make use of this trend of monotonic decrease in the PCC values (from both sides of the δ-search space) and propose a binary search algorithm that (given a threshold value r for the PCC) could be used to identify a value of δ (if one exists, we say there exists a positive δ-spacer) for a real-world network such that PCC(DEC, DEG) ≥ r as well as PCC(DEC, CLC) ≥ r. We show the use of the binary search algorithm to find the maximum Threshold PCC value rmax (such that δ-spacermax is positive) for a real-world network. We observe a very strong correlation between rmax and PCC(DEG, CLC) as well as observe real-world networks with a larger variation in node degree to more likely have a lower rmax value and vice-versa.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.003 |
| 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