Clique Listing Algorithms and Characteristics of Cliques in Random Graphics
Why this work is in the frame
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Bibliographic record
Abstract
In this thesis we address three main problems in clique detection in the area of Graph Theory. i) Most of current methods for clique detection are time consuming (can take exponential time to the size of input graph), so there is a practical limit on size of input graph. In this thesis we propose three different methods for estimating the number of cliques. We examine these methods for various graphs and conclude that they efficiently find the number of cliques within 5% error typically. ii) We compare various versions of the Bron-Kerbosch (BK) clique listing algorithm to discover a method of combining the best features of different versions. We test our new versions of BK for various inputs. iii) We study the characteristics of cliques in random graphs as a function of size and density.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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