Core decomposition spectra of large graphs and their applications in modelling
Bibliographic record
Abstract
Systems with large number of interacting components are often modelled by random graphs and networks. In models of this type, one frequently needs to characterize graph clustering at both local and global level. We propose a method of characterization of clustering in large graphs and networks using the concept of k-core decomposition. The plot of clustering coefficient of k-core versus size of k-core will be called the spectrum of clustering coefficients. We show that k-core spectrum may play an important role in language graphs, such as graphs constructed from language dictionaries, where it can be used to describe some dynamical phenomena by purely static, topological quantities. In the last part of the paper, we propose a random graph model of a dictionary graph for which the k-core spectrum has similar features as in real dictionary graphs. The model is based on generalization of geometric random graphs in which the range parameter varies from vertex to vertex.
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How this classification was reachedexpand
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 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".