Bibliographic record
Abstract
Clustering coefficient (C) is an important structural property to understand the complex structure of a graph. Calculating C is a computationally intensive task. Thereby, sampling-based methods have attracted substantial research for estimating C, and the closely related metric, the number of triangles. Unfortunately, widely used estimators for C are biased. We quantify the bias using Taylor expansion and find that the bias can be determined by the number of shared wedges and triangles in the sample. Based on the understanding of the bias, we give a new estimator that corrects the bias. The results are derived analytically and verified extensively in 56 networks ranging in different size and structure. The experiments reveal that the bias ranges widely from data to data. The relative bias can be as high as 4% or can be negative. For most of the graphs, the bias is small, although every graph does have a bias as quantified by our analytical results. Negative or small biases occur in online social networks where clustering coefficient is typically high. Positive and large biases typically occur in Web graphs, where there are nodes with high degrees but few neighboring nodes connecting with each other.
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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".