Edge ratio and community structure in networks
Bibliographic record
Abstract
A hierarchical divisive algorithm is proposed for identifying communities in complex networks. To that effect, the definition of community in the weak sense of Radicchi [Proc. Natl. Acad. Sci. U.S.A. 101, 2658 (2004)] is extended into a criterion for a bipartition to be optimal: one seeks to maximize the minimum for both classes of the bipartition of the ratio of inner edges to cut edges. A mathematical program is used within a dichotomous search to do this in an optimal way for each bipartition. This includes an exact solution of the problem of detecting indivisible communities. The resulting hierarchical divisive algorithm is compared with exact modularity maximization on both artificial and real world data sets. For two problems of the former kind optimal solutions are found; for five problems of the latter kind the edge ratio algorithm always appears to be competitive. Moreover, it provides additional information in several cases, notably through the use of the dendrogram summarizing the resolution. Finally, both algorithms are compared on reduced versions of the data sets of Girvan and Newman [Proc. Natl. Acad. Sci. U.S.A. 99, 7821 (2002)] and of Lancichinetti [Phys. Rev. E 78, 046110 (2008)]. Results for these instances appear to be comparable.
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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 | 0.001 |
| 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 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".