Modularity maximization in networks by variable neighborhood search
Bibliographic record
Abstract
Finding communities, or clusters, in networks, or graphs, has been the subject of intense studies in the last ten years. The most used criterion for that purpose, despite some recent criticism, is modularity maximization, proposed by Newman and Girvan. It consists in maximizing the sum for all clusters of the number of inner edges minus the expected number of inner edges assuming the same distribution of degrees. Numerous heuristics, as well as a few exact algorithms have been proposed to maximize modularity. We apply the Variable Neighborhood Search metaheuristic to that problem. Computational results are reported for the instances of the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="10 Superscript t h"> <mml:semantics> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>t</mml:mi> <mml:mi>h</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">10^{th}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> DIMACS Implementation Challenge. The algorithm presented in this paper obtained the second prize in the quality modularity (sub)challenge of the referred competition, finding the best known solutions for 11 out of 30 instances.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".