Bibliographic record
Abstract
We study the fundamental problem of butterfly (i.e., (2,2)-bicliques) counting in bipartite streaming graphs. Similar to triangles in unipartite graphs, enumerating butterflies is crucial in understanding the structure of bipartite graphs. This benefits many applications where studying the cohesion in a graph shaped data is of particular interest. Examples include investigating the structure of computational graphs or input graphs to the algorithms, as well as dynamic phenomena and analytic tasks over complex real graphs. Butterfly counting is computationally expensive, and known techniques do not scale to large graphs; the problem is even harder in streaming graphs. In this article, following a data-driven methodology, we first conduct an empirical analysis to uncover temporal organizing principles of butterflies in real streaming graphs and then we introduce an approximate adaptive window-based algorithm, sGrapp, for counting butterflies as well as its optimized version sGrapp-x. sGrapp is designed to operate efficiently and effectively over any graph stream with any temporal behavior. Experimental studies of sGrapp and sGrapp-x show superior performance in terms of both accuracy and efficiency.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".