Visualization of Node-Centric Hierarchical Structures in Directed Graphs
Bibliographic record
Abstract
Force-directed layouts are popular for graph visualization but often ignore edge direction, limiting their use for directed networks. Existing direction-aware methods apply global magnetic fields, revealing only broad hierarchical patterns. In this paper, we introduce a multi-pole magnetic force model that assigns localized polar fields to user-defined nodes ("poles"), attracting nearby nodes based on shortest-path distances. This approach reveals node-centric hierarchies influenced by the selected poles. We enhance traditional force-based algorithms by introducing pole gravity, pole separation, and circular hierarchy forces to improve the clarity of node-centric local structures. Experiments on citation, software, and Twitter networks show fewer edge crossings and misaligned edges, with clearer hierarchical structures than existing force-based methods, along with better quantitative performance metrics. Our technique is released as an open-source Cytoscape plugin ‘CodeNetVis’ for practical analysis of software dependency graphs.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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".