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 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 | 0.002 | 0.008 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".