Control range: a controllability-based index for node significance in directed networks
Why this work is in the frame
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Bibliographic record
Abstract
While a large number of methods for module detection have been developed for undirected networks, it is difficult to adapt them to handle directed networks due to the lack of consensus criteria for measuring the node significance in a directed network. In this paper, we propose a novel structural index, the control range, motivated by recent studies on the structural controllability of large-scale directed networks. The control range of a node quantifies the size of the subnetwork that the node can effectively control. A related index, called the control range similarity, is also introduced to measure the structural similarity between two nodes. When applying the index of control range to several real-world and synthetic directed networks, it is observed that the control range of the nodes is mainly influenced by the network's degree distribution and that nodes with a low degree may have a high control range. We use the index of control range similarity to detect and analyze functional modules in glossary networks and the enzyme-centric network of homo sapiens. Our results, as compared with other approaches to module detection such as modularity optimization algorithm, dynamic algorithm and clique percolation method, indicate that the proposed indices are effective and practical in depicting structural and modular characteristics of sparse directed networks.
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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 | 0.002 | 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 | 0.000 |
| 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 it