Efficiently identifying critical nodes in large complex networks
Bibliographic record
Abstract
The critical node detection problem (CNDP) aims to fragment a graph G=(V,E) by removing a set of vertices R with cardinality |R|≤k, such that the residual graph has minimum pairwise connectivity for user-defined value k. Existing optimization algorithms are incapable of finding a good set R in graphs with many thousands or millions of vertices due to the associated computational cost. Hence, there exists a need for a time- and space-efficient approach for evaluating the impact of removing any v∈V in the context of the CNDP. In this paper, we propose an algorithm based on a modified depth-first search that requires O(k(|V|+|E|)) time complexity. We employ the method within in a greedy algorithm for quickly identifying R. Our experimental results consider small- (≤250 nodes) and medium-sized (≤25,000 nodes) networks, where it is possible to compare to known optimal solutions or results obtained by other heuristics. Additionally, we show results using six real-world networks. The proposed algorithm can be easily extended to vertex- and edge-weighted variants of the CNDP.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".