A Notion of Robustness in Complex Networks
Bibliographic record
Abstract
We consider a graph-theoretic property known as r-robustness which plays a key role in a class of consensus (or opinion) dynamics where each node ignores its most extreme neighbors when updating its state. Previous work has shown that if the graph is r-robust for sufficiently large r, then such dynamics will lead to consensus even when some nodes behave in an adversarial manner. The property of r-robustness also guarantees that the network will remain connected even if a certain number of nodes are removed from the neighborhood of every node in the network and thus it is a stronger indicator of structural robustness than the traditional metric of graph connectivity. In this paper, we study this notion of robustness in common random graph models for complex networks; we show that the properties of robustness and connectivity share the same threshold function in Erdös-Rényi graphs, and have the same values in 1-D geometric graphs and certain preferential attachment networks. This provides new insights into the structure of such networks, and shows that they will be conducive to the types of dynamics described before. Although the aforementioned random graphs are inherently robust, we also show that it is coNP-complete to determine whether any given graph is robust to a specified extent.
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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 | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".