A Comparison of Four Notions of Isomorphism-Based Security for Graphs
Bibliographic record
Abstract
A graph is a powerful abstraction for representing information. We address the problem of publishing a secure version of a graph that does not leak information to an adversary who may possess prior information about portions of the graph, and may have unbounded computational power. In this context, we revisit four notions of security, all of which are based on variants of graph isomorphism, that have been proposed in two different application contexts in the literature. We compare the four notions to one another, first from the standpoint of strength, i.e., whether meeting one notion implies meeting another, and then from the standpoint of computational hardness, i.e., what the exact computational complexity is for the problem of checking whether a graph meets a notion. For the latter, we identify that for two of the notions we consider, the problem is$\mathbf{NP}\text{-complete}$, and for the two others, it isISO-complete, whereISOis the class of problems induced by graph isomorphism. We observe that strength is not necessarily correlated to computational hardness. In summary, our work makes contributions at the foundations of an important notion of security for 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 | 0.013 | 0.036 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.005 |
| Bibliometrics | 0.006 | 0.006 |
| Science and technology studies | 0.003 | 0.021 |
| Scholarly communication | 0.011 | 0.036 |
| Open science | 0.005 | 0.014 |
| Research integrity | 0.005 | 0.011 |
| Insufficient payload (model declined to judge) | 0.005 | 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".