Efficient Algorithms for Attributed Graph Alignment With Vanishing Edge Correlation
Bibliographic record
Abstract
Graph alignment refers to the task of finding the vertex correspondence between two correlated graphs ofnvertices. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the Erdős–Rényi graph pair model, where the two graphs are Erdős–Rényi graphs with edge probability$q_{\mathrm {u}}$, correlated under certain vertex correspondence. To achieve exact recovery of the correspondence, all existing algorithms at least require the edge correlation coefficient$\rho _{\mathrm {u}}$between the two graphs to benon-vanishingas$n\rightarrow \infty $. Moreover, it is conjectured that no polynomial-time algorithm can achieve exact recovery under vanishing edge correlation${\rho _{\mathrm {u}}}\lt 1/\mathrm {polylog}(n)$. In this paper, we show that with a vanishing amount of additionalattribute information, exact recovery is polynomial-time feasible undervanishingedge correlation${\rho _{\mathrm {u}}}\ge n^{-\Theta (1)}$. We identify alocaltree structure, which incorporates one layer of user information and one layer of attribute information, and apply the subgraph counting technique to such structures. A polynomial-time algorithm is proposed that recovers the vertex correspondence for most of the vertices, and then refines the output to achieve exact recovery. The consideration of attribute information is motivated by real-world applications like LinkedIn and Twitter, where user attributes like birthplace and education background can aid alignment.
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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 | 0.015 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.003 | 0.007 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.006 | 0.006 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.011 | 0.007 |
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".