An empirical comparison of connectivity-based distances on a graph and their computational scalability
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Bibliographic record
Abstract
Abstract In this study, we compare distance measures with respect to their ability to capture vertex community structure and the scalability of their computation. Our goal is to find a distance measure which can be used in an aggregate pairwise minimization clustering scheme. The minimization should lead to subsets of vertices with high induced subgraph density. Our definition of distance is rooted in the notion that vertices sharing more connections are closer to each other than vertices which share fewer connections. This definition differs from that of the geodesic distance typically used in graphs. It is based on neighbourhood overlap, not shortest path. We compare four distance measures from the literature and evaluate their accuracy in reflecting intra-cluster density, when aggregated (averaged) at the cluster level. Our tests are conducted on synthetic graphs, where clusters and intra-cluster densities are known in advance. We find that amplified commute, Otsuka–Ochiai and Jaccard distances display a consistent inverse relation to intra-cluster density. We also conclude that the computation of amplified commute distance does not scale as well to large graphs as that of the other two distances.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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