Subgraph ensembles and motif discovery using an alternative heuristic for graph isomorphism
Bibliographic record
Abstract
A heuristic based on vertex invariants is developed to rapidly distinguish nonisomorphic graphs to a desired level of accuracy. The method is applied to sample subgraphs from an Escherichia coli protein interaction network, and as a probe for discovery of extended motifs. The network's structure is described using statistical properties of its N-node subgraphs for N<or=14. The Zipf plots for subgraph occurrences are robust power laws that do not change when rewiring the network while fixing the degree sequence--although many specific subgraphs exchange rank. The exponent for the Zipf law depends on N. Studying larger subgraphs highlights some striking patterns for various N. Motifs, or connected pieces that are overabundant in the ensemble of subgraphs, have more edges, for a given number of nodes, than antimotifs and generally display a bipartite structure or tend toward a complete graph. In contrast, antimotifs, which are underabundant connected pieces, are mostly trees or contain at most a single, small loop.
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How this classification was reachedexpand
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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".