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 $N\ensuremath{\leqslant}14$. 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 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 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".