Graph animals, subgraph sampling, and motif search in large networks
Bibliographic record
Abstract
We generalize a sampling algorithm for lattice animals (connected clusters on a regular lattice) to a Monte Carlo algorithm for "graph animals," i.e., connected subgraphs in arbitrary networks. As with the algorithm in [N. Kashtan et al., Bioinformatics 20, 1746 (2004)], it provides a weighted sample, but the computation of the weights is much faster (linear in the size of subgraphs, instead of superexponential). This allows subgraphs with up to ten or more nodes to be sampled with very high statistics, from arbitrarily large networks. Using this together with a heuristic algorithm for rapidly classifying isomorphic graphs, we present results for two protein interaction networks obtained using the tandem affinity purification (TAP) method: one of Escherichia coli with 230 nodes and 695 links, and one for yeast (Saccharomyces cerevisiae) with roughly ten times more nodes and links. We find in both cases that most connected subgraphs are strong motifs (Z scores >10) or antimotifs (Z scores <-10) when the null model is the ensemble of networks with fixed degree sequence. Strong differences appear between the two networks, with dominant motifs in E. coli being (nearly) bipartite graphs and having many pairs of nodes that connect to the same neighbors, while dominant motifs in yeast tend towards completeness or contain large cliques. We also explore a number of methods that do not rely on measurements of Z scores or comparisons with null models. For instance, we discuss the influence of specific complexes like the 26S proteasome in yeast, where a small number of complexes dominate the k cores with large k and have a decisive effect on the strongest motifs with 6-8 nodes. We also present Zipf plots of counts versus rank. They show broad distributions that are not power laws, in contrast to the case when disconnected subgraphs are included.
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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 | 0.001 | 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".