Hypercube Graph Representations and Fuzzy Measures of Graph Properties
Bibliographic record
Abstract
We describe a novel hypercube graph representation for labeled graphs with arbitrary edge weights in the interval [0, 1]. This representation admits graphical models for weighted adjacency matrices, which are useful in a number of real world applications wherein the strength of connections between graph nodes is important. It enables us to bring to bear a full arsenal of fuzzy set theoretic measures such as fuzzy subsethood, entropy, completeness, and mutual subsethood to the description of graphs. Our hypercube representation also provides a direct similarity metric between pairs of graphs, which is particularly useful for external comparisons among sets of graphs. The unitary complement of this similarity metric in turn provides a distance metric between two graphs, thus enabling us to perform vector processing operations on graphs, e.g., clustering, change detection, hypothesis testing as to the independence of two graphs, feature extraction for neural network and/or statistical classifiers, and antecedent specification for fuzzy mappings. We derive the probability mass function of this metric for two independent random graphs. The hypercube graph representation finds applications in problems where we are dealing with labeled graphs, e.g., computer networks, social networks, graphical information retrieval, and data fusion problems involving virtual networks of events. Of special interest are labeled graphs with fixed vertices whose edges and their corresponding weights vary over time, as well as graphs that evolve in time by the addition of new vertices and edges.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".