Electrical Networks and Algebraic Graph Theory: Models, Properties, and Applications
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Algebraic graph theory is a cornerstone in the study of electrical networks ranging from miniature integrated circuits to continental-scale power systems. Conversely, many fundamental results of algebraic graph theory were laid out by early electrical circuit analysts. In this paper, we survey some fundamental and historic as well as recent results on how algebraic graph theory informs electrical network analysis, dynamics, and design. In particular, we review the algebraic and spectral properties of graph adjacency, Laplacian, incidence, and resistance matrices and how they relate to the analysis, network reduction, and dynamics of certain classes of electrical networks. We study these relations for models of increasing complexity ranging from static resistive direct current (dc) circuits, over dynamic resistor..inductor..capacitor (RLC) circuits, to nonlinear alternating current (ac) power flow. We conclude this paper by presenting a set of fundamental open questions at the intersection of algebraic graph theory and electrical networks.
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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) | 0.000 | 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 it