Generation of random graphs with applications to complex networks
Bibliographic record
Abstract
Given a sequence d of n positive integers, n−1 ≥ d1 ≥ d2 ≥ . . . ≥ dn ≥ 0, different sets of necessary and sufficient conditions have been proposed for the graphicality of such a sequence. When such a graph exists, we can use 2-switches of pairs of independent edges to transform one such graph G into another graph G′ with the same degree sequence. This was proved by various authors. In this thesis we address the question whether a given graph G is at all switchable. Indeed, we show that unswitchable graphs are a proper subclass of split graphs, and exploit this fact to propose efficient algorithms for the recognition and generation of unswitchable graphs. This question of unswitchability is important as switching has been tried as a mechanism for generating a random graph with a given degree sequence or for generating new ones, preserving properties like simplicity or connectedness (this is known as constrained switching). In the second part of this thesis, motivated by the application to the area of so−called complex networks (examples are: protein−protein interaction networks, social networks, metabolic networks etc.), the statistical properties of province-wise transportation networks of Canada are studied and compared with two random graphs, generated using the Erdos-Renyi model and the Configuration model. A method to extract transportation network and network resilience two key practical contributions are discussed in depth. Finally, taking cue from the configuration model, in an appendix we discuss an implementation that generates a directed graph uniformly at random, using a Markov Chain Monte Carlo (MC−MC) method.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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".