Temporal evolution of the degree distribution of alters in growing networks
Bibliographic record
Abstract
Abstract The degree distribution of the neighbors of nodes in a network is a theoretically important tool that is invoked in diverse studies in network science, such as epidemics, network resilience, network search and observability, network synchronization, random walks, opinion dynamics, and other dynamical systems on networks. Many real networks grow, and their properties pertaining to the said phenomena evolve. There is a paucity of theoretical research on how the evolution of these properties depend upon time and upon the structure of the initial network. This paper addresses this problem by providing the first theoretical study of the temporal evolution of the nearest-neighbor degree distribution for arbitrary networks (with any size) in arbitrary times. The posited results enable the analysis of the structural properties of growing networks in the short-time and intermediary time regimes, which are typically ignored in favor of the steady state. We corroborate the solutions via Monte Carlo simulations on various topologies. As a byproduct of the obtained solutions, we also demonstrate that the existing result in the literature on the asymptotic behavior of the Pearson coefficient of growing networks under the preferential attachment mechanism is incorrect, and we present the correct solution.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".