PreprintCC BY 4.0arXiv
Explicit Bounds on the Entropy of Piecewise Hölder Graphon Models
Abstract
We study the entropy of random graphs generated by piecewise Hölder continuous graphons. We first present a result on the rate of convergence of the normalized entropy as the size of the graph grows. The core ideas of the proof are described, with the detailed proof provided in the appendix. From this result, we then derive quantitative bounds on the entropy for the stochastic block model and random geometric graph model. These bounds provide explicit formulae rather than asymptotic statements which have been found previously.
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BibTeX
@misc{loehdewoolard2026explicit,
title = {{Explicit Bounds on the Entropy of Piecewise Hölder Graphon Models}},
author = {Connor Loehde-Woolard and François G. Meyer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.26501},
eprint = {2608.26501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26501},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Explicit Bounds on the Entropy of Piecewise Hölder Graphon Models
AU - Connor Loehde-Woolard
AU - François G. Meyer
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2608.26501
UR - https://arxiv.org/abs/2608.26501
AB - We study the entropy of random graphs generated by piecewise Hölder continuous graphons. We first present a result on the rate of convergence of the normalized entropy as the size of the graph grows. The core ideas of the proof are described, with the detailed proof provided in the appendix. From this result, we then derive quantitative bounds on the entropy for the stochastic block model and random geometric graph model. These bounds provide explicit formulae rather than asymptotic statements which have been found previously.
ER -