Explicit Bounds on the Entropy of Piecewise H\"{o}lder Graphon Models

Connor Loehde-Woolard; François G. Meyer

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arXiv · 2608.26501

Explicit Bounds on the Entropy of Piecewise H\"{o}lder Graphon Models

Connor Loehde-Woolard·François G. Meyer

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Abstract

We study the entropy of random graphs generated by piecewise H\"{o}lder 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 RIS

Connor Loehde-Woolard, François G. Meyer. 2026-08-27. Explicit Bounds on the Entropy of Piecewise H\"{o}lder Graphon Models. https://arxiv.org/abs/2608.26501

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