Explicit Bounds on the Entropy of Piecewise Hölder Graphon Models

• URL: http://arxiv.org/abs/2608.26501v1
• Date: Thu, 27 Aug 2026 00:49:59 GMT
• Title: Explicit Bounds on the Entropy of Piecewise Hölder Graphon Models
• Abstract summary: entropy of random graphs generated by piecewise Hlder continuous graphons.<n>We first present a result on the rate of convergence of the normalized entropy as the size of the graph grows.<n>We then derive quantitative bounds on the entropy for the block model and random geometric graph model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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