Explicit Bounds on the Entropy of Piecewise Hölder Graphon Models

2026-08-26

AI Summary

研究了由分段Hölder连续图模型生成的随机图熵，通过证明归一化熵的收敛速率，为随机块模型和随机几何图模型提供了显式的熵界。

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.

Problem

• Entropy
• Piecewise H\xf6lder continuous graphons
• Stochastic block model
• Random geometric graph model

Innovation

• Entropy
• Piecewise H\xf6lder Continuous Graphons
• Quantitative Bounds