AI 中文总结
该研究针对分段赫尔德连续图生成的随机图，推导了随机块模型与随机几何图模型熵的显式定量界，给出归一化熵收敛速率结果，补充了此前仅有的渐近表述。
AI 中文摘要
我们研究由分段赫尔德连续图生成的随机图的熵。首先给出图规模增长时归一化熵收敛速率的结果，描述证明的核心思路，详细证明见附录。基于该结果，推导随机块模型和随机几何图模型的熵定量界，这些界提供了显式公式，而非此前发现的渐近表述。
英文摘要
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.
Comments13 pages, corrected minor errors
