微正则有限图系综的熵

IF 2.6 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Physics Complexity Pub Date : 2023-05-18 DOI:10.1088/2632-072X/acf01c

T. Kawamoto

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引用次数: 0

摘要

随机图集合的熵在图论和网络科学领域得到了广泛的关注。我们考虑具有规定次数序列的简单图的微正则集合。我们证明了使用Chebyshev–Hermite多项式的生成函数的平均场近似提供了有限图集合熵的估计。我们的估计再现了大图极限下的Bender–Canfield公式。

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Entropy of microcanonical finite-graph ensembles

The entropy of random graph ensembles has gained widespread attention in the field of graph theory and network science. We consider microcanonical ensembles of simple graphs with prescribed degree sequences. We demonstrate that the mean-field approximations of the generating function using the Chebyshev–Hermite polynomials provide estimates for the entropy of finite-graph ensembles. Our estimate reproduces the Bender–Canfield formula in the limit of large graphs.

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来源期刊

Journal of Physics Complexity Computer Science-Information Systems

CiteScore

4.30

自引率

11.10%

发文量

审稿时长

14 weeks