伊哈拉泽塔函数作为分区函数用于网络结构的表征
Jianjia Wang1, Edwin R Hancock2
1School of AI and Advanced Computing, Xi'an Jiaotong-Liverpool University, Suzhou, 215412, China. Jianjia.Wang@xjtlu.edu.cn.
Scientific reports
|August 8, 2024
概括
这项研究将Ihara Zeta函数和统计力学分区函数用于网络分析. 这种联系揭示了对微观和宏观网络结构的洞察,包括热力学特性和相位过渡.
科学领域:
- 网络科学 网络科学
- 代数图形理论的代数图形理论
- 统计力学 统计力学
背景情况:
- 复杂的网络结构通常使用Ihara Zeta函数和统计力学分区函数单独分析.
- 这两种用于网络表征的分析工具之间的潜在协同作用尚未得到充分利用.
- 现有的方法缺乏统一的框架,将微观网络细节与宏观属性连接起来.
研究的目的:
- 在统计力学中建立伊哈拉泽塔函数和分区函数之间的正式联系.
- 为了利用这种关系,对复杂网络进行更深入的结构性表征.
- 探索网络的微观结构与其宏观行为之间的联系.
主要方法:
- 从网络属性中推导热力学量 (例如,).
- 使用伊哈拉泽塔函数的第n阶部分导数来量化质周期频率.
- 与波斯-爱因斯坦统计的分区函数相关的网络质循环计数.
- 在高温和低温极限下调查网络相位过渡.
主要成果:
- 在代数图形理论 (Ihara Zeta函数) 和统计力学 (分区函数) 之间建立了新的联系.
- 热力学属性,如,是从主要循环的频率衍生而来的,并与之联系在一起.
- 该研究确定了网络结构中的相位过渡,在极端温度下存在关键点.
- 数字实验和经验数据验证了衍生网络特征.
结论:
- 统一框架通过弥合微观和宏观视角,为复杂的网络结构提供了更深入的见解.
- 导出的热力学量和相位过渡分析为网络特征提供了新的指标.
- 这种方法增强了将图形理论和统计力学工具与网络科学相结合的分析能力.
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