对于具有高阶相互作用的网络的集群系数.
Gyeong-Gyun Ha1, Izaak Neri1, Alessia Annibale1
1Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom.
Chaos (Woodbury, N.Y.)
|April 1, 2024
概括
我们为超图引入了四方集群系数. 现实世界网络显示高度集群的节点,与随机网络不同,表明需要更高层次的交互来识别复杂的网络结构.
科学领域:
- 网络科学 网络科学
- 图形理论 图形理论
- 复杂的系统复杂的系统.
背景情况:
- 传统的聚类系数分析图表中的对互动.
- 超图,代表更高阶交互,需要专门的指标.
- 了解多路关系的系统中的网络结构至关重要.
研究的目的:
- 引入一个新的对超图的集群系数.
- 在现实世界和随机超图中量化和分析四元集群系数.
- 研究复杂网络中高度集群节点的特征.
主要方法:
- 定向和非定向超图的四重集群系数的定义.
- 计算平均四方集群系数及其分布.
- 与通过配置模型生成的随机超图进行比较.
- 对高度集群节点的节点度和超边缘枢纽度的分析.
主要成果:
- 现实世界的超图表显示出有很大比例的节点具有最大的四元集群系数值.
- 在随机超图模型中没有发现如此高度集群的节点.
- 在真实网络中,高度集群的节点可以具有大度和高hyperedge cardinalities.
- 预测图表上的双向聚类系数无法识别这些高度聚类的节点.
结论:
- 四方集群系数有效地识别了在超图中具有高局部集群的节点.
- 高阶交互对于捕捉复杂的网络结构至关重要,而不是对对分析.
- 现实世界的网络具有独特的结构特性,这些特性在简单的随机模型中无法复制.
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