高阶网络中的距离和超图的度量结构
Ekaterina Vasilyeva1,2, Miguel Romance3,4, Ivan Samoylenko1,5
1The Phystech School of Applied Mathematics and Computer Science, Moscow Institute of Physics and Technology, Institutskiy per., 9, 141701 Dolgoprudny, Moscow Region, Russia.
Entropy (Basel, Switzerland)
|June 28, 2023
概括
我们为超边形引入了一种新的距离度量,捕获超边形内和超边形之间的距离. 该指标揭示了超越对互动的网络结构,并将更高阶网络的中心性指标概括.
科学领域:
- 网络科学 网络科学
- 图形理论 图形理论
- 数据分析 数据分析
背景情况:
- 传统的网络分析通常依赖于对互动,限制了对复杂系统的研究.
- 通过超图表示的更高阶相互作用在许多现实世界现象中至关重要,但在量化分析方面具有挑战性.
- 现有的网络指标可能无法充分捕捉超图的结构性质.
研究的目的:
- 开发一种用于在超图中量化距离的新型度量.
- 将传统的网络中心性指标 (效率,接近,间距) 扩展到超图.
- 揭示对具有更高阶相互作用的复杂网络中的结构特征和节点角色的新见解.
主要方法:
- 引入了一个新的超图距离度量,考虑超边缘内部的节点间距离和超边缘之间的距离.
- 在超图的加权线图上使用计算.
- 将指标应用于合成和大规模的现实世界超图.
- 概括的效率,接近性和中间的中心性对于超图.
主要成果:
- 这种新型指标有效地揭示了合成超图中的结构信息.
- 使用新指标对现实世界超图的分析提供了超越对对相互作用分析的见解.
- 与超图集团预测相比,一般化的中心性测量提供了不同的节点评估,特别是对于具有较大的超边缘的超图.
结论:
- 建议的超图距离度量是分析具有更高阶相互作用的复杂网络的宝贵工具.
- 一般化的中心性措施提供了对高图中节点角色和信息可传输性的更细致的理解.
- 这种方法增强了超越传统对对关系的网络结构的研究.
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