使用时空图的时间演变网络的集群拉普拉斯的网络
Maia Trower1, Natasa Djurdjevac Conrad2, Stefan Klus3
1Maxwell Institute for Mathematical Sciences, University of Edinburgh and Heriot-Watt University, EH8 9BT Edinburgh, United Kingdom.
Chaos (Woodbury, N.Y.)
|January 10, 2025
概括
这项研究引入了一种新的时空图Laplacian用于分析动态图. 它有效地捕捉了社会网络和交通流动等复杂系统中的不断发展的社区.
科学领域:
- 图形理论是指图形的理论.
- 动态系统是动态系统.
- 网络科学 网络科学
背景情况:
- 随时间演变的图表对于建模社交网络和流量等动态系统至关重要.
- 在这些动态图中分析社区结构是一个重大挑战.
- 现有的光谱聚类方法主要设计用于静态图.
研究的目的:
- 为了对动态图形的光谱聚类算法进行概括.
- 开发一个框架来捕捉集群的时间演变.
- 介绍和分析一个时空图的光谱性质.拉普拉斯.
主要方法:
- 使用正规相关性分析进行泛化光谱聚类.
- 定义并研究了拉普拉斯的时空图的光谱性质.
- 通过转移运算符将概念连接到动态系统理论中.
主要成果:
- 拟议的方法有效地捕捉了时间的演变.
- 在基准图表上表现出比现有方法的优势.
- 拉普拉斯的时空图提供了对集群动态的清晰解释.
结论:
- 时空图Laplacian是分析时间演变的图社区的强大工具.
- 这种方法为理解动态网络结构提供了一个强大的方法.
- 该框架适用于定向图和非定向图.
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