论文标题
应用于网络持续同源的Forman-Ricci曲率版本的比较分析
Comparative analysis of Forman-Ricci curvature versions applied to the persistent homology of networks
论文作者
论文摘要
我们提供了Forman-Ricci曲率和持久同源性的概述，以及如何将它们的组合应用于网络研究。我们讨论通常将通常使用的eman-ricci曲率增强曲率公式（仅适用于准Quasonvex增强网络），可以扩展到非Quasiconvex案例。我们应用三个版本的Quasiconvex forman-Ricci曲率（平原，三角形和五角大楼的演说）来建立模型和现实世界中非Quasiconvex网络上的时间过滤。我们的结果表明，在进一步研究了非Quasiconvex公式之前，应使用三角提高的曲率，因为平整曲率省略了太多信息，而五角形五角形的曲率却过于近似，并显着扭曲了结果。
We provide an overview of Forman-Ricci curvature and persistent homology, and how their combination can be applied to the study of networks. We discuss how the usually employed augmented Forman-Ricci curvature formula, only valid for quasiconvex augmented networks, can be extended to the non-quasiconvex case. We apply three versions of quasiconvex Forman-Ricci curvature (plain, triangle-augmented, and pentagon-augmented) to build time filtrations on non-quasiconvex networks, both model and real-world. Our results suggest that triangle-augmented curvature should be used until the non-quasiconvex formula is further studied, as plain curvature omits too much information, and quasiconvex pentagon-augmented curvature is too rough of an approximation and significantly distorts the results.
