Motivated by the methods and results of manifold sampling based on Ricci curvature, we propose a similar approach for networks. To this end we make appeal to three types of discrete curvature, namely the graph Forman-, full Forman- and Haantjes-Ricci curvatures for edge-based and node-based sampling. We present the results of experiments on real life networks, as well as for square grids arising in Image Processing. Moreover, we consider fitting Ricci flows and we employ them for the detection of networks' backbone. We also develop embedding kernels related to the Forman-Ricci curvatures and employ them for the detection of the coarse structure of networks, as well as for network visualization with applications to SVM. The relation between the Ricci curvature of the original manifold and that of a Ricci curvature driven discretization is also studied.

中文翻译：

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网络的几何采样

受基于 Ricci 曲率的流形采样方法和结果的启发，我们提出了一种类似的网络方法。为此，我们利用了三种类型的离散曲率，即基于边缘和基于节点的采样的图 Forman-、全 Forman-和 Haantjes-Ricci 曲率。我们展示了现实生活网络以及图像处理中出现的方形网格的实验结果。此外，我们考虑拟合 Ricci 流，并将它们用于检测网络的主干。我们还开发了与 Forman-Ricci 曲率相关的嵌入内核，并将它们用于检测网络的粗略结构，以及应用到 SVM 的网络可视化。