Discrete curvature on graphs from the effective resistance*
Discrete curvature on graphs from the effective resistance*
复制标题
DOI：
10.1088/2632-072x/ac730d
复制
发表时间：
2022-06-01
影响因子：
2.7
通讯作者：
Lambiotte, Renaud
中科院分区：
文献类型：
--
作者：
Devriendt, Karel;Lambiotte, Renaud
本文介绍了一种新的方法来离散曲率的概念的基础上的有效阻力。我们提出了一个曲率的节点和链接的一个图，并提出了他们的解释为曲率的证据。值得注意的是，我们找到了一些既定的离散曲率（奥利维尔，福尔曼，组合曲率）的关系，并显示证据的情况下，欧几里德随机图的连续曲率收敛。这些电阻曲率既能有效地近似，又能高度服从理论分析，有可能为离散曲率理论及其在数学、网络科学、数据科学和物理学中的许多应用提供新的启发。
This article introduces a new approach to discrete curvature based on the concept of effective resistances. We propose a curvature on the nodes and links of a graph and present the evidence for their interpretation as a curvature. Notably, we find a relation to a number of well-established discrete curvatures (Ollivier, Forman, combinatorial curvature) and show evidence for convergence to continuous curvature in the case of Euclidean random graphs. Being both efficient to approximate and highly amenable to theoretical analysis, these resistance curvatures have the potential to shed new light on the theory of discrete curvature and its many applications in mathematics, network science, data science and physics.