论文标题
来自有效电阻的图表上的离散曲率
Discrete curvature on graphs from the effective resistance
论文作者
论文摘要
本文介绍了一种基于有效阻力概念的新方法来离散曲率。我们提出了图表的节点和链接的曲率，并提供了将其解释为曲率的证据。值得注意的是，我们发现与许多公认的离散曲率（ollivier，forman，组合曲率）的关系，并在欧几里得随机图的情况下显示了与连续曲率收敛的证据。这些抗性曲率既有效地计算且高度适合理论分析，因此有可能对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进行新的启示。
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 calculate 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.
