Discrete Hodge Theory on Graphs: A Tutorial
Discrete Hodge Theory on Graphs: A Tutorial
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图上的离散霍奇理论：教程
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Tom Goldring
中科院分区：
文献类型：
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作者：
James L. Johnson;Tom Goldring
霍奇理论为物理学和工程应用中出现的各种线积分、曲面积分和体积积分提供了统一的观点。霍奇理论在图发展离散版本的微分形式中发现的连续理论，并使图分解成梯度，螺线管，和谐波分量。通过与向量场上的梯度、旋度和拉普拉斯算子的相似性来解释，这些分量在解决某些在图上下文中自然出现的排序和近似问题时很有用。本教程开发了离散霍奇理论的雏形，并提供了几个示例应用程序。
Hodge theory provides a unifying view of the various line, surface, and volume integrals that appear in physics and engineering applications. Hodge theory on graphs develops discrete versions of the differential forms found in the continuous theory and enables a graph decomposition into gradient, solenoidal, and harmonic components. Interpreted via similarity to gradient, curl, and Laplacian operators on vector fields, these components are useful in solving certain ranking and approximations problems that arise naturally in a graph context. This tutorial develops the rudiments of discrete Hodge theory and provides several example applications.