Personalized PageRank has found many uses in not only the ranking of webpages, but also algorithmic design, due to its ability to capture certain geometric properties of networks. In this paper, we study the diffusion of PageRank: how varying the jumping (or teleportation) constant affects PageRank values. To this end, we prove a gradient estimate for PageRank, akin to the Li–Yau inequality for positive solutions to the heat equation (for manifolds, with later versions adapted to graphs).

中文翻译：

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PageRank 的梯度和 Harnack 类型估计

个性化 PageRank 不仅在网页的排名中，而且在算法设计中都有很多用途，因为它能够捕捉网络的某些几何特性。在本文中，我们研究了 PageRank 的扩散：改变跳跃（或隐形传态）常数如何影响 PageRank 值。为此，我们证明了 PageRank 的梯度估计，类似于热方程正解的 Li-Yau 不等式（对于流形，后来的版本适用于图）。