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arXiv · 2412.20591

Local ultrametric approximation of graph distance based Laplacian diffusion

Patrick Erik Bradley
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Abstract

The error estimation for eigenvalues and eigenvectors of a small positive symmetric perturbation on the spectrum of a graph Laplacian is related to Gau{\ss} hypergeometric functions. Based on this, a heuristic polynomial-time algorithm for finding an optimal locally ultrametric approximation of a graph-distance power Laplacian matrix via the Vietoris-Rips graph based on the graph distance function is proposed. In the end, the error in the solution to the graph Laplacian heat equation given by extension to a locally p-adic equation is estimated.

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Patrick Erik Bradley. 2024-12-29. Local ultrametric approximation of graph distance based Laplacian diffusion. https://arxiv.org/abs/2412.20591

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