RANDOM WALKS, CONDUCTANCE, AND RESISTANCE FOR THE CONNECTION GRAPH LAPLACIAN

被引：0
|
作者：
Cloninger, Alexander [1 ,2 ]
Mishne, Gal [2 ]
Oslandsbotn, Andreas [3 ]
Robertson, Sawyer J. [1 ,2 ]
Wan, Zhengchao [2 ]
Wang, Yusu [2 ]
机构：
[1] Department of Mathematics, University of California San Diego, La Jolla, CA,92093, United States
[2] Halıcıoğlu Data Science Institute, University of California San Diego, La Jolla, CA,92093, United States
[3] Department of Informatics, University of Oslo, Oslo, Norway
来源：
SIAM Journal on Matrix Analysis and Applications | 2024年 / 45卷 / 03期
关键词：
Laplace transforms;
D O I：
10.1137/23M1595400
中图分类号：
学科分类号：
摘要：
We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality of Dirichlet-type and Poisson-type problems on connection graphs. Additionally, we delve into random walks, taking into account both node transitions and vector rotations. This approach introduces novel concepts of effective conductance and resistance matrices for connection graphs, capturing mean rotation matrices corresponding to random walk transitions. Thereby, it provides new theoretical insights for network analysis and optimization. © 2024 Society for Industrial and Applied Mathematics.
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页码：1541 / 1572
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