We express the discrete Ricci curvature of a graph as the minimal eigenvalue of a family of matrices, one for each vertex of a graph whose entries depend on the local adjacency structure of the graph. Using this method we compute or bound the Ricci curvature of Cayley graphs of finite Coxeter groups and affine Weyl groups. As an application we obtain an isoperimetric inequality that holds for all Cayley graphs of finite Coxeter groups
Ricci curvature, graphs and eigenvalues / Siconolfi, Viola. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - STAMPA. - 620:(2021), pp. 242-267. [10.1016/j.laa.2021.02.026]
Ricci curvature, graphs and eigenvalues
Viola Siconolfi
2021-01-01
Abstract
We express the discrete Ricci curvature of a graph as the minimal eigenvalue of a family of matrices, one for each vertex of a graph whose entries depend on the local adjacency structure of the graph. Using this method we compute or bound the Ricci curvature of Cayley graphs of finite Coxeter groups and affine Weyl groups. As an application we obtain an isoperimetric inequality that holds for all Cayley graphs of finite Coxeter groups| File | Dimensione | Formato | |
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