Eigenvalue ratios of nonnegatively curved graphs

Abstract

We derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality $CD(0,\infty )$. This estimate is independent of the size of the graph and provides a general method to obtain higher order spectral estimates. The operation of taking Cartesian products is shown to be an efficient way for constructing new weighted graphs satisfying $CD(0,\infty )$. We also discuss a higher order Cheeger constant ratio estimate and related topics about expanders.

References in corpus (4)

• Multi-way dual Cheeger constants and spectral bounds of graphs
• Improved Cheeger's Inequality: Analysis of Spectral Partitioning Algorithms through Higher Order Spectral Gap
• An optimal dimension-free upper bound for eigenvalue ratios
• Multi-way expanders and imprimitive group actions on graphs

Cited by in corpus (12)

• Multi-way dual Cheeger constants and spectral bounds of graphs
• The Graph Curvature Calculator and the curvatures of cubic graphs
• Volume doubling, Poincaré inequality and Guassian heat kernel estimate for nonnegative curvature graphs
• Curvature and higher order Buser inequalities for the graph connection Laplacian
• Ricci curvature on birth-death processes
• Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians
• Li-Yau inequality under $CD(0,n)$ on graphs
• Liouville property and non-negative Ollivier curvature on graphs
• Liouville theorem for bounded harmonic functions on manifolds and graphs satisfying non-negative curvature dimension condition
• Perpetual cutoff method and discrete Ricci curvature bounds with exceptions
• Stochastic completeness for graphs with curvature dimension conditions
• Bakry-Émery Ricci curvature of doubly warped product of weighted spaces