Eigenvalue Ratios of Non-Negatively Curved Graphs

We derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality CD (0, ∞). 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, ∞). We also discuss a higher-order Cheeger constant-ratio estimate and related topics about expanders.

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