121 citations · 538 across the 72 of their papers we have counts for
4 papers · 2 filters
Spectral classes of regular, random, and empirical graphs
Jiao Gu, Jürgen Jost, Shiping Liu +1
We define a (pseudo-)distance between graphs based on the spectrum of the normalized Laplacian, which is easy to compute or to estimate numerically. It can therefore serve as a rou…
Eigenvalue ratios of nonnegatively curved graphs
Shiping Liu, Norbert Peyerimhoff
We derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality . This estimate is independent of the size of…
Spectral distances on graphs
Jiao Gu, Bobo Hua, Shiping Liu
By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using L^p Wasserstein distances between probability measures, we define the corres…
Multi-way dual Cheeger constants and spectral bounds of graphs
Shiping Liu
We introduce a set of multi-way dual Cheeger constants and prove universal higher-order dual Cheeger inequalities for eigenvalues of normalized Laplace operators on weighted finite…