121 citations · 538 across the 72 of their papers we have counts for
9 papers · 1 filter
Signatures, lifts, and eigenvalues of graphs
Shiping Liu, Norbert Peyerimhoff, Alina Vdovina
We study the spectra of cyclic signatures of finite graphs and the corresponding cyclic lifts. Starting from a bipartite Ramanujan graph, we prove the existence of an infinite towe…
Cheeger constants, structural balance, and spectral clustering analysis for signed graphs
Fatihcan M. Atay, Shiping Liu
We introduce a family of multi-way Cheeger-type constants on a signed graph such that if and only if has balanced connected…
Another characterization of tilted algebras
Shiping Liu
We give a new characterization of tilted algebras by the existence of certain special subquivers in their Auslander-Reiten quiver. This result includes the existent characterizatio…
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…
An optimal dimension-free upper bound for eigenvalue ratios
Shiping Liu
On a closed weighted Riemannian manifold with nonnegative Bakry-Émery Ricci curvature, it is shown that the ratio of the -th to first eigenvalues of the weighted Laplacian is do…