121 citations · 538 across the 72 of their papers we have counts for
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Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs. II. Implementation
David Cushing, Supanat Kamtue, Shiping Liu +3
In this second part of a sequence of two papers, we discuss the implementation of a curvature flow on weighted graphs based on the Bakry-Émery calculus. This flow can be adapted to…
Bounding the diameter and eigenvalues of amply regular graphs via Lin-Lu-Yau curvature
Xueping Huang, Shiping Liu, Qing Xia
An amply regular graph is a regular graph such that any two adjacent vertices have common neighbors and any two vertices with distance have common neighbors. We prove a…
Discrete Bakry-Émery curvature tensors and matrices of connection graphs
Chunyang Hu, Shiping Liu
Liu, Münch, and Peyerimhoff introduced the notion of Bakry-Émery curvature for connection graphs as a means to derive Buser-type bounds on the eigenvalues of connection Laplacians.…
Nodal domain theorems for -Laplacians on signed graphs
Chuanyuan Ge, Shiping Liu, Dong Zhang
We establish various nodal domain theorems for -Laplacians on signed graphs, which unify most of the existing results on nodal domains of graph -Laplacians and arbitrary symm…
Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs. I. Theory
David Cushing, Supanat Kamtue, Shiping Liu +3
In this sequence of two papers, we introduce a curvature flow on (mixed) weighted graphs which is based on the Bakry-Émery calculus. The flow is described via a time-continuous evo…
Symmetric Matrices, Signed Graphs, and Nodal Domain Theorems
Chuanyuan Ge, Shiping Liu
In 2001, Davies, Gladwell, Leydold, and Stadler proved discrete nodal domain theorems for eigenfunctions of generalized Laplacians, i.e., symmetric matrices with non-positive off-d…