121 citations · 538 across the 72 of their papers we have counts for
8 papers · 1 filter
The Graph Curvature Calculator and the curvatures of cubic graphs
David Cushing, Riikka Kangaslampi, Valtteri Lipiäinen +2
We classify all cubic graphs with either non-negative Ollivier-Ricci curvature or non-negative Bakry-Émery curvature everywhere. We show in both curvature notions that the non-nega…
Comparative analysis of two discretizations of Ricci curvature for complex networks
Areejit Samal, R. P. Sreejith, Jiao Gu +3
We have performed an empirical comparison of two distinct notions of discrete Ricci curvature for graphs or networks, namely, the Forman-Ricci curvature and Ollivier-Ricci curvatur…
Magnetic sparseness and Schrödinger operators on graphs
Michel Bonnefont, Sylvain Golénia, Matthias Keller +2
We study magnetic Schrödinger operators on graphs. We extend the notion of sparseness of graphs by including a magnetic quantity called the frustration index. This notion of magnet…
A note on eigenvalue bounds for non-compact manifolds
Matthias Keller, Shiping Liu, Norbert Peyerimhoff
In this article we prove upper bounds for the Laplace eigenvalues below the essential spectrum for strictly negatively curved Cartan-Hadamard manifolds. Our bound is given in…
Rigidity properties of the hypercube via Bakry-Emery curvature
Shiping Liu, Florentin Münch, Norbert Peyerimhoff
We give rigidity results for the discrete Bonnet-Myers diameter bound and the Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if the underlying graph is a…
Distance bounds for graphs with some negative Bakry-Émery curvature
Shiping Liu, Florentin Münch, Norbert Peyerimhoff +1
We prove distance bounds for graphs possessing positive Bakry-Émery curvature apart from an exceptional set, where the curvature is allowed to be non-positive. If the set of non-po…
Ollivier-Ricci idleness functions of graphs
David Bourne, David Cushing, Shiping Liu +2
We study the Ollivier-Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most linear pa…
Auslander-Reiten components with bounded short cycles
Shiping Liu, Jinde Xu
We study Auslander-Reiten components of an artin algebra with bounded short cycles, namely, there exists a bound for the depths of maps appearing on short cycles of non-zero non-in…