121 citations · 538 across the 72 of their papers we have counts for
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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…
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…