Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
From MaRDI portal
Publication:390203
DOI10.4310/MRL.2012.v19.n6.a2zbMath1297.05143arXiv1105.3803OpenAlexW2964129753MaRDI QIDQ390203
Shiping Liu, Frank Bauer, Juergen Jost
Publication date: 22 January 2014
Published in: Mathematical Research Letters (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1105.3803
Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Markov processes (60J99) Random walks on graphs (05C81)
Related Items (49)
Continuous and discrete SIR-models with spatial distributions ⋮ Li-Yau inequality on finite graphs via non-linear curvature dimension conditions ⋮ Gradient flows in metric random walk spaces ⋮ An eigenvalue localization theorem for stochastic matrices and its application to Randić matrices ⋮ Differential geometric treewidth estimation in adiabatic quantum computation ⋮ Volume growth, spectrum and stochastic completeness of infinite graphs ⋮ An estimate of the first non-zero eigenvalue of the Laplacian by the Ricci curvature on edges of graphs ⋮ Systematic evaluation of a new combinatorial curvature for complex networks ⋮ The Graph Curvature Calculator and the Curvatures of Cubic Graphs ⋮ Spectral classes of regular, random, and empirical graphs ⋮ Metric measure spaces and synthetic Ricci bounds: fundamental concepts and recent developments ⋮ Curvature on graphs via equilibrium measures ⋮ Geometric and spectral properties of directed graphs under a lower Ricci curvature bound ⋮ Unnamed Item ⋮ Normalized graph Laplacians for directed graphs ⋮ Cahn–Hilliard equations on random walk spaces ⋮ Torsional Rigidity in Random Walk Spaces ⋮ Discrete Ricci curvatures for directed networks ⋮ Large scale Ricci curvature on graphs ⋮ The Geometric Meaning of Curvature: Local and Nonlocal Aspects of Ricci Curvature ⋮ Volume and diameter of a graph and Ollivier's Ricci curvature ⋮ Curvature and Higher Order Buser Inequalities for the Graph Connection Laplacian ⋮ Exact and asymptotic results on coarse Ricci curvature of graphs ⋮ Multi-way dual Cheeger constants and spectral bounds of graphs ⋮ Diffusion determines the recurrent graph ⋮ Forman curvature for complex networks ⋮ Simulated versus reduced noise quantum annealing in maximum independent set solution to wireless network scheduling ⋮ On the mean square displacement of a random walk on a graph ⋮ Sectional curvature of polygonal complexes with planar substructures ⋮ On coset leader graphs of structured linear codes ⋮ Lower bound of coarse Ricci curvature on metric measure spaces and eigenvalues of Laplacian ⋮ Ollivier's Ricci curvature, local clustering and curvature-dimension inequalities on graphs ⋮ Network geometry and complexity ⋮ Ricci curvature of finite Markov chains via convexity of the entropy ⋮ Ricci curvature, circulants, and a matching condition ⋮ Forman-Ricci flow for change detection in large dynamic data sets ⋮ Generalized Ricci curvature and the geometry of graphs ⋮ Cheeger constants, structural balance, and spectral clustering analysis for signed graphs ⋮ Eigenvalue asymptotics for Schrödinger operators on sparse graphs ⋮ The heat flow on metric random walk spaces ⋮ Condensed Ricci curvature of complete and strongly regular graphs ⋮ A note on comparison theorems for graphs ⋮ Inner-outer curvatures, Ollivier-Ricci curvature and volume growth of graphs ⋮ Distance bounds for graphs with some negative Bakry-Émery curvature ⋮ Coverings and the heat equation on graphs: Stochastic incompleteness, the Feller property, and uniform transience ⋮ Ollivier Ricci curvature for general graph Laplacians: heat equation, Laplacian comparison, non-explosion and diameter bounds ⋮ The Ricci curvature of gluing graph of two complete graphs ⋮ Ricci curvature on polyhedral surfaces via optimal transportation ⋮ Spectral distances on graphs
This page was built for publication: Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
